1. 3D modeling

2. Modeling and visualization Reality model Picture 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 V1XYZ V2 V3 V4 V5 V6 V7 V8 v1 v5 v2 v4 v6 v3 v7v8

10. Table of edges E1 V1V2 E2V2V3 E3V3V4 E4V4V1 E5V1V5 E6V2V6 E7V3V7 E8V4V8 E9V5V6 E10V6V7 E11V7V8 E12V8V5 v1 v5 v4v3 v7v8 e1 v2 e2 e3 e4 e5 e6 e7e8 e9 e10 e11 e12

11. Table of faces P1E1E2E3E4 P2E1E5E6E9 P3E2E6E7E10 P4E3E7E8E11 P5E4E8E5E12 P6E9E10E11E12 v5 e1 e2 e3 e4 e5 e7e8 e9 e11 e12 P1 e6 e10 P3 P4

12. Table of solids QP1P2P3P4 P5P6

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. 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} }