1. Parametric/Implicit Forms
Dr. Scott Schaefer

2. Implicit Curves/Surfaces

3. Implicit Curves/Surfaces

4. Implicit Curves/Surfaces

5. Simple Implicit Surfaces
Spheres
Planes
Cylinders
Cones
Tori

6. Implicit Curves/Surfaces
Advantages
Easy to determine inside/outside
Easy to determine if a point is on the surface
Disadvantages
Hard to generate points on the surface

7. Parametric Curves/Surfaces
Geri’s Game Copyright Pixar

8. Parametric Curves/Surfaces1 2 3 4 5 6 -1
-0.5
0.5

9. Parametric Curves/Surfaces1 2 3 4 5 6 -1
-0.5
0.5

10. Parametric Curves/Surfaces

11. Parametric Surfaces

12. Piecewise Functions -2 -1 1 2
0.2
0.4
0.6
0.8

13. Piecewise Functions -2 -1 1 2
0.2
0.4
0.6
0.8

14. Piecewise Functions -2 -1 1 2
0.2
0.4
0.6
0.8

15. Piecewise Functions -2 -1 1 2
0.2
0.4
0.6
0.8 -2 -1 1 2
0.5
1.5
2.5 3

16. Piecewise Functions -2 -1 1 2
0.2
0.4
0.6
0.8 -2 -1 1 2
0.5
1.5
2.5 3

17. Parametric Curves/Surfaces
Advantages
Easy to generate points on the curve/surface
Separates x/y/z components
Disadvantages
Hard to determine inside/outside
Hard to determine if a point is on the curve/surface