The RenderMan Interface - Paul Bourke

step returns 0 if value is less than min; otherwise it returns 1. smoothstep returns 0
if value is less than min, 1 if value is greater than or equal to max, and performs a
smooth Hermite interpolation between 0 and 1 in the interval min to max.
float filterstep ( float edge, s1; ...parameterlist...)
float filterstep ( float edge, s1, s2; ...parameterlist...)
This function provides an analytically antialiased step function. In its two argument
form, it takes parameters identical to step, but returns a result which is filtered over
the area of the surface element being shaded. If the optional s2 parameter is provided,
the step function is filtered in the range between the two values. This lowpass
filtering is similar to that done for texture maps (for reference, see Section 15.7,
Texture Mapping Functions). The parameterlist provides control over the filter function,
and may include the following parameters: ”width” (aka ”swidth”), the amount to
“overfilter” is s; ”filter”, the name of the filter kernel to apply. The filter may be any
of the following: ”box”, ”triangle”, ”catmull-rom”, or ”gaussian”. The default filter is
”catmull-rom”.
float spline ( [string basis;] float value; float f1, f2, ..., fn, fn1 )
float spline ( [string basis;] float value; float fvals[] )
color spline ( [string basis;] float value; color c1, c2, ..., cn, cn1 )
color spline ( [string basis;] float value; color cvals[] )
point spline ( [string basis;] float value; point p1, p2, ..., pn, pn1 )
point spline ( [string basis;] float value; point pvals[] )
vector spline ( [string basis;] float value; vector v1, v2, ..., vn, vn1 )
vector spline ( [string basis;] float value; vector vvals[] )
spline fits a spline to the control points given. At least four control points must always
be given. If value equals 0, f2 (or c2, p2, v2) is returned; if value equals 1, fn (or cn,
pn, vn) is returned. The type of the result depends on the type of the arguments.
If the first argument to spline is a string, it is interpreted as the name of a cubic spline
basis function. The basis may be any one of ”catmull-rom”, ”bezier”, ”bspline”, ”hermite”,
or ”linear”. If the optional basis name is not supplied, ”catmull-rom” is assumed,
resulting in the control points being interpolated by a Catmull-Rom spline. In the
case of Bezier and Hermite spline bases, the number of spline knots must be 4n+3
and 4n+2, respectively. In the case of linear spline basis, the first and last knot are
unused, but are nonetheless required to maintain consistency with the cubic bases.
For all spline types, an array of values may be used instead of a list of values to
specify the control points of a spline.
float Du ( float p ), Dv ( float p ), Deriv ( float num; float den )
color Du ( color p ), Dv ( color p ), Deriv ( color num; float den )
vector Du ( point p ), Dv ( point p ), Deriv ( point num; float den )
vector Du ( vector p ), Dv ( vector p ), Deriv ( vector num; float den )
These functions compute the derivatives of their arguments. The type returned depends
on the type of the first argument. Du and Dv compute the derivatives in the
u and v directions, respectively. Deriv computes the derivative of the first argument
with respect to the second argument.
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