Programming Art

A Lunch and Learn for FreshBooks, April 2020

RE: Procedural Texturing in Computer Graphics

Reference

L1distanceV(P0, P1)
    Manhattan distance between two vectors (2d or 3d)

L2distanceV(P0, P1)
    Euclidean distance between two vectors (2d or 3d)

addV(Pa, Pb)
    Returns a vector whose components are the sum of the components from the inputs

bell(x)
    Smooth bell, value zero for input 0 or 1, max value at input = 0.5

bellV(P)
    Smooth bell, value zero for input 0 or 1, max value at input = 0.5; applied to each component of a vector

clamp(x)
    Given a value, returns zero if the value<0, one if value>1 otherwise the value itself

clampV(Pa, Pb, x)
    Restricts each component of a vector to range(0,1)

fractal(x, fn, scale, octaves=4, lac=1.7, dim=0.5882352941176471)
    "Given a scalar value, a function of a scalar value, and the scale of the detail;
    and optionally, a number of octaves, lacunarity (float>1) and dimension(float<1),
    returns a fractal summation of the signal

fractalV(P, fn, scale, octaves=4, lac=1.7, dim=0.5882352941176471)
    "Given a position, a multi-dimensional noise function, and the scale of the detail;
    and optionally, a number of octaves, lacunarity (float>1) and dimension(float<1),
    returns a fractal summation of the signal

mix(a, b, x)
    Linear mix: returns a for x=0, b for x=1 or linear blend for x in the range(0,1)

mixV(Pa, Pb, x)
    Linear blend of each component of input vectors

mulV(Pa, Pb)
    Returns a vector whose components are the product of the components from the inputs

simnoise2d(P)
    Returns a 2d motion vector; each component in range(-1,1)

simnoise3d(P)
    Returns a 3d motion vector; each component in range(-1,1)

smoothstep(x)
    C4-Smooth transition from zero to one, given an input in the range(0,1)

smoothstepCubic(x)
    C2-Smooth transition from zero to one, given an input in the range(0,1)

smoothstepCubicV(P)
    C2-Smooth transition from zero to one, applied to each component of a vector

smoothstepV(P)
    C4-Smooth transition from zero to one, applied to each component of a vector

spline(x, *args)
    Interpolates the arguments, varying across them as input varies from zero to one

subV(Pa, Pb)
    Returns a vector whose components are the difference of the components from the inputs

tilenoise2d(P)
    Constant value returned for each lattice; return triple in range +/- 1

tilenoise3d(C)
    Constant value returned for each lattice; return triple in range +/- 1

valuenoise1d(x, seed=0)
    Smooth blended value returned for each lattice; returns range +/- 1, 3d tuple

valuenoise2d(P)
    Smooth blended value returned for each lattice; returns range +/- 1, 3d tuple

valuenoise3d(P)
    Smooth blended value returned for each lattice; returns range +/- 1, 3d tuple

voronoinoise2d(P, distancefn=L2distanceV)
    Returns distance (scalar), position (2d)

voronoinoise3d(P, distancefn=L2distanceV)
    Returns distance (scalar), position (3d)