Intro
As described in this article, checkerboard patterns can be filterable analytically, which makes them a great candiadate for quality procedural texturing. Many other patterns accept simple analytic integrals and can therefore be filterable (antialiased) analytically. This article is a short (for now) collection of them. Generalizations are pretty easy, for example getting a variery of dot/line patterns is straightforward, so I have only documented the basic ones for you to combine on your one:
The List
Box filtered checkerboardfloat checkers( in vec2 p, in vec2 dpdx, in vec2 dpdy )
{
vec2 w = max(abs(dpdx), abs(dpdy));
vec2 i = 2.0*(abs(fract((p-0.5*w)*0.5)-0.5)-
abs(fract((p+0.5*w)*0.5)-0.5))/w;
return 0.5 - 0.5*i.x*i.y;
}
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Box filtered gridfloat grid( in vec2 p, in vec2 dpdx, in vec2 dpdy )
{
const float N = 10.0; // grid ratio
vec2 w = max(abs(dpdx), abs(dpdy));
vec2 a = p + 0.5*w;
vec2 b = p - 0.5*w;
vec2 i = (floor(a)+min(fract(a)*N,1.0)-
floor(b)-min(fract(b)*N,1.0))/(N*w);
return (1.0-i.x)*(1.0-i.y);
}
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Box filtered squaresfloat squaresid( in vec2 p, in vec2 dpdx, in vec2 dpdy )
{
const float N = 3.0;
vec2 w = max(abs(dpdx), abs(dpdy));
vec2 a = p + 0.5*w;
vec2 b = p - 0.5*w;
vec2 i = (floor(a)+min(fract(a)*N,1.0)-
floor(b)-min(fract(b)*N,1.0))/(N*w);
return 1.0-i.x*i.y;
}
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Box filtered crossesfloat crosses( in vec2 p, in vec2 dpdx, in vec2 dpdy )
{
const float N = 3.0;
vec2 w = max(abs(dpdx), abs(dpdy));
vec2 a = p + 0.5*w;
vec2 b = p - 0.5*w;
vec2 i = (floor(a)+min(fract(a)*N,1.0)-
floor(b)-min(fract(b)*N,1.0))/(N*w);
return 1.0-i.x-i.y+2.0*i.x*i.y;
}
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