1. DEFINING OBJECTS - 3D REPRESENTATIONS Surface representations Polygon tables 3D curves and curved surfaces Sweep representations Constructive solid geometry Octrees

2. Two classes of representations Surface Solid

3. Surface representations Polygon surfaces

4. Surface representations Object triangulation

5. Succession of models WireframeSurface patch

6. Surface patch Surface shading

7. Surface representation Surface Vertex Edge

8. Vertices

9. Wire-frame

10. Surface V1 V2 V3 V4 V5 V6V7 V8 V2 V1 V2 V3 V4 V5 V6V7 V8 V2

11. Vertex table

12. Define vertex table (vertices and edges) 2468 2 4 6 8 X Y Z 2 V1 V2 V3 V4 V5 V6 V7V8

13. Consistency checking every vertex is listed as an endpoint of at least two lines every polygon is closed each polygon has at least one shared edge if edge table contains pointers to polygons

14. Hierarchical definitions –interaction: groups of primitives can be interactively manipulated together, irrespective of a method of construction. –storage efficiency: definition of repeated symbol needs to be stored only once –common visual properties: groups of primitives can be given the same attributes, for example colour, transparency, visibility etc. –common transformation: groups of primitives can be all transformed together (for example rotated)

16. Advanced representations for curves and curved surfaces (3D) parametric equations Bézier curves and surfaces splines and spline surfaces B-splines ß-splines fractal surfaces

17. Advanced representations for solids Sweep representations Constructive Solid Geometry (CSG) Octrees

18. Sweep representations

20. Constructive solid geometry A B A - B A  B Volume = set of points

21. Octrees 01 23 0123 0123 0123 01 23

22. 0 1 2 3 4 5 6 7

23. Define vertex table (vertices and edges) 2468 2 4 6 8 X Y Z 2 V1 V2 V3 V4 V5 V6 V7V8 V11 V12 V13 V14 V15V16 V17V18 V9 V19 V20 V10