1. 3D Object Representations graphics scenes contain solid geometric objects trees, flowers, clouds, rocks, water representations surface ↔interior models procedural models physically based models boundary representations (B-reps) space-partitioning representations

2. Polygon Surfaces (1) set of surface polygons enclose object interior = Boundary Representation (“B- rep”) wireframe representation of a cylinder with back (hidden) lines removed

3. polygon tables (B-rep lists) geometric and attribute tables vertex, edge, polygon tables consistency, completeness checks

4. Polygon Surfaces: Data Structure

5. Polygon Surfaces: Plane Equation Ax+ By+ Cz+ D = 0 Cartesian coefficients A,B,C,D normal (A,B,C) distance to origin D

6. Polygon Meshes efficient data structures for tiled surfaces triangle strip n-2 triangles for n vertices

7. quadrilateral mesh (n-1)x(m-1) quadrilaterals

8. Curved Lines and Surfaces defined by mathematical functions (implicit, explicit, parametrically) set of data points (surface fitting) tesselation to get polygon mesh aproximation triangles quadrilaterals... (planar?!)

9. Quadric Surfaces defined by second degree equations (quadrics) – sphere – ellipsoid – torus – paraboloid – hyperboloid

10. Quadric Surfaces: Sphere implicit parametric φ φ θ π θ π φ θ π φ π sin cos sin, - cos cos, - /2 /2 z r y r x r = = ≤ ≤ x2 + y2 + z2 = r2