From 3c21556ef64541274968ddcd0931898cc58a1ef2 Mon Sep 17 00:00:00 2001
From: polyfloyd <floyd@polyfloyd.net>
Date: Sat, 19 May 2018 14:47:40 +0200
Subject: [PATCH] Add chebyshev.glsl

---
 chebyshev.glsl | 54 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 54 insertions(+)
 create mode 100644 chebyshev.glsl

diff --git a/chebyshev.glsl b/chebyshev.glsl
new file mode 100644
index 0000000..52fcff1
--- /dev/null
+++ b/chebyshev.glsl
@@ -0,0 +1,54 @@
+float chebyshev(float x, int n){
+	const int MAX_POWER = 16;
+	vec2 tvec = vec2( 1., x);
+	mat2 m = mat2 (0., -1., 1., 2.*x);
+	for( int i = 2; i < MAX_POWER; i += 1){
+		if( i > n ) return tvec.y;
+		tvec = m*tvec;
+	}
+	return tvec.y;
+}
+
+//https://github.com/hughsk/glsl-hsv2rgb/blob/master/index.glsl
+vec3 hsv2rgb(vec3 c) {
+	vec4 K = vec4(1.0, 2.0 / 3.0, 1.0 / 3.0, 3.0);
+	vec3 p = abs(fract(c.xxx + K.xyz) * 6.0 - K.www);
+	return c.z * mix(K.xxx, clamp(p - K.xxx, 0.0, 1.0), c.y);
+}
+
+void mainImage( out vec4 fragColor, in vec2 fragCoord )
+{
+	vec2 uv = fragCoord / max(iResolution.x, iResolution.y);
+	uv *= 2.5;
+	uv.x -= 1.2;
+	uv.y -= 0.5;
+
+	float timex = iTime * .21;
+	float tx = cos(timex)*chebyshev(uv.x, 2)  + sin(timex)* chebyshev(uv.x, 5) ;
+	float timey = iTime * 0.2;
+	float ty = cos(timey)*chebyshev(uv.y, 3) + sin(timey)* chebyshev(uv.y, 7) ;
+
+	float t2 = iTime * .5;
+	float csigma = cos(t2);
+	float s2sigma = 1. - csigma*csigma;
+	//next formula was taken from this paper
+	//http://boj.pntic.mec.es/~jcastine/Trabajos%20matematicos_archivos/cmj122-127.pdf
+	float b = tx*tx + ty*ty - 2.0*tx*ty*csigma + s2sigma;
+	float w = 3.*fwidth(b);
+	//float w = .2;
+
+	b *= 2.;
+	float bFloor = floor(b);
+	b = smoothstep(w,0.,abs(fract(b) -.5))/fwidth(b);
+
+	//b*= step(abs(uv.x), 1.);
+	//b*= step(abs(uv.y), 1.);
+
+	vec3 color = hsv2rgb(vec3(bFloor/10.+fract(iTime*0.1),1.,1.));
+
+	color *= b;
+
+	fragColor = vec4(color, 1.0);
+}
+
+// https://www.shadertoy.com/view/MtBBRG