Parametric/Implicit Forms Dr. Scott Schaefer

Implicit Curves/Surfaces

Implicit Curves/Surfaces

Implicit Curves/Surfaces

Simple Implicit Surfaces Spheres Planes Cylinders Cones Tori

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

Parametric Curves/Surfaces Geri’s Game Copyright Pixar

Parametric Curves/Surfaces 1 2 3 4 5 6 -1 -0.5 0.5

Parametric Curves/Surfaces 1 2 3 4 5 6 -1 -0.5 0.5

Parametric Curves/Surfaces

Parametric Surfaces

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

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

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

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

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

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