Procedural Texture Functions

Lists and Functions

The following functions are available for use in the creation of procedural textures. These are based on the code provided in the following book:

Texturing and Modeling A Procedural Approach by Kenton Musgrave, Darwyn Peachey, Ken Perlin, Steven Worley (Cambridge, MA: Academic Press, Inc., 1994). ISBN: 0-12-228760-6.

Consult this book for additional insight into the use of these functions.

boxstep()

boxstep() - Returns 0 if x is less than a, a linear interpolation between 0 and 1 if x is greater than or equal to a and less than or equal to b, and 1 if x is greater than b. This function is a smoother version of step() using a linear ramp. The function boxstep() is defined like this:

float boxstep(float a, float b, float x) {

return clamp((x-a)/(b-a),0.0f, 1.0f);

}

$image\boxstep_wmf.gif$

The boxstep() function.

For comparison, note that step() returns values of 0 when x is less than a and 1 when x is greater than or equal to a. This function is not part of the SDK but step() is defined like this:

float step(float a, float x) {

return (float)(x >= a);

}

$image\step_wmf.gif$

The step() function.

Parameters:

float a - The limit for the x value where the function will return 0.
float b - The limit for the x value where the function will return 1.
float x - A floating point value.

smoothstep()

smoothstep() - This function is similar to step(), but instead of a sharp transition from 0 to 1 at a specified threshold, it makes a gradual transition from 0 to 1 beginning at threshold a and ending at threshold b. To do this, this function uses a cubic function whose slope is 0 at a and b and whose value is 0 at a and 1 at b. This function thus provides a still smoother version of step() using a cubic spline. The smoothstep() function is used (instead of step()) in many procedural textures because sharp transitions often result in artifacts.

$image\smooth_wmf.gif$

The smoothstep() function.

Parameters:

float a - The limit for the x value where the function will return 0.
float b - The limit for the x value where the function will return 1.
float x - A floating point value.

clamp()

clamp() - returns a when x is less than a, the value of x when x is between a and b, and the value b when x is greater than b. The function clamp() is defined as follows:

float clamp( float x, float a, float b) {

return (x < a ? a : (x > b ? b : x));

}

$image\clamp_wmf.gif$

The clamp() function.

Parameters:

float x - A floating point value.
float a - A floating point value.
float b - A floating point value.

threshold()

threshold() - Returns 0 if x is less than a, 1 if x is greater than b, otherwise it returns x.

bias()

bias() - This function performs a mapping across the unit interval [0, 1] where the result is within the unit interval. That is, if b is within the interval 0 to 1, the result of bias() is within the interval 0 to 1. This function is defined such that bias(a, 0.5)=a. The function looks like:

float bias(float a, float b) {

return (float)pow(a, log(b) / log(0.5f));

}

$image\bias_wmf.gif$

The bias() function.

gain()

gain() - This function performs a mapping across the unit interval [0, 1] where the result is within the unit interval. That is, if b is within the interval 0 to 1, the result of gain() is within the interval 0 to 1. This function is defined such that gain(a, 0.5)=a. Above and below 0.5, this function consists of two scaled down bias() curves forming an S-shaped curve. The function looks like:

float gain(float a, float b)

{

float p = (float)log(1.0f - b) / (float)log(0.5f);

if (a < .001f)

return 0.f;

else if (a > .999f)

return 1.0f;

if (a < 0.5f)

return (float)pow(2 * a, p) / 2;

else

return 1.0f - (float)pow(2.0 * (1. - a), (double)p) / 2;

}

$image\gain_wmf.gif$

The gain() function.

The following are noise functions over 1, 2, 3, 4 and dimensions. They return values in the range [-1,1].

noise1() - An approximation of white noise blurred to dampen frequencies beyond some value.
noise2() - An approximation of white noise blurred to dampen frequencies beyond some value in two dimensions.
noise3() - A noise function in three dimensions implemented by a pseudo-random tricubic spline. This function is an approximation of white noise blurred to dampen frequencies beyond some value.
noise4() - This function is an approximation of white noise blurred to dampen frequencies beyond some value in three dimensions, and time.
noise3ds() - A noise function in three dimensions implemented by a pseudo-random tricubic spline. This is the same as noise3() scaled up by factor of 1.65 and clamped to -1,+1. The macro NOISE can be used to map the value returned from the noise3DS() function into interval [0,1].
turbulence() - This turbulence function is a simple fractal generating loop built on top of the noise function. It is used to make marble, clouds, explosions, etc. It returns a value in the range [0, 1].
Perm() - Takes the low 9 bits of the an input value and returns a number in that range (0-512) .
fBm1() - A fractional Brownian motion fractal (or fBm for short) that returns a floating point value. This version of the fBm is said to be "homogeneous" (the same everywhere) and "isotropic" (the same in all directions). There are versions of this function that accept an input floating point, Point2, and Point3 value.
spline() - a one-dimensional Catmull-Rom interpolating spline through a set of knot values. The spline() function Used to map a number into another number. The parameter of the spline is a floating point value. If x is 0, the result is the second knot value. If x is 1, the result is the final knot value. For values between 0 and 1, the value interpolates smoothly between the values of the knots from the second knot to the second to last knot. The first and last knot values determine the derivatives of the spline at the endpoint.

$image\spline_wmf.gif$

The spline () function.

color_spline() - A variant of the spline() function for mapping colors.
FLOOR() - A fast version of the standard C function floor(). It returns a floating-point value representing the largest integer that is less than or equal to x.
frac() - Returns the fraction (non-integer) part of the value passed. This is defined as x - (float)FLOOR(x).
fmax() - Returns the larger of two values (returns the second value in the case of equality).
fmin() - Returns x if it is less than y; otherwise it returns y.
AComp() - Performs an alpha-composite of one color (ctop) on top of another (cbot), assuming pre-multiplied alpha.

Cellular Texture Functions

CellFunction() - This is the noise function used by the 3ds Max Cellular texture. The idea is that there is a set of cells randomly distributed through space. This function returns the distances to the closest cells. Developers using this function should refer to: A Cellular Basis Function by Steven Worley, and published in the SIGGRAPH 1996 Conference Procedings.
FractalCellFunction() - A fractal version of CellFunction(). It has additional parameter for iterations and lacunariy.
RandFromCellID() - Returns a random number in the range 0.0 to 1.0 based on a cell identifier.

Procedural Texture Functions

boxstep()

smoothstep()

clamp()

threshold()

bias()

gain()

Cellular Texture Functions

See Also: