Geometric Elements by peteronline125

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									3D Spatial Principles and
 Modeling Techniques
Geometric Elements

3D Entities
 – Right cone?
     Axis perpendicular to base
 – Oblique cone?
     Axis not perpendicular to base
 – Truncated cone or frustum of a
     Tip of cone cut off
3D: Cones
    Geometric Elements
3D Entities
Defining Cylinders
– A single-curved ruled surface formed by a
  vertical, finite, straight-line element
  (generatrix) revolved parallel to a vertical or
  oblique axis directrix and tangent to a
  horizontal circular or elliptical directrix.
– Right cylinder
     Axis perpendicular to base
– Oblique cylinder
     Axis not perpendicular to base
– If base is circle, cylinder is circular. If base is
  elliptical, cylinder is elliptical
3D: Cylinders
Geometric Elements
 3D Entities
 Defining Polyhedra
  – Polyhedron: a symmetrical or
    asymmetrical 3-D geometric
    surface or solid object with
    multiple polygonal sides. The
    sides are plane ruled surfaces.
  – Regular polyhedra
      Have regular polygons for faces
      tetrahedron, hexahedron,
      octahedron, dodecahedron,
3D: Polyhedra
          Geometric Elements
   n., pl. -drons or -dra (-drə).
   A polyhedron with four faces.
   [Late Greek tetraedron, from Greek, neuter of tetraedros, four-faced :
      tetra-, tetra- + hedrā, face of a geometric solid.]
   Etymology: New Latin, from Late Greek tetraedron, neuter of tetraedros having
      four faces, from Greek tetra- + hedra seat, face
    Translations for: Tetrahedron
Nederlands (Dutch) viervlak
Français (French) tétraèdre
Deutsch (German) Tetraeder (Vierflächner, dreiseitige Pyramide)
Ελληνική (Greek) τετράεδρο
Italiano (Italian) tetraedro
Português (Portuguese) tetraedro (m)
Русский (Russian) тетраэдр, четырехгранник, (воен.) пирамидальный
    противотанковый надолбник
Español (Spanish) tetraedro
Svenska (Swedish) tetraeder (geom.)
中国话 (Simplified Chinese) 四面体
中國話 (Traditional Chinese) 四面體
Geometric Elements
 3D Entities
 Defining Prisms
 – Polygonal prism
     Polyhedron with two equal parallel faces,
     called bases, and lateral faces that are
     Right or oblique
 – Pyramid
     Polyhedron that has a polygon for a base
     and lateral faces that have a common
     intersection point called a vertex.
     Right, oblique, or truncated(frustum)
3D: Prisms
3D: Pyramids
3D: Math!
3D: Math!
             Cool Stuff
        Why 3D?

3D is Reality
3D is Easier to Understand
3D is More Fun
    3D Models

Three Types of 3D
Wireframe Models
Vertices (Points)
Edges (Lines, Arcs,
No Surface Information
No Volume Information
Wireframe Models

–Easy to Construct
–Visualization Difficulties
–No Data
   Surface Modeling
Defines Surface Features as
Well as Edges
Development Driven by
Shipping, Automotive,
Aerospace Industries
Highly Mathematical;
‘Control Point’ Concept
    Solid Modeling
Defines Volumetric Data as
Well as Surfaces, Edges
‘Real World’ Design - Used
by All Industries
Provides Added Value in
Concurrent Engineering
–Smart Models
         Solid Primitives
Basic Geometric Forms (Additive)
– Cube, Cylinder, Wedge, etc.
– Can Be Combined to Create Complex
– Simple and Fast for Computer to
 Process and Display
– Limited Flexibility in Design (e.g.:
 impossible to make a hole)
       Solid Modeling

CSG - Constructive Solid
–Boolean Operations
–Makes Primitives More Useful
        Solid Modeling
B-rep : Boundary Representation
– Object Surfaces Used to Define the
  Solid Model
– Surfaces Have ‘Inside’ & ‘Outside’
– Display of Curved Surfaces can be a
  Problem – slow system
   Mathematically Intense
   Solution: Faceted Representation
         Solid Modeling
Hybrid Modelers- combine CSG & BREP
– CSG type commands – easier to model
– BREP output – easier to display to screen
– Most modelers store data in both
– Support both Boolean operations and
  complex surfaces as modeling tools to
  make solids
– Exact precision may be lost if both
  structures are utilized, as data is moved
  from one to the other
        Solid Modeling

Constraint-based Modeling
– Relates geometry together/modifiable
– Changes update throughout model
– Mating parts can be associated
Advantage: Design Specifications
Change Often – Allows for
Goal: Capture Designer’s Intent –
    Solid Modeling

Building the Features
–Basic Sweep (protrusion)
–Revolved Sweep
–Advanced Sweep
   Sweep along path(s)
        Solid Modeling
Design Intent
and Constraints
      Solid Modeling

Boolean Operations

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