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Parametric Shapes & Lighting 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

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Parametric shapes lighting l.jpg

Parametric Shapes & Lighting

Jared Jackson

Stanford - CS 348b

June 6, 2003


Or how i went to stanford graduate school to learn basket weaving l.jpg

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


Shapes from parametric paths l.jpg

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 paths4 l.jpg

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


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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


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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


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Other Parameters: Shapes

  • There are several built-in 2D shapes:

    • Circle (tube)

    • Square (box, disc)

    • Star

    • And more


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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


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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))))”


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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))”


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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


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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


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Parametric Lights


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A Final Image


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