website articles
filterable procedurals

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 checkerboard (https://www.shadertoy.com/view/XlcSz2)

float filteredCheckers( 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; }
Box filtered grid (https://www.shadertoy.com/view/XtBfzz)

float filteredGrid( in vec2 p, in vec2 dpdx, in vec2 dpdy ) { const float N = 10.0; 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)*(1.0-i.y); }
Box filtered squares

float filteredSquares( 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; }
Box filtered crosses

float filteredCrosses( 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; }
Box filtered XOR pattern (https://www.shadertoy.com/view/tdBXRW)

float filteredXor( in vec2 p, in vec2 dpdx, in vec2 dpdy ) { float xor = 0.0; for( int i=0; i<8; i++ ) { vec2 w = max(abs(dpdx), abs(dpdy)) + 0.01; vec2 f = 2.0*(abs(fract((p-0.5*w)/2.0)-0.5)- abs(fract((p+0.5*w)/2.0)-0.5))/w; xor += 0.5 - 0.5*f.x*f.y; dpdx *= 0.5; dpdy *= 0.5; p *= 0.5; xor *= 0.5; } return xor; }