3D modeling

1
3D modeling
2
Modeling and visualization
Picture
model
Reality
modeling
Visualization
3
3D modeling

• Grid (voxel)
• Vector

4
Voxel modeling
0 not in the solid 1 in the solid
5
Quadrant tree (4-tree, QuadTree)
6
Octant tree (8-tree, OcTree)
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Vector modeling

• B-reprezentation
• Primitive solids
• 2 ½ D modeling
• CSG modeling

8
B reprezentation (boundary)
9
Table of vertecies
V1 X Y Z
V2
V3
V4
V5
V6
V7
V8
v1
v2
v4
v3
v5
v6
v7
v8
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Table of edges
E1 V1 V2
E2 V2 V3
E3 V3 V4
E4 V4 V1
E5 V1 V5
E6 V2 V6
E7 V3 V7
E8 V4 V8
E9 V5 V6
E10 V6 V7
E11 V7 V8
E12 V8 V5
e1
v1
v2
e4
e2
v4
v3
e3
e6
e5
e7
e8
v5
e9
e12
v7
v8
e10
e11
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Table of faces
P1 E1E2E3E4
P2 E1E5E6E9
P3 E2E6E7E10
P4 E3E7E8E11
P5 E4E8E5E12
P6 E9E10E11E12
e1
e4
e2
P1
e3
P3
e6
e5
e7
e8
P4
v5
e9
e12
e10
e11
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Table of solids
Q P1P2P3P4P5P6
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Primitive solids modeling
Box Two oposite vertecies Or Two oposite
vertecies of the base and the height
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Primitive solids in AutoCAD

• Box
• Sphere
• Cylinder
• Cone
• Wedge
• Torus
• .

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2 ½ D modeling

• Modeling of 3D solids by transformations of 2D
  objects
• Move/Extrude
• Rotate/Revolve
• i.e. moving along a curve

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Extrude

• Rectangle ? Box
• Circle ? Cylinder

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Revolve

• Rectangle ? Cylinder
• Triangle ? Cone
• Circle ? Sphere / Torus

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Computer Solid Geometry (CSG) modeling

• Set operation
• Union
• Intersection
• Subtract / Erase
• CSG tree

19
CSG tree
Set operations
Resulting solid
Primitive solids
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CSG tree
subtract union
box0,0,04,4,1
cylinder4,2,0,4,2,1,1
cylinder3,3,03,3,5,0.5