1. Parametric Shapes & Lighting Jared Jackson Stanford - CS 348b June 6, 2003

2. - or - How I Went to Stanford Graduate School to Learn Basket Weaving

3. Shapes from Parametric Paths A parametric path in multiple dimensions requires only one variable Circle: u -> 0 to 1 x(u) = sin(2 pi u), y(u) = cos(2 pi u), z(u) = 0

4. Shapes from Parametric Paths Mapping a 2D path along the 3D path gives a 3D parametric shape For a torus, trace a circle along a parametric path This requires that we know the normal to the path

5. shapes/parametric.cc Create a shape using S-Expressions for –x, y, z –dx, dy, dz –Ex: sin (2 pi u) -> (sin (mult 2 (mult pi x))) Other parameters include: –Radius of the 2D shape –Twist angle of the 2D shape –Min and max of u –Number of samples to take along u

6. Parametric Torus Surface “parametric” “x” “mult 2 (cos (mult 2 (mult x pi)))” “y” “mult 2 (sin (mult 2 (mult x pi)))” “z” “0” “dx” “mult -1 (sin (mult 2 (mult x pi)))” “dy” “cos (mult 2 (mult x pi))” “dz” “0” “radius” “0.3” “samples” 20 “min” 0 “max” 1

7. Other Parameters: Shapes There are several built-in 2D shapes: –Circle (tube) –Square (box, disc) –Star –And more

8. Other Parameters: Complex Shapes Shapes can also be described as a 2D parametric path using S-Expressions “shape” “complex” “cx” “sub 1 (pow x 3)” “cy” “x” “csamples” 20

9. Other Parameters: Radius The radius is a scaling factor on the 2D shape that can also be specified as an S- Expression “radius” “0.2” “radius” “add 0.3 (mult 0.1 (cos (mult 2 (mult x pi))))”

10. Other Parameters: Twist The twist parameter rotates the 2D shape within its plane before mapping it along the path “twist” “cos (mult 2 (mult x pi))”

11. Basket Weaving x(u) = (r1) * cos(2 pi u) y(u) = 0.75 * u z(u) = (r1) * sin(2 pi u) radius(u) = 0.35

12. Parametric Lights Lights can also follow a 3D parametric path The sample points then act as point light sources Light intensity is divided across the number of sample points

13. Parametric Lights

14. A Final Image