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```									PERSPECTIVE DRAWING GUIDE

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005

EXERCISE                                                                  PAGE
1       CUBE IN ONE-POINT PERSPECTIVE                                  1-2
CUBE IN TWO-POINT PERSPECTIVE                                  3-4
CUBE IN THREE-POINT PERSPECTIVE                                5-6
2    ONE-POINT PERSPECTIVE PLAN PROJECTION                          7-8
3    DIVIDE AND PROPORTION                                            9
4    SHADOWS - SUNLIGHT                                              10
SHADOWS - RAY LIGHT                                             11
5    SHADOWS - FRONT AND BACKLIT                                     12
6    PYRAMIDS - STANDING/TIPPED                                      13
7    CIRCLES IN ONE-POINT PERSPECTIVE                                14
CIRCLES IN TWO-POINT PERSPECTIVE                                15
8    CYLINDER - STANDING                                             16
CYLINDER - ROLLED                                               17
BOX WITH SWINGING FLAPS                                         18
9    CONES - STANDING/TIPPED                                         19
DOME                                                            20
10       INTERSECTING ROLLED CYLINDERS                                   21
COMPOUND FORM (PLAN PROJECTION)                                 22
11       COMPOUND FORM (3-D GRID)                                        23
12-POINT ELLIPSE                                                24
12       REFLECTIONS                                                     25
13       FINAL PROJECT                                                 26-27

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 1: CUBE IN ONE-POINT PERSPECTIVE                                                                    1

The cube is the single most basic form in draft-
ing, so it is easy to help begin the understanding
of perspective. In one-point perspective, the face
of the cube is always “true”, meaning it has the ac-
tual height and width dimensions because this face
is always coplanar to the picture plane. All other
sides of the cube vanish to a single point, the van-
1                     2                            ishing point, to imply depth.

To begin, ﬁrst a horizon/eye level (H/EL) is estab-
lished and a cone of vision is created. The H/EL is
simply the diameter of the cone of vision (CoV)- a
semicircle. Where the H/EL intersects with the CoV
are the diagonal vanishing points (DVP), and the
midpoint of the H/EL is the center of vision (CV).

Follow the steps, use light construction lines initial-
ly, then darken the completed object with the ap-
propriate line weights. This setup will apply to all
3                     4
exercises that follow.

1) Complete the set up above
2) Locate a square within the cone of vision
3) Connect all four corners of the square to the
CV
4) Connect the corners to the opposing DVPs
5) Draw vertical lines where the lines from step 3
and 4 intersect - this establishes the depth
6) Connect the lines in the back and complete the
cube
5                     6

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 1: CUBE IN ONE-POINT PERSPECTIVE                                                          2

This exercise is to construct six cubes
that share the same vanishing point,
and placed throughout one single
cone of vision to provide a variety of
views. The objects shown here are
modiﬁed cubes, by proportion and
subtraction.

Notice the objects that are the farthest
away from the center of vision (or clos-
est to the edge of the cone of vision),
they appear distorted due to the fact
that the frontal surfaces remain “true”
while the rest are in perspective, this
gives the objects an awkward and
skewed appearance. Therefore, one-
point perspective drawings are not
used most often. They are, however,
the simplest and easiest to construct.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 1: CUBE IN TWO-POINT PERSPECTIVE                                                                 3

Unlike in one-point, a two-point perspective cube
does not align with the picture plane. Therefore,
there is not a face that is of true measurement.
However, There is one side/edge that is coplanar
to the picture plane, and it is the only edge that is
“true”. This edge is determined on the location of
the cube in the cone of vision, and it is the deter-
mining factor of the height for the remaining cube.
1                     2
To begin, set up the cone of vision in the same man-
ner as in one-point perspective. However, instead
of the DVPs, those points will be labeled as RVP
and LVP, as in right and left vanishing points. The
base/plan of the cube (or the object) should be de-
termined so it can be arranged and projected into
the perspective, hence the method’s name of “plan
projection.”

1) Start a line from each of the VPs and intersect
them anywhere along the CoV. This should form a
3                     4
right angle and should be then form the base of the
cube
2) Establish a ground line (GL). This is the ground
on which your cube will be rested. The closer it is
to the horizon, the more you are looking at the cube
from eye level. Then project the front corner of the
square onto the horizon line, establishing the CV,
and the outer corners to the GL
3) Connect the center/front line at GL to the RVP
and LVP. Then connect the corners at GL to the
CV. Where they intersect the ﬁrst two lines in this
5                     6
step will establish the edges of the cube

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 1: CUBE IN TWO-POINT PERSPECTIVE                                                              4

4) Swing an arc the same distance
as one side of the base on the front
edge to establish the height of the
cube. Then connect the end of this
line to each of the VPs
5) Fill in the vertical lines and connect
each to the VPs as the cube slowly
takes shape
6) Establish the back of the cube

Two-point perspective is most com-
monly used because of its ease of
construction and relative accuracy.
Note that the farther away from the H/
EL the more apparent the distortion,
because there is still a third dimen-
sion (or axis) being disregarded. So it
is still not a perfect depiction of reality,
but it is an ideal compromise between
difﬁculty and accuracy.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 1: CUBE IN THREE-POINT PERSPECTIVE                                                                                                         5

The most accurate depiction of reality is three-point
perspective, because it takes into consideration all
three dimensions (x,y,z). Since all three axis are in
perspective, there is no “true” surface or edge.

To begin, set up the cone of vision (CoV) as in two-
point perspective.

1) Find the midpoint on the H/EL and label it m.
Locate and label point X anywhere along the H/EL.
Connect this point vertically downward to intersect
with the CoV, this will be the vertical measuring line
(vmp). The intersection should be labeled SPx. Lo-
cate any point n along the vmp and draw lines to
both the LVP and RVP. Extend the two lines from
n to intersect with the CoV and label the points Y
and Z.
2) Draw lines connecting the LVP to Z and RVP
to Y. Extend these lines and they should intersect
along the vmp line. This intersection is the third
vanishing point (VP3). Now all three horizons and
measuring lines are established.
3) Find the midpoint on each of the two other mea-
suring lines, from LVP and RVP to VP3, and label
each point m. Draw an arc from each point m that
connects the VPs. Label where the arc intersects
at line RVP-Z point SPz, and at LVP-Y point SPy.
The SPs (x,y,z) indicate the corners of the cube.
Simply connect each to the opposing VPs and the
cube will slowly appear.
4) To eliminate the distortion of the large cube (rep-
resenting its closeness to viewer), it is proportioned
Illustrations from Jay Doblin’s Perspective: A New System For Designers.                   and divided into a smaller and more usable one.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 1: CUBE IN THREE-POINT PERSPECTIVE                                                        6

In the smaller picture is a three-point
perspective cube that is at a perfect
45-degree on all three horizons. It is
much simpler to construct but uncom-
mon in real life applications.

1) Compose a perfect circle (CoV)
and label the center n
2) From n draw three measuring lines
outward at 120 degrees apart
3) Where these lines intersect with
the CoV label the points RVP, LVP
and VP3
3) Draw a circle at n, and where it
intersects with the three measuring
lines will be the corners (x,y,z) of the
cube
4) Connect these corners to the op-
posing VPs and the complete the
cube

Three-point perspective is the most
accurate depiction of reality. How-
ever, its accuracy does not justify the
difﬁculty and the time it takes to con-
struct. Therefore, it is often preferred
over by two-point perspective.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 2: ONE-POINT PERSPECTIVE PLAN PROJECTION                                                  7

As a quick exercise to put the one-
point perspective to a more practical
use, a simple table is designed. First,
the orthographics (two dimensional
views) of the table is constructed.

Using the plan view, a picture plane
(PP) is deﬁned. This the plane on
which the view is taken and where all
measurements are “true”. Next, es-
tablish (again on the plan) a station
point (SP). Imagine this point as the
PP
eyes relative to the object. Lastly,
vertically below the SP, establish a
central vanishing point (CVP).
SP
To begin constructing the perspective,
setup the drawing as shows, with the                                                 CVP
side view to the side and the plan view
above the ﬁnal perspective. Project
from the plan above each point of the
table directly to the SP. Where the
lines intersects the PP is where it will
appear in perspective. In this case,
since the front of the table is directly
on the PP, the true table front can be
copied into the perspective view. The
rest of the table will converge toward
the CVP.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 2: ONE-POINT PERSPECTIVE PLAN PROJECTION                                                   8

Once the orthographics for the room
is constructed, create a grid system
as shown. This two dimensional grid
will be translated into three to help the
construction of the room. The follow-
ing ﬁve steps are the guidelines for all
plan projection perspective drawings:

1) Construct the orthographics for the
object, which includes the top/plan
view, the side and the front view
2) Set up the drawing. Place the plan
within the cone of vision, and align
the orthographics accordingly on the
layout. Be sure to place the side/front
views along the ground line
3) Transform the plan into three-di-
mension using the same method as
creating the base of a cube
4) Use the elevations (front/side
views of the orthographic to project
the height of the object to the picture
plane
5) Construct the object using all
available views in the same manner
as creating the cube

In this one-point perspective room,
there is one single vanishing point
to which all depth converges. In the
case of a two-point, the objects will
converge to the opposing vanishing
points along the horizon.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 3: DIVIDE AND PROPORTION                                                                 9

A cube is the most basic and simplest
form, and it is quite boring. However,
simply by dividing and proportioning it
one can create more complex objects.
As a matter of fact, most shapes can
be broken down into cubes, or partial
cubes.

A simple cube can be divided into
smaller cubes. For example, by con-
necting the diagonals, a face can
be divided into quadrants, and each
quadrant can be divided into more by
doing the same, and so forth. Or as
shown on the right, one can be divided
into nine squares, and so forth. Simi-
larly, by combining multiple cubes, the
same effect can be achieved.

Shown on the far right are a couple
of examples of creating objects from
dividing and proportion, a set of steps
and a diamond.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 4: SHADOWS - SUN LIGHT                                                                 10

Sunlight is also referred to as paral-
lel light, because it comes from the
same direction for all objects [within
the same view]. Therefore the shad-
ows of each object will be cast in the
same opposite direction.

The most simple method of cast-
ing a shadow is to break down the
object into its composition, the lines
or “sticks”. By casting each line at a
time, the projected image will form
naturally.

The angle of the sun must be deter-
mined at ﬁrst. On the right (top), the
angle is set at 45. Simply project the
top of the segment onto the ground
at 45 degrees, where this projection
intersects the base of the segment is
the end of the shadow. To help keep
the lines distinct, especially on more
complex objects, label each point on
the object and their corresponding
shadow, and in the end simply con-
nect the shadow points in the same
order as in the object. If an object
is ﬂoating, establish the ground ﬁrst,
and project all lines to that ground.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 4: SHADOWS - RAY LIGHT                                                                                    11

light source

Ray light is a projecting light, or re-
ferred to as artiﬁcial light such as a
light bulb. Similar to sunlight, shad-
ows for ray light are determined by
the same two factors - altitude (angle)
and direction of the light source. Un-
like sunlight however, ray light can be
placed in a manner which multiple ob-
jects in a single view can have shad-      plan light
ows in various directions (as shown
on right).

First establish the angle and direction,
they must be align vertically. Then
project the light in the same manner
as in the sunlight exercise. Label
the points as necessary to help keep
them organized.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 5: SHADOWS - FRONT AND BACKLIT                                                            12

Front and backlit shadows simply im-
ply the direction from which the light
source casts the shadows. Front lit
objects have the light source in front,
thus the shadows are cast behind the
objects. Contrarily, backlit objects
have the light source from behind,
casting shadows in front of them. All
the shadows are constructed in the
same manner as the previous exer-
cises, with addition attention paid to
the location of the light source to pro-
duce the desired effects.

On the right, the two diagrams illus-
trate the ideal altitude and direction
of light to create shadows, indicated
by the hatched areas. Below are two
more diagrams illustrating the front
and backlit setup for sunlight. Note
that the shadow vanishing point (SVP)
must be located on the H/EL, with the
auxiliary vanishing point (AVP), the
angle of the light, directly above or be-
low. In the case of ray light, the SVP
can be above or below the H/EL.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 6: PYRAMIDS - STANDING/TIPPED                                                           13

A pyramid is another form that can be
derived from a simple cube. It is sim-
ply a square base that converges into
a single point at a certain height.

A standing pyramid is quite basic,
simply follow the steps in drafting a
cube but only establish a single point
to which the base will connect. How-
ever, a tipped cone is much more
challenging. To be able to draft in
perspective accurately the slope of
the tipped surface, the orthographics
must be constructed.

First draft the orthographics of the
standing variation. Then draw an arc
with the same length of the sloped
surface from the corner to the side
in which the pyramid is to be tipped.
This arc establishes the new “base”
of the tipped object. Simply ﬁnish the
object by drawing the arc length from
the new tip back in the original direc-
tion, and another arc with the length
of the original base to establish the
ﬁnal corner. Finish the plan view and
proceed to project it into two-point
perspective.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 7: CIRCLES IN ONE-PERSPECTIVE                                                            14

A circle in perspective (CIP) is simply
an ellipse. First create a grid in one-
point perspective. Begin to ﬁll in the
ellipse and use the grid as a guide.
The vertices intersect the midpoint
[in perspective] of each box. Perfect
freehand drawing the shape of an el-
lipse simply by repetition and practice.
Notice the gradual rotation and elon-
gation of the ellipses as they move
further away from the center of vision.
This is due to distortion and should be
avoided.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 7: CIRCLES IN TWO-PERSPECTIVE                                                             15

Constructing a circle in two-point per-
spective is similar to that in one-point.
First create a cube, and include the
orthogonal lines as guides. Again,
practice freehand drawing the el-
lipse forms and ﬁll in the ellipses onto
the surfaces. Note in the examples
that the central axes of the cubes
are shown; they connect to the cor-
responding vanishing points. For the
majority, these axes double as the mi-
nor axes of the ellipse. The concept
is that the minor axis converges to the
vanishing point and the major axis is
perpendicular to the axis of the form.
Only exception is when the surface is
so close to the edge of the view that
is becomes distorted, and should be
avoided. These axes can be very
helpful in creating the correct ellipse.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 8: CYLINDER - STANDING                                                                   16

A standing cylinder is simply an ex-
truded circle. Instead of using the
previous hand-sketch method of cre-
ating the CIP, here is a point-by-point
method that is more accurate.

This method requires the use of a grid
on the plan view. Select points along
the circumference, equally spaced is
more desirable, and create a grid us-
ing such points. Using the plan pro-
jection method, convert the circle and
the grid into a three-dimensional plan.
Once the plan is converted, simply
connect the corresponding points
within the grid to form the circle - now
an ellipse.

Project a second plan at a set height,
and repeat the same process for the
top of the cylinder.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 8: CYLINDER - ROLLED                                                                     17

A rolled cylinder is simply a cylin-
der standing on its side. The point-
to-point method used to construct a
standing cylinder will be used here.

Start by creating a grid over the ortho-
graphics. Translate this grid in three-
dimension ﬁrst to the front face of the
cylinder, therefore place this grid vir-
tually. Duplicate this grid for the rear
face of the cylinder. Connect the two
faces by their tangents and the cylin-
der is complete.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 8: BOX WITH SWINGING FLAPS                                                               18

This exercise is to use the concept of
circles in perspective to locate a point
(or object) along an arc, such as a
open door.

Orthographics must ﬁrst be construct-
ed, and the angle of the ﬂaps are de-
termined. An arc is drawn to indicate
the “swing” of the ﬂap. A grid is then
imposed to deﬁne the arc.

Simply draw the box and add the ﬂaps
on using the point-by-point method as
in the rolled cylinder exercise, except
here only a portion of the circle (the
arc) is necessary. Once the point for
the ﬂap is locate, repeat the process
to deﬁne the other end of the ﬂap and
connect the two.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 9: CONES - STANDING/TIPPED                                                               19

The cone is a similar form to the pyra-
mid. Instead of a square base, it has
a circular one. For a standing cone,
simply draft the base, a circle, in per-
spective and converge into a single
point at a certain height.

A tipped cone is much more complex.
To be able to draft in perspective ac-
curately the tipped surface - the circu-
lar base, the orthographics must be
constructed. Follow the steps for tip-
ping the side views of a pyramid.

First impose a grid on the perfectly
circular base of the standing cone.
Using the side views, translate this
grid onto the plan view. Note on the
true plan view, the circular base is an
ellipse due to the sloped orientation.

To construct the perspective, simply
convert the plan grid into three-di-
mension, and project the height using
the orthographics. Finally, connect all
the points for the CIP and converge
its tangents to the tip of the cone.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 9: DOME                                                                                   20

The dome is simply half a sphere,
and since a sphere is a perfect circle
in all perspective, a dome is easily a
perfect semi-circle.

Construct the orthographics for the
dome. Create a grid on both the plan
and side views, then translate the plan
grid into three-dimension. Once this
is completed, use translate the side
view grid into the perspective at the
diameter (or quadrant) of the circle.
Do this twice at 90 degrees apart, this
will deﬁne the main axes of the dome,
also the highest point, along its diam-
eter.

Once the two semi-CIP (arcs) are
drafted, simply use a compass and
connect to your best ability a perfect
arc that passes through all points - the
two vertices on the plan and the inter-
section of the two arcs. You will notice
that it is impossible for a single arc to
intersect with all these points. How-
ever, there should be two that come
very close. Simply converge the two
for a close ﬁt. This discrepancy is
due to the fact that this is a two-point
perspective, where the third (vertical)
vanishing axis is disregarded, thus
creating this minor distortion.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 10: INTERSECTING ROLLED CYLINDERS                                                        21

Intersecting two cylinders is an intro-
duction to more complex and com-
pound objects. For this exercise, two
rolled cylinders are used.

As with many of the exercises, the or-
thographics are crucial and essential
in order to construct the perspective
drawing. Here, the object must be
draw and their intersection properly
located, as desired, in plan and side
views. Follow the same steps for the
single rolled cylinder exercise and
place a grid on each individual cyl-
inders. It may be beneﬁcial for both
circles to share grid lines, however,
depending on the size differences, it
may be necessary to use a smaller
grid for the smaller circle.

The second and most important part
process is identifying the actual inter-
section of the cylinders, in this case -
the plan view. Carefully translate the
intersection points from the side and
front views to the plan view. Once
all the intersection points are estab-
lished, continue with the typical steps
and construct the perspective draw-
ing.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 10: COMPOUND FORM (PLAN PROJECTION)                                                    22

As an introduction to compound forms,
an object is designed to be drawn us-
ing the plan projection method. The
object simulates a vehicle, with a
dome as the main body and several
intersecting cylinders as the wheels.

As with previous exercises, the ortho-
graphics of the vehicle are drawn, and
grids are constructed over the circu-
lar forms. The plan is then translated
into three-dimension, and the height
is then projected to form the ﬁnal ob-
ject.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 11: COMPOUND FORM (3-D GRID)                                                            23

Another method of constructing per-
spective drawings is through the use
of a three-dimensional grid. The con-
cept is to create a grid in the ortho-
graphics, then directly translate this
grid in perspective, so the ﬁnal object
can be drawn by deﬁning location of
its individual component without the
use of the plan.

In the sample drawing, a simply race
car is constructed in the orthograph-
ics. A grid is imposed over the views
to deﬁne the location of each line and
shape. The grid is directly translated
into the perspective in three-dimen-
sion. Note the omittance of the plan
in three-dimension.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 11: 12-POINT ELLIPSE                                                                      24

This method of drawing an ellipse (CIP) is a short-
cut to the point-by-point method. Instead of having
to create a grid on the orthographic view, and hav-
ing to translate that grid in three-dimension, a grid
is directly created in perspective as guidelines for
the ellipse.

1) Divide the surface into quadrant by ﬁnding its
center
1                       2                      2) Divide each quadrant into more quadrants in the
same manner
3) Connect the diagonal lines between the outmost
4) Connect all the points at various intersections
as shown

Notice the ellipse is much more facetted than one
that would be constructed from the point-by-point
method, simply because this method provides much
fewer points for connection. Use this method only
as a guideline, sketch over with a smoother ellipse
by hand afterwards.

3                       4

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 12: REFLECTIONS                                                                        25

Reﬂection is simply the mirror image of an object on
a different surface. The following steps apply when
creating simply reﬂections on a surface that is par-
allel to the object and perpendicular to the ground.

1                  2   1) Establish the reﬂecting surface in relations to the
object
2) Locate the midpoint of the object and extend it
through the “mirror” to the vanishing point. Where
this line intersects with the mirror will deﬁne the
midway distance between the mirrored and actual
object
3) Extend the sides of the object to the same van-
ishing point. Draw diagonal lines from the corners
crossing through the intersecting point. Extend the
3                  4   diagonal lines to establish the corners of the mir-
rored object
4) Extend the top edges of the object into the mirror
and connect them with the base lines established in
step 3 and deﬁne the front face of the object
5) Repeat steps 3 and 4 for the rear face
6) Attach the two faces and the object is now re-
ﬂected

5                  6

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 12: REFLECTIONS                                                                          26

Setting up the objects correctly is key
to creating interesting reﬂections, they
should be fairly close to one another.

Sloped and angled surfaces are more
difﬁcult for constructing reﬂections. In
order to establish the correct reﬂec-
tions, orthographics of these objects
must ﬁrst be created. The purpose of
the orthographics is to help deﬁne the
perpendicular relationship between
the object and the mirror, without
them, it is impossible to ﬁnd the per-
pendicular in perspective.

Once the perpendicular is established,
it can be translated into the perspec-
tive drawing. Simply follow the same
steps as the simple reﬂections, using
the perpendicular line (instead of the
vanishing line) as the axis of which
the object is reﬂected.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005
EXERCISE 13: FINAL PROJECT                                                                         27

The ﬁnal project is a combination of all
the previous exercises. It is a small,
portable USB hard drive. The object
is a composition of many different el-
ements, including a dish (reversed
dome), a partial cone, a half-cylinder
and other rectilinear forms.

Many details are added to the object
as well to improve its appearance.
The edges are rounded to provide
smoothness and ﬂuidity. Parting lines
are drawn to establish some realism.
Slices (section lines) are added on
the object to better illustrate its form.
Lastly, a ray light, backlit shadow is
created.

Raymond Chan . IDS 116 . Perspective Drawing . Summer 2005

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