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)

7. Vector modeling • B-reprezentation • Primitive solids • 2 ½ D modeling • CSG modeling

8. B reprezentation (boundary)

9. Table of vertecies v1 v2 v4 v3 v5 v6 v8 v7

10. Table of edges e1 v1 v2 e4 e2 v4 e3 v3 e6 e5 e8 e7 v5 e9 e12 v8 v7 e10 e11

11. Table of faces e1 e4 P1 e2 e3 P3 e6 e5 e8 P4 e7 v5 e9 e12 e10 e11

12. Table of solids

13. Primitive solids modeling Box Two oposite vertecies Or Two oposite vertecies of the base and the height

14. Primitive solids in AutoCAD • Box • Sphere • Cylinder • Cone • Wedge • Torus • ….

15. 2 ½ D modeling • Modeling of 3D solids by transformations of 2D objects • Move/Extrude • Rotate/Revolve • …… i.e. moving along a curve

16. Extrude • Rectangle → Box • Circle → Cylinder

17. Revolve • Rectangle → Cylinder • Triangle → Cone • Circle → Sphere / Torus

18. Computer Solid Geometry (CSG) modeling • Set operation • Union • Intersection • Subtract / Erase • CSG tree

19. CSG tree Set operations Resulting solid Primitive solids

20. CSG tree subtract{ union{ box{[0,0,0][4,4,1]} cylinder{[4,2,0],[4,2,1],1} } cylinder{[3,3,0][3,3,5],0.5} }