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

Parametric Shapes & Lighting

Jared Jackson

Stanford - CS 348b

June 6, 2003

- or -How I Went to

Stanford Graduate Schoolto Learn Basket Weaving

Shapes from Parametric Paths

• A parametric path in multiple dimensions requires only one variable

• Circle: u -> 0 to 1x(u) = sin(2 pi u), y(u) = cos(2 pi u), z(u) = 0

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

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

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

Other Parameters: Shapes

• There are several built-in 2D shapes:– Circle (tube)

– Square (box, disc)

– Star

– And more

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

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))))”

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))”

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

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

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

Parametric Lights

A Final Image