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Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Chapter 13: Visualization Techniques
Helmut Simonis
Cork Constraint Computation Centre
Computer Science Department
University College Cork
Ireland
ECLiPSe ELearning Overview
Helmut Simonis Visualization Techniques 1
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Licence
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Attribution-Noncommercial-Share Alike 3.0 Unported License.
To view a copy of this license, visit http:
//creativecommons.org/licenses/by-nc-sa/3.0/ or
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Helmut Simonis Visualization Techniques 2
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Outline
1 Introduction
2 Visualization by Annotation
3 Visualization Interface
4 Conclusions
Helmut Simonis Visualization Techniques 3
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
What we want to introduce
Why visualize?
How to visualize constraint programs
Visualization Interface
Visualization Tool
Helmut Simonis Visualization Techniques 4
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Outline
1 Introduction
2 Visualization by Annotation
3 Visualization Interface
4 Conclusions
Helmut Simonis Visualization Techniques 5
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Background
Gift grant from Cisco Systems/Silicon Valley Community
Foundation
Cisco owns open-sourced ECLiPSe system
How to expand user-base?
Self-taught course in constraint programming
Intended for Cisco engineers/programmers
Open source/available to community
Website
http://4c.ucc.ie/~hsimonis/ELearning/index.htm
Helmut Simonis Visualization Techniques 6
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Format
Video lectures
Slides
Handout
Exercises
Helmut Simonis Visualization Techniques 7
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Problems Handled in Course
Must have puzzles!
Send+More=Money
Sudoku
N-queens
Shikaku
Helmut Simonis Visualization Techniques 8
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Practical Example Problems
Test plan generation (BIBD)
Progressive party problem
Routing and wavelength assignment
Optical network design
Car sequencing
Costas arrays
Sports scheduling
Still to come
Production scheduling
Nurse rostering
Airport stand allocation
Helmut Simonis Visualization Techniques 9
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Intention
Realistic, life like problems
Must address scalability issues
Often, problem not completely specified
Issue: Hard to verify by hand
Complexity still limited, not real problems
No attempt at integration
Helmut Simonis Visualization Techniques 10
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
How do we understand behavior?
Mental model
Formal analysis
Debugging
Tracing
Life visualization
Post-mortem analysis
Helmut Simonis Visualization Techniques 11
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
How do we understand behavior?
Mental model
Formal analysis
Debugging
Tracing
Life visualization
Post-mortem analysis
Helmut Simonis Visualization Techniques 12
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Why Visualize?
Understand what is done
Understand what is done in which order
Understand what is not done
Understand when to give up
Helmut Simonis Visualization Techniques 13
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Conceptual Model
Stable state at defined program points
Granularity
Assign value
Post constraint
Show stable state after propagation
Do not show individual propagation steps
Helmut Simonis Visualization Techniques 14
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Visualizers
Search tree
Variables
Constraints
Helmut Simonis Visualization Techniques 15
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Visualization Tool
Developed in Java
Show two panes: tree and state
Navigate along timeline
Helmut Simonis Visualization Techniques 16
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Visualization Tool: Car Sequencing
Helmut Simonis Visualization Techniques 17
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
How many visualizers do we need?
Develop few primitives
Cell based view
Domain vector
Allow aggregation
Vector/matrix
General layout
Which global constraints require more?
Task based view for cumulative
Matching/flow based representation does not scale
Helmut Simonis Visualization Techniques 18
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
How to Interpret Visualization
Search tree
Good/bad choices
Place of backtracking
State
Missing propagation
Helmut Simonis Visualization Techniques 19
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Costas Array Search tree (Size 16)
Deep backtracking
Third choice wrong
Last choice wrong
1
1
2 Value selection
2
4
3
5 6
strategy useless
4
114611 124619
335881
4
3 361038 5 7 8 9 10 11
5
4950 7156 5581 6966 9250
14515 21155 16169 19916 26568
3 4 5
6
627 801
1897
4
3 2442 7 8 9 10 12 13
9
47 45 61 66 66
150 127 176 200
3 4 7
200
8 9 10 12 14 15
7
24 20 20 4 17 11 28
77 60 58 15 46 34 98
3 4 7 8
10
6
14
12 14
12
3 7 9
Helmut Simonis Visualization Techniques 20
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Costas Array Search tree (Size 16)
Deep backtracking
Third choice wrong
Last choice wrong
1
1
2 Value selection
2
4
3
5 6
strategy useless
4
114611 124619
335881
4
3 361038 5 7 8 9 10 11
5
4950 7156 5581 6966 9250
14515 21155 16169 19916 26568
3 4 5
6
627 801
1897
4
3 2442 7 8 9 10 12 13
9
47 45 61 66 66
150 127 176 200
3 4 7
200
8 9 10 12 14 15
7
24 20 20 4 17 11 28
77 60 58 15 46 34 98
3 4 7 8
10
6
14
12 14
12
3 7 9
Helmut Simonis Visualization Techniques 21
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Costas Array Search tree (Size 16)
Deep backtracking
Third choice wrong
Last choice wrong
1
1
2 Value selection
2
4
3
5 6
strategy useless
4
114611 124619
335881
4
3 361038 5 7 8 9 10 11
5
4950 7156 5581 6966 9250
14515 21155 16169 19916 26568
3 4 5
6
627 801
1897
4
3 2442 7 8 9 10 12 13
9
47 45 61 66 66
150 127 176 200
3 4 7
200
8 9 10 12 14 15
7
24 20 20 4 17 11 28
77 60 58 15 46 34 98
3 4 7 8
10
6
14
12 14
12
3 7 9
Helmut Simonis Visualization Techniques 22
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Costas Array Search tree (Size 16)
Deep backtracking
Third choice wrong
Last choice wrong
1
1
2 Value selection
2
4
3
5 6
strategy useless
4
114611 124619
335881
4
3 361038 5 7 8 9 10 11
5
4950 7156 5581 6966 9250
14515 21155 16169 19916 26568
3 4 5
6
627 801
1897
4
3 2442 7 8 9 10 12 13
9
47 45 61 66 66
150 127 176 200
3 4 7
200
8 9 10 12 14 15
7
24 20 20 4 17 11 28
77 60 58 15 46 34 98
3 4 7 8
10
6
14
12 14
12
3 7 9
Helmut Simonis Visualization Techniques 23
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Missing Propagation
The model is
doing this
Helmut Simonis Visualization Techniques 24
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Missing Propagation
It could be doing
that!
Helmut Simonis Visualization Techniques 25
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Comparison (Search Tree, size 16)
Initial Model Improved Model
1
1
2
2
1
1
3
2 4 5 6
2
3 4
55029 61250
4 5 6
106926
3
119643
4 5 8 9 11
4
114611
335881
4
124619
3 361038 5 7 8 9 10 11 5
5 2729 3284 2980 3668 4011
4950 7156 5581 6966 9250
3 4 5 5186 6345 5726 7056 7927
3 4 5
14515 21155 16169 19916 26568
627
3 2442
4
801
7
6
8 9 10 12 13
6
1897 351 373
9 667 727
3 4 7 8 12 13
47 45 61 66 66
150 127 176 200
3 4 7
200
8 9 10 12 14 15
7
7
30 23 24 43 35
3 8
24 20 20 4 17 11 28
77 60 58 15 46 34 98
3 4 7 8
55 37 43 82 66
10
14
6
12 14 8
8
12 4
3 7 9 15
9
3 14 15
10
1 3
2 4
12 14
Helmut Simonis Visualization Techniques 26
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Progressive Party Problem, 9 Time Periods
root
- - -
1
2804 1686
4251 2929 7
2
11
3
5
4
3
5
2
6
2
7
9
8
1
9
1
10
4
11
6
12
4
13
12
14
8
15
3 6 9 10
16
3
17
9
18
3
19
13
20
1
21
8
22
9
23
13
24
6
25
5
26
8
27
6
30
10
31
3
32
8
33
1
34
5
35
9
36
11
37
9
38
7
39
12
40
1
41
2
42
13
43
5
44
6
45
6
46
8
47
11
48
2
49
2
50
2
51
7
52
6
53
4
54
3 4
55
3 4
56
3
57
7
59
5
60
9
61
10
62
11
63
4
64
8
65
3
66
7
67
2
68
7
69
12
70
13
71
2
72
6
73
4
74
9
75
1
76
1
77
3
78
10
80
8
81
1
82
8
83
3 2 1 6
84
3
85
2
88
8
89
5
90
9
91
10
92
7
93
6
94
13
95
2
96
6
97
1
98
3
99
3
100
4
101
9
102
11
103
2
104
7
105
4
106
10
107
11 4
108
1
2
12
111
12
117
9
118
1
119
11
120
4
121
6
122
12
123
2
124
8
125
10
126
2
127
8
128
1
129
3
130
7 4
132
7
133
3
134
10 6 13 5
135
5 8 7
9 9 11
6 5
136
6 7
137
13
138
13
146
3
147
2
148
4
149
9
150
8
151
7
152
7
153
6
154
13
155
5
156
5
157
6
158
1
159
10
160
9
161
1
162
10
163
2
164
4
165
12
166
11 3
167
12 11
175
6
176
7
177
1
178
8
179
3
180
10 5 1
181
277 210
387 298 4
182
11
183
9
184
9
185
13 2
186
2
4 12 5
187
8
10
10
190
13
191
5
193
11
194
8
204
1
205
10
206
3
207
2
208
9
209
5
210
12
211
3
212
8
213
11 6
214
29
60 4
215
7
216
7
217
13 1 11
219
2 6
7 13 8 11
220
1
2 4 13 6 2
221
1
3
6 9 8 13
222
6 9 8
224
5 9
233
4 2
234
2
3
4
235
6 7
236
34
64 5
237
1
238
11 3
239
19
25
6
240
10
241
11
242
8 13
244
2
3 12 8
248
8 12
249
12 11 4
250
9 10
Helmut Simonis Visualization Techniques 27
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
2 Restarts Before Solution Found
root
- - -
1
2804 1686
4251 2929
7
2
11
3
5
4
3
5
2
6
2
7
9
8
1
9
1
10
4
Helmut Simonis Visualization Techniques 28
208
9 Introduction
209
5 Visualization by Annotation
210
12 Visualization Interface
211
3 Conclusions
212
8
Value Choice Strategy Not Focused
29
213
11 6
214
4
60
215
7
216
7
217
13 1 11
219
2 6
7 13
8 11
220
1
2
4 13 6 2
221
1
3
6 9 8 13
222
6 9 8
224
5 9
233
4 2
234
2
3
4
235
6 7
236
34
64
5
237
1
238
11 3
239
19
25
6
240
10
241
11
242
8 13
244
2
3
12 8
248
8 12
249
12 11 4
250
9 10
Helmut Simonis Visualization Techniques 29
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Progressive Party
Clearly impossible to explore search space
Either many solutions or good value selection
Value selection at end rather poor
Probably many solutions
Helmut Simonis Visualization Techniques 30
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Missing Propagation: Shikaku
9 9 29 13 29 29 29 33
1 1 1 9 1 16 29 22 25 29 29
4 6
9 9 16 13 29 22 29 33 30
1 1 9 9 16 16 16 25 29 33
6 3 2
13 9 13 10 13 10 22 16 25 22 25 22 30 33 30
1 9 9 13 13 13 13 25 25 25
4 3
10 14 13 22 16 30 22 30 30 26
1 10 10 10 13 10 19 10 22 25 30 30
4 4
14 22 22 19 30 26 30 34
2 2 2 13 17 17 22 25 26 30
9
14 26 22 26 22 26 31 30 34
2 2 2 13 17 14 19 17 22 26 26 26
4
22 17 22 19 26 23 22 26 31 30
2 2 2 14 14 17 14
19 17 14
17 26 34
9 4
19 23 22 31 26 34
3 5 5 5 17 17 19 17 19 17 31 31
6 8
31 23 31 26 34
3 5 5 5 18 19 22 19 19 31 31
6 6 4
20 23 22 32 31 27 32
3 6 6 6 18 19 20 19
23 19
31 34
9 4 6
32 23 32 27 35 34
3 6 6 6 18 20 22 20 23 32 32
4 4
23 32 27 35 32
3 6 6 6 18 20 23 23 23 35
6 2
15 15 23 20 27 24 27 32 27 36
3 11 11 11 11 15 11 23 15 23 23 35
4
15 7 15 11 15 11 27 23 27 24 27 23 32 27 36 27
4 7 7 15 15 20 15 23 15 15 15 15
8
7 27 15 27 15 27 15 27 24 21 27 24 23 36
4 7 12 7 7 7
15 7 15 7
27 27 27
6 6
7 12 7 24 15 24 24 28 27 36 28 36 28
4 4 12 12 15 21 24 24 27 24 27 24
2 4
8 12 8 21 15 21 28 24 36 36
4 4 4 4 15 21 21 28 28 28
4 3 6
8 36 36 36 28 36 36
4 8 8 8 8 21 24 28 28 36
4 6
Helmut Simonis Visualization Techniques 31
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Outline
1 Introduction
2 Visualization by Annotation
3 Visualization Interface
4 Conclusions
Helmut Simonis Visualization Techniques 32
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
sendmory(L,Output,IgnoreFixed):-
L=[S,E,N,D,M,O,R,Y],
L :: 0..9,
create_visualization([output:Output,
ignore_fixed:IgnoreFixed,
width:8,
height:10],Handle),
add_visualizer(Handle,
vector(L),
[display:expanded]),
alldifferent(L),draw_visualization(Handle),
S #\= 0,draw_visualization(Handle),
M #\= 0,draw_visualization(Handle),
Helmut Simonis Visualization Techniques 33
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
sendmory(L,Output,IgnoreFixed):-
L=[S,E,N,D,M,O,R,Y],
L :: 0..9,
create_visualization([output:Output,
ignore_fixed:IgnoreFixed,
width:8,
height:10],Handle),
add_visualizer(Handle,
vector(L),
[display:expanded]),
alldifferent(L),draw_visualization(Handle),
S #\= 0,draw_visualization(Handle),
M #\= 0,draw_visualization(Handle),
Helmut Simonis Visualization Techniques 34
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
sendmory(L,Output,IgnoreFixed):-
L=[S,E,N,D,M,O,R,Y],
L :: 0..9,
create_visualization([output:Output,
ignore_fixed:IgnoreFixed,
width:8,
height:10],Handle),
add_visualizer(Handle,
vector(L),
[display:expanded]),
alldifferent(L),draw_visualization(Handle),
S #\= 0,draw_visualization(Handle),
M #\= 0,draw_visualization(Handle),
Helmut Simonis Visualization Techniques 35
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
sendmory(L,Output,IgnoreFixed):-
L=[S,E,N,D,M,O,R,Y],
L :: 0..9,
create_visualization([output:Output,
ignore_fixed:IgnoreFixed,
width:8,
height:10],Handle),
add_visualizer(Handle,
vector(L),
[display:expanded]),
alldifferent(L),draw_visualization(Handle),
S #\= 0,draw_visualization(Handle),
M #\= 0,draw_visualization(Handle),
Helmut Simonis Visualization Techniques 36
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
sendmory(L,Output,IgnoreFixed):-
L=[S,E,N,D,M,O,R,Y],
L :: 0..9,
create_visualization([output:Output,
ignore_fixed:IgnoreFixed,
width:8,
height:10],Handle),
add_visualizer(Handle,
vector(L),
[display:expanded]),
alldifferent(L),draw_visualization(Handle),
S #\= 0,draw_visualization(Handle),
M #\= 0,draw_visualization(Handle),
Helmut Simonis Visualization Techniques 37
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
sendmory(L,Output,IgnoreFixed):-
L=[S,E,N,D,M,O,R,Y],
L :: 0..9,
create_visualization([output:Output,
ignore_fixed:IgnoreFixed,
width:8,
height:10],Handle),
add_visualizer(Handle,
vector(L),
[display:expanded]),
alldifferent(L),draw_visualization(Handle),
S #\= 0,draw_visualization(Handle),
M #\= 0,draw_visualization(Handle),
Helmut Simonis Visualization Techniques 38
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
name_variables(Handle,L,
[’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
Pairs),
root(Handle),
search(Pairs,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 39
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
name_variables(Handle,L,
[’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
Pairs),
root(Handle),
search(Pairs,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 40
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
name_variables(Handle,L,
[’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
Pairs),
root(Handle),
search(Pairs,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 41
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
name_variables(Handle,L,
[’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
Pairs),
root(Handle),
search(Pairs,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 42
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
name_variables(Handle,L,
[’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
Pairs),
root(Handle),
search(Pairs,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 43
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
name_variables(Handle,L,
[’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
Pairs),
root(Handle),
search(Pairs,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 44
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sendmore Program Annotated
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
name_variables(Handle,L,
[’S’,’E’,’N’,’D’,’M’,’O’,’R’,’Y’],
Pairs),
root(Handle),
search(Pairs,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 45
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sudoku Program Annotated
model(Matrix,Method,Output):-
Matrix[1..9,1..9] :: 1..9,
create_visualization([output:Output,
width:9,
height:9],Handle),
add_visualizer(Handle,
domain_matrix(Matrix),
[display:text]),
draw_visualization(Handle),
(for(I,1,9),
param(Matrix,Method,Handle) do
Method:alldifferent(Matrix[I,1..9]),
draw_visualization(Handle,[focus:row(I)]),
Method:alldifferent(Matrix[1..9,I]),
draw_visualization(Handle,[focus:col(I)])
),
Helmut Simonis Visualization Techniques 46
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Sudoku Program Annotated
(multifor([I,J],[1,1],[7,7],[3,3]),
param(Matrix,Method,Handle) do
Method:alldifferent(Matrix[I..I+2,J..J+2]),
draw_visualization(Handle,
[focus:block(I,J,3,3)])
),
extract_array(Handle,row,Matrix,NamedList),
root(Handle),
search(NamedList,1,input_order,
tree_indomain(Handle,_),
complete,[]),
solution(Handle),
close_visualization(Handle).
Helmut Simonis Visualization Techniques 47
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 4
7
5
8
6
9 8 4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
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4
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9 1 7 4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
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9 8
4 5 6
7 8 9
4
7
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8 3 2
6
9
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
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6
9
4
7
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8
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9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
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6
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
8 9 6
9
4
7
5
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4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
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6
9
4 5 6
7 8 9
4
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4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
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9 1 4
4
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4 5 6
7 8 9
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
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4
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4
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4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
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Helmut Simonis Visualization Techniques 48
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 4
7
5
8
6
9 8 4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
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4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
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6
9
4
7
5
8
6
9
4
7
5
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9 1 7 4
7
5
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4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
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6
9
4
7
5
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6
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4
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5
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9 8
4 5 6
7 8 9
4
7
5
8 3 2
6
9
4
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5
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
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4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
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4 5 6
7 8 9
4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
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9 1 4
4
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4 5 6
7 8 9
4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
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6
9
4
7
5
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4
7
5
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6
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4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
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Back to Start Skip Animation
Helmut Simonis Visualization Techniques 49
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9
4
7
5
8
6
9 1 7 4
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9
4 5
7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5 6
8 93 2 4 5
7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
8
6
9
4
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5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
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5
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4
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4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
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9 1 4
4
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4 5 6
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
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9
4
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4
7
5
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4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
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9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 50
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9 1 7 4
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5 6
8 93 2 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 9 4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 3 7 6 4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
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6
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4
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1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
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9
4 5 6
7 8 9
4
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1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7 1 4
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4 5 6
7 8 9
4
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1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7
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9
4
7
5
8
6
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4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
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9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 51
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 3 2 3 2 3 2 3 2 3 2 3
5 6
8 9
4 5
8
6
9
4 5
8
6
9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9 8
4 5 6
7 8 9 3 2
4 5 6 4
7 8 9 7
5 6
8 9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4 5 6 4 5
7 8 9 7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7 1 4
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7
5
8
6
9
4
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5
8
6
9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4 5 6
7 8 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 52
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6
8 9
4 5 6 4 5 6
8 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5 6 4 5 6
8 7 8 9 8
4 5 6
7 8 9 3 2
4 5 6 4
7 8 9 7
5 6
8 9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5 6
8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4 5 6 4 5
7 8 9 7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4
8 9 8 7
5
8
6
9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4 5 6
7 8 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 53
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5 6
8 9 8 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5 6
9 7 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6
8 9 8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 6
7 8 9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 6
7 8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5 6
8 9 8 7 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 54
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5
9 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6
8 9 8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5
9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 55
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5
9 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5
9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 56
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4
9 7
5
89
4 5 6
7 9 3 24 5
7
6
9
1 3 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 8 4 5 6
7 8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 5 6 4 5 6
7 8 9 7 8 99 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 57
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4
9 7
5
89
4 5 6
7 9 3 24 5
7
6
9
1 3 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4
7
5 4 5 6 4 5 6
7 7 8 4 5 6
7
4
7
5 6
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 5 6 4 5 6
7 8 9 7 8 99 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 58
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89
4 5 6
7 93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6 4 5
7
6 4 5
7 8 6 4
7
5 6
1 3 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 6 4 5
9 7 8
6
9 9 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4 5
9 7 8 9
4 5
7 8
6 4 5
9 7 8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4 5
9 7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4 5
9 7 8 9
4 6 4 5 6
9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 59
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89
4 5 6
7 93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9 9
4
8 2 5 4
7 9
1 3 1 2 3 2 32 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6 4 5
7 8
6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 4 5
8 9 4 5
8
4 5
8
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5
7 8 9
4 5
7 8
6 4 5 6
9 7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5
7 8 9
4 5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5
7 8 9
4 6 4 5
9 7 8
6
9 6 4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 60
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9 7
5 6 4 5 6 4 5
9 7 8 9 7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4 5 6 4 5
7 8 9 7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5
8 9
4 6
9 7
5 6
9 64 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 61
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9
6 4
8 9 8
6
9
4
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 8 1 4
4 5 6 4 5
9
4
7
5
8 9
4 5 6 4 5
7 8 9 7 8
6
9
4 5
7 8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5 6
8
4 5
9
4
7
5
8 9
4 6
9 7
5 6
9 64 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 62
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5
7
5 6
9 7
5 6
9
3 2 2 3 2 3 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 5
8
6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4
8
6
9
4
8
6
9
1 3 1 2 1 2 3 2 3 1 3 1 2 3 1 2 3
5 6
7 8 9 1 4
4 5 6
8
4 5
9
4
7
5
8 9
4 5
7 8
4 5
7 8
6
9
4 5
7 8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5 6
8
4 5
9
4
7
5
8 9
4 6
9 7
5 6
9 6
4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 63
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5
7
5 6
9 7
5 6
9
3 2 2 3 2 3 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 5
8
6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4
8
6 4
9
6
8 9
3 2 2 3 2 3 3 2 3 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8
5
7 8
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6 4 5 6 4 5
7 8 9 8
4 5
9 7 8 9
4 6
9 7
5 6
9 6
4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 64
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 1 2 3
3 1 2
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7
5 6
8 4 5
7
4 5 6
7
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6
9
4
8
4 6 4
9
6
8 9
3 2 2 3 2 3 3 2 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5 6 4 5 6 4 5
7 8 9 8
4 5
9 7 8 9
4 6
9 7
5 6
9 6 4
7
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 65
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 1 2 3
3 1 2
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
9 3 2
4 5
7
1 3 1 3 3 1 3
7 9
4 4
7 6 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7
5 6
8 4 5
7
4 5 6
7
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 4 5
8
1 3
3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6
9
4
8
4 6 4
9
6
8 9
3 2 2 3 2 3 3 2 2 3
5
7 8
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
7 8 9
5
8
5 5
9 7 8 9 9 7
5
9 6 7 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 66
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 1
3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6
9
5 6
8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
9 3 2
4 5
7
1 3 1 3 3 1 3
7 9
4 4
7 6 9
4
9 8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
7 9
5 6 4 5 4 5
7
4 6
7
5 6 4 5
7 8 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4 5
9 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5
7 8
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
7 8 9
5
8
5 5
9 7 8 9 9 7
5
9 6
7 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 67
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 1 2 3 1 1
3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 3
5 6
9
5 6 5
9 1 7 5 6
9
4 5
8
4 6
9
5 6
8 9
1 1 1 1 1
7
5 6
9
5 6 5 4 5
9 7 9 8 7
5 6
9 3 24 5
7
1 3 1 3 3 1 3
7 9
4 4
7 9 6
4
9 8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
7
5 6
9 4 5 4 5
7
4 6
7
5 6 4 5
7 8 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4 5 4
9 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5
4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8 7
6
9
5 6
7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
7 8 9
5
8
5 5
9 7 8 9 9 7
5
9 7 9 6 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 68
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 2 3 1 3 1 2 1 3
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 2 3 2 3 3 2 3
5 6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1 1
7
5 6
9
5 6 5
9
4 5
9 8 3 2
5 6 4 5
9 7
1 3 1 3 3 1 3
7 9
4 4
7 9 6
4
9 8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
7
5 6
9 4 5 4 5
7
4 6
7
5 6 4 5
7 8 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4 5 4
9 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5
4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8 7
6
9
5 6
7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
7 8 9
5
8
5 5
9 7 8 9 9 7
5
9 7 9 6 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 69
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 2 3 1 1 1
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 2 3 2 3
5 6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1 1
7
5 6
9
5 6 5
9
4 5
89 3 2
5 6 4 5
9 7
3 3 1 3
1 4 6 4
7 9 9
4
8 2 5 7 9
2 3 2 3 1 2 3 1 3 1 3
5 9 2 4 5
7
4 6
7 8
5 6 4 5
7 7
5 6
2 1 2 1 2 1
8 3 7 6 4 5
9 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5
4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5
7 8
6
9
5 6
8
5
1 4 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
7 8 9
5
8
5 5
9 7 8 9 9 7
5
9 67 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 70
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 2 3 1 1 1
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1
7
6
9
5 6 5
9
4 5
89 3 2
5 6 4 5
9 7
3 3 3
1 4 6 7 9 9 8 2 5 7 9
3 3 1 3 1 3 1 3
5 9 2 4
7
4 6
7
6 4
7 8 7
6
2 1 2 1 2 1
8 3 7 6 4 5
9 4 5
1 3 3 1 3 1 3 1 1 3
2 7 5
4
9
8 9
4 6 4
9 8
4 6
9
6
8 9
3 2 2 3
3 3 2 3
7
6
9
5 6
8 1 4
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
3 1 2 1 3 2 3 2 3 1 2 3 1 2
7 9
5
8
5 5
9 7 8 9 9 7
5
9 67 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 71
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 2 3 2 3 1 1 1
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1
7
6
9 3 2
5 6 5
9
4 5
89
5 6 4 5
9 7
3 3 3
1 4 6 8 2 5 7 9 9 7 9
3 3 1 3 1 3 1 3
5 9 2 8 4
7
4
7
4
7 7
6
8 3 7 6 2 5 9 4 1
1 3 3 1 3 1 3 1 1 3
2 7 5 4
8 9
4
9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 3 3 2 3
7
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
3 1 2 1 3 2 3 2 3 1 2 3 1 2
7 9
5
8 6 5
4 5
9 7 8 9 9 7
5
9 7 9
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 72
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 3 2 3 1 1
4 5 6
8 5
9
6
9
6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
9 1 7 6 4 5
9 8
6
9
5 6
8 9
1 1 1
7
6
9 3 2
5 6 5
9
4 5
89
6 4 5
9 7
3 3 3
1 4 6 8 2 5 7 9 9 7
3 3 1 3 3 3
5 9 2 8 4
7
4
7 7 7
6
8 3 7 6 2 5 9 4 1
1 3 3 1 3 1 3 1 3
2 7 5 4
8 9
4
9
6 4
9 8
6
9
6
8 9
3 2 2 3 3 3 2 3
7
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
3 1 2 1 3 2 3 3 1 2 3 1 2
7 9
5
8 6 5
4 5
9 7 8 9 9 7 9 7 9
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 73
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 3 2 3 1 1
4 5 6
8 5
9
6
9
6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
9 1 7 6 4 5
9 8
6
9
5 6
8 9
1 1 1
7
6
9 3 2
5 6 5
9
4 5
89
6 4 5
9 7
3 3 3
1 4 6 8 2 5 7 9 9 7
3 3 1 3 3 3
5 9 2 8 4
7
4
7 7 7
6
8 3 7 6 2 5 9 4 1
1 3 3 1 3 1 3 1 3
2 7 5 4
8 9
4
9
6 4
9 8
6
9
6
8 9
3 2 3 3 3 2 3
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
3 1 1 3 2 3 3 1 2 3 1 2
9
5
8 6 5
4 5
9 7 8 9 9 7 9 7 9
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 74
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 3 2 3 1 1
4 5 6
8 5
9
6
9
6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
9 1 7 6 4 5
9 8
6
9
5 6
8 9
1 1 1
7
6
9 3 2
5 6 5
9
4 5
89
6 4 5
9 7
3 3 3
1 4 6 8 2 5 7 9 9 7
3 3 1 3 3 3
5 9 2 8 4
7
4
7 7 7
6
8 3 7 6 2 5 9 4 1
1 3 3 3 1 3 1 3
2 7 5 4
9 8 9
6 4
9 8
6
9
6
8 9
3 3 2 3 3 2 3
6
9 1 4
5 6
8
5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
3 1 1 3 2 3 3 2 3 1 2
9
5
8 6 5
4
9 7 8 9 9 7 9 7 9
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 75
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Forward Checking)
1 2 2 3 3 2 3 1 1
4 5 6
8 5
9
6
9
6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
9 1 7 6 4 5
9 8
6
9
5 6
8 9
1 1 1
7
6
9 3 2
5 6 5
9
4 5
8
9
6 4 5
9 7
3 3 3
1 4 6 8 2 5 7 9 9 7
3 3 1 3 3 3
5 9 2 8 4
7
4
7 7 7
6
8 3 7 6 2 5 9 4 1
1 3 3 3 1 3 1 3
2 7 5 4
9 8 9
6
9 8 9 8 9
3 3 2 3 3 2 3
6
9 1 4
5 6
8
5
9 7 8 9
5
7 8 7
5
9 7 8 9
3 1 1 3 2 3 3 2 3 1 2
9
5
8 6 5
4
9 7 8 9 9 7 9 7 9
Back to Start
Helmut Simonis Visualization Techniques 76
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
After Setup (Forward Checking)
1 2 2 3 3 2 3 1 1
4 5 6
8 5
9
6
9
6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
9 1 7 6 4 5
9 8
6
9
5 6
8 9
1 1 1
7
6
9 3 2
5 6 5
9
4 5
8
9
6 4 5
9 7
3 3 3
1 4 6 8 2 5 7 9 9 7
3 3 1 3 3 3
5 9 2 8 4
7
4
7 7 7
6
8 3 7 6 2 5 9 4 1
1 3 3 3 1 3 1 3
2 7 5 4
9 8 9
6
9 8 9 8 9
3 3 2 3 3 2 3
6
9 1 4
5 6
8
5
9 7 8 9
5
7 8 7
5
9 7 8 9
3 1 1 3 2 3 3 2 3 1 2
9
5
8 6 5
4
9 7 8 9 9 7 9 7 9
Helmut Simonis Visualization Techniques 77
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 4
7
5
8
6
9 8 4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 1 7 4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5
8 3 2
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
8 9 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9 1 4
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
Skip Animation
Helmut Simonis Visualization Techniques 78
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 4
7
5
8
6
9 8 4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 1 7 4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5
8 3 2
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9 1 4
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 79
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9
4
7
5
8
6
9 1 7 4
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9
4 5
7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5 6
8 93 2 4 5
7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9 1 4
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 80
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9 1 7 4
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5 6
8 93 2 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 9 4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 3 7 6 4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7 1 4
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 81
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 3 2 3 2 3 2 3 2 3 2 3
5 6
8 9
4 5
8
6
9
4 5
8
6
9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9 8
4 5 6
7 8 9 3 2
4 5 6 4
7 8 9 7
5 6
8 9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4 5 6 4 5
7 8 9 7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7 1 4
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4 5 6
7 8 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 82
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6
8 9
4 5 6 4 5 6
8 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5 6 4 5 6
8 7 8 9 8
4 5 6
7 8 9 3 2
4 5 6 4
7 8 9 7
5 6
8 9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5 6
8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4 5 6 4 5
7 8 9 7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4
8 9 8 7
5
8
6
9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4 5 6
7 8 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 83
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5 6
8 9 8 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5 6
9 7 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6
8 9 8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 6
7 8 9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 6
7 8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5 6
8 9 8 7 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 84
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5
9 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6
8 9 8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5
9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 85
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5
9 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5
9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 86
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4
9 7
5
89
4 5 6
7 9 3 24 5
7
6
9
1 3 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 8 4 5 6
7 8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 5 6 4 5 6
7 8 9 7 8 99 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 87
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4
9 7
5
89
4 5 6
7 9 3 24 5
7
6
9
1 3 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4
7
5 4 5 6 4 5 6
7 7 8 4 5 6
7
4
7
5 6
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 5 6 4 5 6
7 8 9 7 8 99 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 88
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89
4 5 6
7 93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6 4 5
7
6 4 5
7 8 6 4
7
5 6
1 3 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 6 4 5
9 7 8
6
9 9 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4 5
9 7 8 9
4 5
7 8
6 4 5
9 7 8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4 5
9 7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4 5
9 7 8 9
4 6 4 5 6
9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 89
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89
4 5 6
7 93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9 9
4
8 2 5 4
7 9
1 3 1 2 3 2 32 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6 4 5
7 8
6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 4 5
8 9 4 5
8
4 5
8
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5
7 8 9
4 5
7 8
6 4 5 6
9 7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5
7 8 9
4 5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5
7 8 9
4 6 4 5
9 7 8
6
9 6 4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 90
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9 7
5 6 4 5 6 4 5
9 7 8 9 7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4 5 6 4 5
7 8 9 7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5
8 9
4 6
9 7
5 6
9 64 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 91
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9
6 4
8 9 8
6
9
4
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 8 1 4
4 5 6 4 5
9
4
7
5
8 9
4 5 6 4 5
7 8 9 7 8
6
9
4 5
7 8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5 6
8
4 5
9
4
7
5
8 9
4 6
9 7
5 6
9 64 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 92
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5
7
5 6
9 7
5 6
9
3 2 2 3 2 3 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 5
8
6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4
8
6
9
4
8
6
9
1 3 1 2 1 2 3 2 3 1 3 1 2 3 1 2 3
5 6
7 8 9 1 4
4 5 6
8
4 5
9
4
7
5
8 9
4 5
7 8
4 5
7 8
6
9
4 5
7 8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5 6
8
4 5
9
4
7
5
8 9
4 6
9 7
5 6
9 6
4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 93
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5
7
5 6
9 7
5 6
9
3 2 2 3 2 3 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 5
8
6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4
8
6 4
9
6
8 9
3 2 2 3 2 3 3 2 3 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8
5
7 8
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6 4 5 6 4 5
7 8 9 8
4 5
9 7 8 9
4 6
9 7
5 6
9 6
4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 94
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 1 2 3
3 1 2
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7
5 6
8 4 5
7
4 5 6
7
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6
9
4
8
4 6 4
9
6
8 9
3 2 2 3 2 3 3 2 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5 6 4 5 6 4 5
7 8 9 8
4 5
9 7 8 9
4 6
9 7
5 6
9 6 4
7
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 95
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 1 2 3
3 1 2
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
9 3 2
4 5
7
1 3 1 3 3 1 3
7 9
4 4
7 6 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7
5 6
8 4 5
7
4 5 6
7
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 4 5
8
1 3
3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6
9
4
8
4 6 4
9
6
8 9
3 2 2 3 2 3 3 2 2 3
5
7 8
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
7 8 9
5
8
5 5
9 7 8 9 9 7
5
9 6 7 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 96
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 1
3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6
9
5 6
8 9
1 1 1 1
7 4 5 6 4 5 4 5
9 7 9 8 7
5 6
9 3 24 5
7
1 3 1 3 3 1 3
7 9
4
6 4
7 9
4
9 8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4
95 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
7
5 6
8 9 8 1 4
5 6 5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
7
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 6 7 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 97
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 1 2 3 1 1
3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 3
5 6
9
5 6 5
9 1 7 5 6
9
4 5
8
4 6
9
5 6
8 9
1 1 1 1
7 5 6 5
9
4 5
89
5 6
9 3 2
4 5
1 3 1 3 3 1 3
9
4
6 9
4
7 9
4
8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
5 6
9 4 5 4 5
7
4 6
7 8
5 6 4 5
7 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4 5
9 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5
8
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 6
7 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 98
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 2 3 1 3 1 2 1 3
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 2 3 2 3 3 2 3
5 6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1
7 5 6 5
9
4 5
89 3 2
5 6 4 5
9
1 3 1 3 3 1 3
9
4
6 9
4
7 9
4
8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
5 6
9 4 5 4 5
7
4 6
7 8
5 6 4 5
7 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4 5
9 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5
8
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 67 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 99
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 2 3 2 3 1 1 1
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 2 3 2 3
5 6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1
7 5 6 5
9
4 5
89 3 2
5 6 4 5
9
3 3 1 3
1 4 6 4
7 9 9
4
8 2 5 7 9
2 3 2 3 1 2 3 1 3 1 3
5 9 2 4 5
7
4 6
7 8
5 6 4 5
7 7
5 6
2 1 2 1 2 1
8 3 7 6 4 5
9 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5
4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5
8
6
9
5 6
8
5
1 4 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 67 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 100
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 1 1
4 5 6
8 5 6 5 6
9 7
5
7
6
9 7
5 6
9
3 2 3 2 3
6
9
5 6 5
1 9 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1
7 6 5
4 9 8 9 3 2 4 5
3 3 3
1 4 6 7 9 8 2 5
9 7 9
3 3 1 3
5 9 2 4
7
4
1
6
8 6 4
7
8 3 7 6 2 5 9 4 1
3 1 3 1 3 1
2 7 4
8
4
9 5 6 4
8
4 6
6
8 9
9
2 3 2 3 3 2 3
6 5 6
8
5 5
9 7 8 9 1 4 5
7 8 7
6 5 6
9 7 8 9
3 1 2 1 3 2 3 2 3 1 2
9
5
8
5 5
9 7 8 9 7 6
9 4 7 9
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 101
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 1
4 8 5 6 7 7 9 7 9
3 2 3 2 3
9
5
1 9 7 4 5
8
6
9
5
8 9
1 1
7 6 5
4 8 9 3 2 5
3 3 3
1 4 6 7 9 9 8 2 5 7 9
3 3 3
5 9 2 7
4
1 8 6 4
7
8 3 7 6 2 5 9 4 1
3 1 3 1 3
2 7 4 8 9 5 6 8 8 9
9
2 3 2 3 3 2 3
6 5
8 9 7 8 9 1 4 5
7 8 7
5
9 7 8 9
3 1 2 1 2 3 1 2
9
5
8
5
8 9 7 6 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 102
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 1
4 8 5 6 7 7 9 7 9
3 2 3 2 3
9
5
1 9 7 4 5
8
6
9
5
8 9
1 1
7 6 5
4 8 9 3 2 5
3 3 3
1 4 6 7 9 9 8 2 5 7
3 3 3
5 9 2 7
4
1 8 6 7
8 3 7 6 2 5 9 4 1
3 1 3 1 3
2 7 4 8 9 5 6 8 8 9
9
2 3 2 3 3 2 3
6 5
8 9 7 8 9 1 4 5
7 8 7
5
9 7 8 9
3 1 2 1 2 3 1 2
9
5
8
5
8 9 7 6 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 103
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 1
4 8 5 6 7 7 9 7 9
3 2 3 2 3
9
5
1 9 7 4 5
8
6
9
5
8 9
1 1
7 6 5
4 8 9 3 2 5
3 3 3
1 4 6 7 9 9 8 2 5 7
3 3 3
5 9 2 7
4
1 8 6 7
8 3 7 6 2 5 9 4 1
3 1 3 1 3
2 7 4 8 9 5 6 8 8 9
9
3 2 3 3 2 3
6 5
8 9 7 8 9 1 4 5
7 8 7
5
9 7 8 9
3 1 1 2 3 1 2
9
5
8
5
8 9 7 6 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 104
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 1
4 8 5 6 7 7 9 7 9
3 2 3 2 3
9
5
1 9 7 4 5
8
6
9
5
8 9
1 1
7 6 5
4 8 9 3 2 5
3 3 3
1 4 6 7 9 9 8 2 5 7
3 3 3
5 9 2 7
4
1 8 6 7
8 3 7 6 2 5 9 4 1
3 1 3 1 3
2 7 4 8 9 5 6 8 8 9
9
3 2 3 3 2 3
6 5
8 9 8 9 1 4 5
7 8 7
5
9 7 8 9
3 1 1 2 3 1 2
9
5
8
5
8 9 7 6 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 105
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Bounds Consistency)
1 2 2 3 1 1
4 8 5 6 7 7 9 7 9
3 2 3 2 3
9
5
1 9 7 4 5
8
6
9
5
8 9
1 1
7 6 5
4 8 9 3 2 5
3 3 3
1 4 6 7 9 9 8 2 5 7
3 3 3
5 9 2 7
4
1 8 6 7
8 3 7 6 2 5 9 4 1
3 1 3 1 3
2 7 4 8 9 5 6 8 8 9
9
3 2 3 3 2 3
6 5
8 9 8 9 1 4 5
7 8 7
5
9 7 8 9
3 1 1 2 3 1 2
9
5
8
5
8 9 7 6 4
Back to Start
Helmut Simonis Visualization Techniques 106
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
After Setup (Bounds Consistency)
1 2 2 3 1 1
4 8 5 6 7 7 9 7 9
3 2 3 2 3
9
5
1 9 7 4 5
8
6
9
5
8 9
1 1
7 6 5
4 8 9 3 2 5
3 3 3
1 4 6 7 9 9 8 2 5 7
3 3 3
5 9 2 7
4
1 8 6 7
8 3 7 6 2 5 9 4 1
3 1 3 1 3
2 7 4 8 9 5 6 8 8 9
9
3 2 3 3 2 3
6 5
8 9 8 9 1 4 5
7 8 7
5
9 7 8 9
3 1 1 2 3 1 2
9
5
8
5
8 9 7 6 4
Helmut Simonis Visualization Techniques 107
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 4
7
5
8
6
9 8 4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 1 7 4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5
8 3 2
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
8 9 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9 1 4
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
Skip Animation
Helmut Simonis Visualization Techniques 108
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 4
7
5
8
6
9 8 4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 1 7 4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5
8 3 2
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9 1 4
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 109
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9
4
7
5
8
6
9 1 7 4
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9
4 5
7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5 6
8 93 2 4 5
7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 9 6
9
4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8 3 7 6
6
9
4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9 1 4
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 110
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9 1 7 4
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9 8
4 5 6
7 8 9
4
7
5 6
8 93 2 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 9 4 5 6
7 8 9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5
8 86
9
4 5 6
7 8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 3 7 6 4 5 6 4
7 8 9 7
5
89 6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7 1 4
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4
7 8 9 7 8 9 7
5 6
8 9 6 4
7
5
8
6
9 4
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Helmut Simonis Visualization Techniques 111
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 7
5 6
9 8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 3 2 3 2 3 2 3 2 3 2 3
5 6
8 9
4 5
8
6
9
4 5
8
6
9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5
7 8
6
9
4 5
7 8
6
9 8
4 5 6
7 8 9 3 2
4 5 6 4
7 8 9 7
5 6
8 9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5
7 8
6
9 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4 5 6 4 5
7 8 9 7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7 1 4
5
8
6
9
4
7
5
8
6
9
4 5 6
7 8 9
4
7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4 5 6
7 8 9 4
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Helmut Simonis Visualization Techniques 112
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6
8 9
4 5 6 4 5 6
8 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5 6 4 5 6
8 7 8 9 8
4 5 6
7 8 9 3 2
4 5 6 4
7 8 9 7
5 6
8 9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6
8 9
4 5 6
8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4 5
7 8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4 5 6 4 5
7 8 9 7 8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4
7
5
8
6
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4
7
5
8
6
9
4 5 6
7 8 9
4
7
5 6 4 5 6 4 5
8 9 7 8 9 7 8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4
8 9 8 7
5
8
6
9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4 5 6
7 8 9 4
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Helmut Simonis Visualization Techniques 113
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5 6
8 9 8 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5 6
9 7 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6
8 9 8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 6
7 8 9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 6
7 8 9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 6
7 8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5 6
8 9 8 7 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
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Helmut Simonis Visualization Techniques 114
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5
9 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 2 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6
8 9 8 6 4 5 6 4 5 6
7 8 9 7 8 9 8 2 5 4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5
9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
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Helmut Simonis Visualization Techniques 115
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6 4
8 9
5 6 4 5 6 4 5
8 9 8 9 8
6
9
1 1 1 1 1 1
7
5 6 4 5 6 4 5
9 9 7 8
4 5 6
9
4 5 6 4
7 3 2
9 7
5 6
9
1 3 1 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5
9 8
4 5 6 4 5 6 4 5 6 4
7 8 9 7 8 9 7 8 9 7
5 6
8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9 9
4 5 6 4 5 6
7 8 9 7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5 6
7 8 9
4 5 6 4
7 8 9 7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5 6 4 5 6 4 5 6
7 8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
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Helmut Simonis Visualization Techniques 116
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4
9 7
5
89
4 5 6
7 9 3 24 5
7
6
9
1 3 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6
8 9
4 5 4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 8 4 5 6
7 8 9
4
7
5
8
6
9
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 5 6 4 5 6
7 8 9 7 8 99 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 117
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4
9 7
5
89
4 5 6
7 9 3 24 5
7
6
9
1 3 1 3 1 3 1 3
7 9
4
6 4
7
4
9 7 9 8 2 5 4
7 9
1 3 1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4
7
5 4 5 6 4 5 6
7 7 8 4 5 6
7
4
7
5 6
1 3 1 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 5 6 4 5 6
7 8 9 7 8 99 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9
4 5 6
7 8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4
7
5
8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5 4 5 6 4 5 6
8 9 7 8 9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 118
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89
4 5 6
7 93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6 4 5
7
6 4 5
7 8 6 4
7
5 6
1 3 2 3 1 2 3 1 2 3 1 2 3
7 3 7 6
5 6
8 9
4 6 4 5
9 7 8
6
9 9 4
7
5
8
6
9
4
7
5
8
6
9
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4 5
9 7 8 9
4 5
7 8
6 4 5
9 7 8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4 5
9 7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4 5
9 7 8 9
4 6 4 5 6
9 7 8 9 6 4
7
5
8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 119
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 4 5 6
8 9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89
4 5 6
7 93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9 9
4
8 2 5 4
7 9
1 3 1 2 3 2 32 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6 4 5
7 8
6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 4 5
8 9 4 5
8
4 5
8
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5
9
4 5
7 8 9
4 5
7 8
6 4 5 6
9 7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5
9
4 5
7 8 9
4 5 6
7 8 9
4 5
7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8 9
4 5
7 8 9
4 6 4 5
9 7 8
6
9 6 4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 120
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6 4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
2 7 5 4 5 4
9 7
5
8 9 7
5 6 4 5 6 4 5
9 7 8 9 7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
7 8 9 8 1 4
5 6 4 5 6 4 5 4
9 7
5
8 9
4 5 6 4 5
7 8 9 7 8
6
9
4
7
5
8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
7
5 6 4 5 6 4 5
8 9 8
4
9 7
5
8 9
4 6
9 7
5 6
9 64 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 121
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 2 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
5 6
9 7
5 6
9
3 2 2 3 2 3 2 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
6 4 5 6 4 5
9 8 9 8
6
9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
6
9
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 2 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5 6
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9
6 4
8 9 8
6
9
4
8
6
9
1 3 1 2 1 2 3 2 3 1 2 3 1 2 3 1 2 3
5 6
7 8 9 8 1 4
4 5 6 4 5
9
4
7
5
8 9
4 5 6 4 5
7 8 9 7 8
6
9
4 5
7 8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5 6
8
4 5
9
4
7
5
8 9
4 6
9 7
5 6
9 64 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 122
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5
7
5 6
9 7
5 6
9
3 2 2 3 2 3 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 5
8
6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 8 9 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4
8
6
9
4
8
6
9
1 3 1 2 1 2 3 2 3 1 3 1 2 3 1 2 3
5 6
7 8 9 1 4
4 5 6
8
4 5
9
4
7
5
8 9
4 5
7 8
4 5
7 8
6
9
4 5
7 8
6
9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6
7 8 9
4 5 6
8
4 5
9
4
7
5
8 9
4 6
9 7
5 6
9 6
4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 123
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 3 1 2 3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5
7
5 6
9 7
5 6
9
3 2 2 3 2 3 3 2 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 5
8
6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7
4
7
5 6
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 5
8
4 5
8
1 3 3 1 3 1 3 1 3 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4
8
6 4
9
6
8 9
3 2 2 3 2 3 3 2 3 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8
5
7 8
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2 3
5 6 4 5 6 4 5
7 8 9 8
4 5
9 7 8 9
4 6
9 7
5 6
9 6
4 5
7 8
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 124
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 1 2 3
3 1 2
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
93 24 5
7
1 3 1 3 3 1 3
7 9
4
6
4
7 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7
5 6
8 4 5
7
4 5 6
7
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6
9
4
8
4 6 4
9
6
8 9
3 2 2 3 2 3 3 2 2 3
5 6
7 8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5 6 4 5 6 4 5
7 8 9 8
4 5
9 7 8 9
4 6
9 7
5 6
9 6 4
7
6
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 125
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 1 2 3
3 1 2
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6 4 5 6
9 8 9
1 1 1 1 1
7
5 6 4 5 6 4 5
9
4 5
9 7 89 7
5 6
9 3 2
4 5
7
1 3 1 3 3 1 3
7 9
4 4
7 6 9
4
9 8 2 5 4
7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 2 3
7 9
5 6 4 5 4 5
7
4 6
7
5 6
8 4 5
7
4 5 6
7
1 2 1 2 1 2 1 2
5
8 3 7 6 4 5
9 4 4 5
8
1 3
3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6
9
4
8
4 6 4
9
6
8 9
3 2 2 3 2 3 3 2 2 3
5
7 8
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
7 8 9
5
8
5 5
9 7 8 9 9 7
5
9 6 7 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 126
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 1
3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 3
5 6 4 5 6 4 5
8 9 8 9 1 7 5 6
9
4 5
8
4 6
9
5 6
8 9
1 1 1 1
7 4 5 6 4 5 4 5
9 7 9 8 7
5 6
9 3 24 5
7
1 3 3 3 1 3
7 4 6
9
4
7 9
4
9 8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
7 9
5 6 4 5 4 5
7
4 6
7 8
5 6 4 5
7 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4
95 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 4
9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
7
5 6
8 9 8 1 4
5 6 5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
7
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 6 7 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 127
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 1 2 3 1 1
3 1 2 3
4 5 6
8 7
5
9
6
9 7
5 6
9 7
5 6
9 7
7
5 6
9
3 2 2 3 2 3 3 2 3
5 6
9
5 6 5
9 1 7 5 6
9
4 5
8
4 6
9
5 6
8 9
1 1 1 1
7 5 6 5
9 4 8 5 6
9 3 2
4 5
1 3 3 3 1 3
9 4 6 9 7 9 8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
5 6
9 4 5 4 5
7
4 6
7 8
5 6 4 5
7 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4 5
9 4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 9
4
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5
8
6
9 1 4
5 6
8
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 76 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 128
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 2 3 1 3 1 2 1 3
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 2 3 2 3 3 2 3
5 6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1
7 5 6 5
9 4 8 5 6
9 3 2
5
1 3 3 3 1 3
4 6
9 7 9 9 8 2 5 7 9
1 3 1 2 3 2 3 2 3 1 2 3 1 3 1 3
9
5 6 4 5
7
5 4 6
7
5 6 4 5
7 8 7
5 6
1 2 1 2 1 2 1
5
8 3 7 6 4 5
9
4 5
8
1 3 3 1 3 1 3 1 1 3
2 7 5 9
4
8 9
6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5 6
8 9
5 6
8 1 4
5 5
9 7 8 9
5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 67 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 129
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 2 2 3 2 3 2 3 1 1 1
4 5 6
8 5
9
6
9
5 6
9 7
5
7
6
9 7
5 6
9
3 2 2 3 2 3
5 6
9
5 6 5
9 1 7 5 6 4 5
9 8
4 6
9
5 6
8 9
1 1 1
7 5 6 5
9 4 8 5 6
9 3 2
5
3 3 1 3
1 4 6 7 9 9 8 2 5 7 9
2 3 2 3 1 2 3 1 3 1 3
5 9 2 7
5 4 6
7
5 6 4 5
7 8 7
5 6
2 1 2 1 2 1
8 3 7 6 4 5
9
4 5
8
3 1 3 1 3 1 1 3
2 7 4
8 9 5 6 4
9 8
4 6
9
6
8 9
3 2 2 3 2 3 3 2 3
5 6
8 9
5 6
8
5 5
9 7 8 9 1 4 5
7 8 7
6 5 6
9 7 8 9
1 3 1 2 1 2 3 2 3 2 3 1 2 3 1 2
5
8 9
5
8
5 5
9 7 8 9 9 7
5
9 67 9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 130
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
1 1
4 2 8 5 6 3 1 7
6
9 7
5 6
9
3 3
5
6
9 1 5
9 7 2 4 6 8
7 6 1 4 8 9 5 3 2
3 3 3
1 4 6 7 9 8 2 5
9 7 9
3 1 3
5 9 2 7 4 1 8 4
7 6
8 3 7 6 2 5 9 4 1
3 1 3
2 7 4 8 9 5 6 8 1 6
8 9
3 3 2
6 8 2 5
9 1 4 5
7 8 7
6
9 5
3 2 3
1
9 5 8 7 6 2
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 131
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
4 2 8 5 6 3 1 7 9 7 9
3 3
5
9 1 9 7 2 4 6 8
7 6 1 4 8 9 5 3 2
3 3 3
1 4 6 7 9 8 2 5
9 7 9
3 3
5 9 2 7 4 1 8 7 6
8 3 7 6 2 5 9 4 1
3 3
2 7 4 9 5 6 8 1 9
3 3
6 8 2 9 1 4 7 7 9 5
3 3
1
9 5 8 7 6 2
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 132
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
4 2 8 5 6 3 1 7 9 7 9
3 3
5
9 1 9 7 2 4 6 8
7 6 1 4 8 9 5 3 2
3 3 3
1 4 6 7 9 8 2 5
9 7
3 3
5 9 2 7 4 1 8 7 6
8 3 7 6 2 5 9 4 1
3 3
2 7 4 9 5 6 8 1 9
3 3
6 8 2 9 1 4 7 7 9 5
3 3
1
9 5 8 7 6 2
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 133
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
4 2 8 5 6 3 1 7 9 7 9
3 3
5
9 1 9 7 2 4 6 8
7 6 1 4 8 9 5 3 2
3 3 3
1 4 6 7 9 8 2 5
9 7
3 3
5 9 2 7 4 1 8 7 6
8 3 7 6 2 5 9 4 1
3 3
2 7 4 9 5 6 8 1 9
3 3
6 8 2 9 1 4 7 7 9 5
3 3
1
9 5 8 7 6 2
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 134
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
4 2 8 5 6 3 1 7 9 7 9
3 3
5
9 1 9 7 2 4 6 8
7 6 1 4 8 9 5 3 2
3 3 3
1 4 6 7 9 8 2 5
9 7
3 3
5 9 2 7 4 1 8 7 6
8 3 7 6 2 5 9 4 1
3 3
2 7 4 9 5 6 8 1 9
3 3
6 8 2 9 1 4 7 7 9 5
3 3
1
9 5 8 7 6 2
9 4
Back to Start Skip Animation
Helmut Simonis Visualization Techniques 135
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Propagation Steps (Domain Consistency)
4 2 8 5 6 3 1 7 9 7 9
3 3
5
9 1 9 7 2 4 6 8
7 6 1 4 8 9 5 3 2
3 3 3
1 4 6 7 9 8 2 5
9 7
3 3
5 9 2 7 4 1 8 7 6
8 3 7 6 2 5 9 4 1
3 3
2 7 4 9 5 6 8 1 9
3 3
6 8 2 9 1 4 7 7 9 5
3 3
1
9 5 8 7 6 2
9 4
Back to Start
Helmut Simonis Visualization Techniques 136
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
After Setup (Domain Consistency)
4 2 8 5 6 3 1 7 9 7 9
3 3
95 91 7 2 4 6 8
7 6 1 4 8 9 5 3 2
3 3 3
1 4 6 7 9 8 2 5
9 7
3 3
5 9 2 7 4 1 8 7 6
8 3 7 6 2 5 9 4 1
3 3
2 7 4 9 5 6 8 1 9
3 3
6 8 92 1 4 7 7 9 5
3 3
91 5 8 7 6 2
9 4
Helmut Simonis Visualization Techniques 137
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Comparison
Forward Checking Bounds Consistency Domain Consistency
1 2 2 3 3 2 3 1 1 1 2 2 3 1 1
4 5 6
8 5
9
6
9
6
9 7
5
7
6
9 7
5 6
9 4 8 5 6 7 7 9 7 9 4 2 8 5 6 3 1 7 9 7 9
3 2 3 2 3 3 2 3 2 3 3 3
6
9
5 6 5
9 1 7 6 4 5
9 8
6
9
5 6
8 9 9
5
1 9 7 4 5
8
6
9
5
8 9 95 91 7 2 4 6 8
1 1 1 1 1
7
6
9
5 6 5
3 2
9
4 5
8
9
6 4 5
9 7 7 6 5
4 8 9 3 2 5
7 6 1 4 8 9 5 3 2
3 3 3 3 3 3 3 3 3
1 4 6 8 2 5 7 9 9 7 1 4 6 7 9 9 8 2 5 7 1 4 6 7 9 9 8 2 5 7
3 3 1 3 3 3 3 3 3 3 3
5 9 2 8 4
7
4
7 7 7
6
5 9 2 7
4
1 8 6 7 5 9 2 7 4 1 7 8 6
8 3 7 6 2 5 9 4 1 8 3 7 6 2 5 9 4 1 8 3 7 6 2 5 9 4 1
1 3 3 3 1 3 1 3 3 1 3 1 3 3 3
2 7 9 5
4
8 9
6
9 8 9 8 9 2 7 4 8 9 5 6 8 9 8 9 2 7 4 9 5 6 8 1 9
3 3 2 3 3 2 3 3 2 3 3 2 3 3 3
6
9
5 6
8
5
1 4
9 7 8 9
5
7 8 7
5
9 7 8 9 6 5
8 9 8 9 1 4 5
7 8 7
5
9 7 8 9 6 8 92 1 4 7 7 9 5
3 1 1 3 2 3 3 2 3 1 2 3 1 1 2 3 1 2 3 3
9
5
8
5
9 7 6 4 8 9 9 7 9 7 9 9
5
8
5
8 9 7 6 4 91 5 8 9 7 6 2 4
Helmut Simonis Visualization Techniques 138
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Instrumented indomain
tree_indomain_generic(Term,Handle,Handle,Type):-
Handle = visualization{ignore_fixed:IgnoreFixed,
var_arg:VarArg,
name_arg:NameArg,
focus_arg:FocusArg},
arg(VarArg,Term,X),
((integer(X),IgnoreFixed = yes) ->
true
;
arg(NameArg,Term,Name),
arg(FocusArg,Term,Focus),
get_domain_as_list(X,L),
get_domain_size(X,Size),
reorganize_domain(X,L,Type,K),
try_value(Handle,X,K,Name,Size,Focus)
).
Helmut Simonis Visualization Techniques 139
Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Instrumented indomain
try_value(Handle,X,[V|_],Name,Size,Focus):-
((X = V, true) ->
try(Handle,Name,Size,V),
focus_option(Focus,FocusOption),
draw_visualization(Handle,FocusOption)
;
failure(Handle,Name,Size,V),
fail_option(Focus,V,FailOption),
draw_visualization(Handle,FailOption),
fail
).
try_value(Handle,X,[_|R],Name,Size,Focus):-
try_value(Handle,X,R,Name,Size,Focus).
Helmut Simonis Visualization Techniques 140
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
Outline
1 Introduction
2 Visualization by Annotation
3 Visualization Interface
TreeLog Format
VisualizerLog Format
4 Conclusions
Helmut Simonis Visualization Techniques 141
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
Architecture (Current)
Program + Annotation
ECLiPSe
TreeLog VisualizationLog
Viz
Treemap SVG Graph Statistics
Inkscape Browser Batch VizTool
Annotated Image PDF
Helmut Simonis Visualization Techniques 142
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
Architecture (Planned)
Program + Annotation
ECLiPSe
TreeLog VisualizationLog
Viz
Treemap SVG Graph Statistics
Inkscape Browser Batch VizTool
Annotated Image PDF
Helmut Simonis Visualization Techniques 143
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
CP-Inside
Program + Annotation
CP-Inside
TreeLog VisualizationLog
Viz
Treemap SVG Graph Statistics
Inkscape Browser Batch VizTool
Annotated Image PDF
Helmut Simonis Visualization Techniques 144
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
Generic Tool
Program + Annotation
Your Favourite Tool
TreeLog VisualizationLog
Viz Your Favourite Analysis
Treemap SVG Graph Statistics
Inkscape Browser Batch VizTool
Annotated Image PDF
Helmut Simonis Visualization Techniques 145
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
TreeLog Format
XML based description
Record information about nodes in search tree
Choices
Failures
Success
Redundant information to ease generation
Helmut Simonis Visualization Techniques 146
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
TreeLog Example
<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<tree version="1.0" >
<root id="0"/>
<try id="1" parent="0" name="S" size="1" value="9" />
<fail id="2" parent="1" name="E" size="4" value="4" />
<try id="3" parent="1" name="E" size="4" value="5" />
<try id="4" parent="3" name="N" size="1" value="6" />
<try id="5" parent="4" name="D" size="1" value="7" />
<try id="6" parent="5" name="M" size="1" value="1" />
<try id="7" parent="6" name="O" size="1" value="0" />
<try id="8" parent="7" name="R" size="1" value="8" />
<try id="9" parent="8" name="Y" size="1" value="2" />
<succ id="9"/>
<fail id="10" parent="1" name="E" size="4" value="6" />
<fail id="11" parent="1" name="E" size="4" value="7" />
</tree>
Helmut Simonis Visualization Techniques 147
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
TreeLog Example
<?xml version="1.0" encoding="UTF-8" standalone="yes"?> S
9
<tree version="1.0" >
<root id="0"/> E
4 5 6 7
<try id="1" parent="0" name="S" size="1" value="9" />
N
<fail id="2" parent="1" name="E" size="4" value="4" /> 6
<try id="3" parent="1" name="E" size="4" value="5" /> D
<try id="4" parent="3" name="N" size="1" value="6" /> 7
<try id="5" parent="4" name="D" size="1" value="7" /> M
<try id="6" parent="5" name="M" size="1" value="1" /> 1
<try id="7" parent="6" name="O" size="1" value="0" /> O
0
<try id="8" parent="7" name="R" size="1" value="8" />
<try id="9" parent="8" name="Y" size="1" value="2" /> R
8
<succ id="9"/>
Y
<fail id="10" parent="1" name="E" size="4" value="6" /> 2
<fail id="11" parent="1" name="E" size="4" value="7" />
</tree>
Helmut Simonis Visualization Techniques 148
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
VisualizerLog Format
XML based description
Describe state of variables and/or constraints at specific
stages
Where annotated in program
For every node in tree
Linked to search tree log
Helmut Simonis Visualization Techniques 149
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
VisualizerLog Example
<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<visualization version="1.0" >
<visualizer id="1" type="vector" display="expanded" x="0" y="0"
width="8" height="10" group="1" min="0" max="9" />
<state id="1" tree_node="-1" >
<visualizer_state id="1" >
<dvar index="1" domain="0 .. 9" />
<dvar index="2" domain="0 .. 9" />
<dvar index="3" domain="0 .. 9" />
<dvar index="4" domain="0 .. 9" />
<dvar index="5" domain="0 .. 9" />
<dvar index="6" domain="0 .. 9" />
<dvar index="7" domain="0 .. 9" />
<dvar index="8" domain="0 .. 9" />
</visualizer_state>
</state>
...
Helmut Simonis Visualization Techniques 150
Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
VisualizerLog Example
...
<state id="2" tree_node="-1" >
<visualizer_state id="1" >
<dvar index="1" domain="1 .. 9" />
<dvar index="2" domain="0 .. 9" />
<dvar index="3" domain="0 .. 9" />
<dvar index="4" domain="0 .. 9" />
<dvar index="5" domain="0 .. 9" />
<dvar index="6" domain="0 .. 9" />
<dvar index="7" domain="0 .. 9" />
<dvar index="8" domain="0 .. 9" />
</visualizer_state>
</state>
...
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Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
VisualizerLog Example
...
<state id="5" tree_node="1" >
<visualizer_state id="1" >
<integer index="1" value="9" />
<dvar index="2" domain="4 .. 7" />
<dvar index="3" domain="5 .. 8" />
<dvar index="4" domain="2 .. 8" />
<integer index="5" value="1" />
<integer index="6" value="0" />
<dvar index="7" domain="2 .. 8" />
<dvar index="8" domain="2 .. 8" />
<focus group="-" index="1" />
</visualizer_state>
</state>
...
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Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
VisualizerLog Example
...
<state id="6" tree_node="2" >
<visualizer_state id="1" >
<integer index="1" value="9" />
<dvar index="2" domain="4 .. 7" />
<dvar index="3" domain="5 .. 8" />
<dvar index="4" domain="2 .. 8" />
<integer index="5" value="1" />
<integer index="6" value="0" />
<dvar index="7" domain="2 .. 8" />
<dvar index="8" domain="2 .. 8" />
<failed group="-" index="2" value="4" />
</visualizer_state>
</state>
...
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Introduction
Visualization by Annotation TreeLog Format
Visualization Interface VisualizerLog Format
Conclusions
VisualizerLog Example
...
<state id="14" tree_node="9" >
<visualizer_state id="1" >
<integer index="1" value="9" />
<integer index="2" value="5" />
<integer index="3" value="6" />
<integer index="4" value="7" />
<integer index="5" value="1" />
<integer index="6" value="0" />
<integer index="7" value="8" />
<integer index="8" value="2" />
</visualizer_state>
</state>
...
</visualization>
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Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Outline
1 Introduction
2 Visualization by Annotation
3 Visualization Interface
4 Conclusions
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Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Conclusions
New ELearning course for ECLiPSe
Open source material, Creative Commons BY-NC-SA
license
Application driven
Modelling with global constraints
Customizing search
Effort only justifiable through Cisco grant
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Introduction
Visualization by Annotation
Visualization Interface
Conclusions
Visualization
Design choice: System independent
Provide enough information to user of system, not to tool
developer
Relatively few primitives, extensible for specific global
constraints
XML intermediate format, open for specific analysis
Helmut Simonis Visualization Techniques 157
