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
• Circle: u -> 0 to 1
x(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 SExpression
“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
Quic kT i me™ and a T IFF (Unc ompres s ed) dec ompres s or are needed t o s ee thi s pi c ture.
QuickTi me™ and a T IFF (Uncom pressed) decom pressor are needed to see t his pict ure.
Parametric Lights
A Final Image