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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

Parametric Shapes & Lighting

Jared Jackson

Stanford - CS 348b

June 6, 2003

shapes from parametric paths
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
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
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
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
Other Parameters: Shapes
  • There are several built-in 2D shapes:
    • Circle (tube)
    • Square (box, disc)
    • Star
    • And more
other parameters complex shapes
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
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
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
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
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