INTERPOLATION

A linear interpolation between two values, A and B, based on X.
The data type returned will be the same as the two input values.
The result is calculated by (1-X)*A + X*B;
For best results, the mixing value, X should lie in the range [0,1].
refer to page 331 in the RenderMan Companion.

This function returns the linear interpolation between A and B at X.

This function returns a value picked from a curve by the float C.
The value returned will of the same data type as the knots, K.
The curve is generated by fitting an interpolatory spline to the knot inputs.
The basis for the spline calculation is indicated by the the input string B.
The default basis is "catmull-rom".  Bases "bezier", "bspline", "hermite"
and "linear" are also available.  Bases "bezier" and "hermite" require
more knots, 4n+3 and 4n+2 respectively as opposed to 2n+2.

This function returns a value picked from a curve by the float C.
The value returned will of the same data type as the knots, K.
The curve is generated by fitting an interpolatory spline to the knot inputs.
The basis for the spline calculation is indicated by the the input string B.
The default basis is "catmull-rom".  Bases "bezier", "bspline", "hermite"
and "linear" are also available.  Bases "bezier" and "hermite" require
more knots, 4n+3 and 4n+2 respectively as opposed to 2n+2.

This function returns is 0 if B < A.
This function returns is 1 if B >= A.

This function returns a clamped linear interpolation between A and B.

This function returns 0 if X < A; 1 if X >= B;
otherwise a smooth S-curve interpolation between 0 and 1.

This function returns a smoothed value between [0,1]
based on where the edge lies in [MID-FUZ,MID+FUZ].
MID is the median value of the edge.
FUZ is the width of the fuzzing.
EDG is the edge in need of fuzzing.

This function dampens the edge from 1 to 0.
BOT is the base value of the edge.
TOP is the top value of the edge.
FUZ is the width of the dampening.
EDG is the edge in need of dampening.

This function returns a smoothed depression.
FUZ is the width of the fuzzing.
EDG is the edge in need of fuzzing.

This function returns a smoothed value between [0,1]
based on where the edge lies in [LO-FUZ,HI+FUZ].
LO  is the lowest value of the edge.
HI  is the greatest value of the edge.
FUZ is the width of the fuzzing.
EDG is the edge in need of fuzzing.

This function returns a smoothed pulse.
WID is the width of the pulse.
FUZ is the width of the fuzzing.
EDG is the edge to be pulsed.

This function filters the EDG value over the area of THR,
using WID as the width and FLT as the filtering kernel.

This function filters the EDG value over the area between A and B,
using WID as the width and FLT as the filtering kernel.

This function returns a filter width.

Result is a width to ramp across to get smooth antialiasing.
This value is used in texture mapping as well.
EDG is the edge to be antialiased.
MIN is the minimum filter width.