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# Parametric Shapes Lighting Jared Jackson - PowerPoint PPT Presentation

Parametric Shapes & Lighting Jared Jackson Stanford - CS 348b June 6, 2003 - or - How I Went to Stanford Graduate School to Learn Basket Weaving Shapes from Parametric Paths A parametric path in multiple dimensions requires only one variable

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### Parametric Shapes & Lighting

Jared Jackson

Stanford - CS 348b

June 6, 2003

### - or -How I Went toStanford Graduate Schoolto Learn Basket Weaving

• 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

• 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

• 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

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

• There are several built-in 2D shapes:

• Circle (tube)

• Square (box, disc)

• Star

• And more

• 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

• 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))))”

• The twist parameter rotates the 2D shape within its plane before mapping it along the path

“twist” “cos (mult 2 (mult x pi))”

• x(u) = (r1) * cos(2 pi u)

• y(u) = 0.75 * u

• z(u) = (r1) * sin(2 pi u)

• radius(u) = 0.35

• 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