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// -----------------------------------------------------------------------------
// Copyright (c) 2014, Nicolas P. Rougier. All Rights Reserved.
// Distributed under the (new) BSD License.
// -----------------------------------------------------------------------------
// --- ellipse
// Created by Inigo Quilez - iq/2013
// License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
float marker_ellipse(vec2 P, float size)
{
// Alternate version (approximation)
float a = 1.0;
float b = 2.0;
float r = 0.5*size;
float f = length( P*vec2(a,b) );
f = length( P*vec2(a,b) );
f = f*(f-r)/length( P*vec2(a*a,b*b) );
return f;
/*
vec2 ab = vec2(size/3.0, size/2.0);
vec2 p = abs( P );
if( p.x > p.y ){
p = p.yx;
ab = ab.yx;
}
float l = ab.y*ab.y - ab.x*ab.x;
float m = ab.x*p.x/l;
float n = ab.y*p.y/l;
float m2 = m*m;
float n2 = n*n;
float c = (m2 + n2 - 1.0)/3.0;
float c3 = c*c*c;
float q = c3 + m2*n2*2.0;
float d = c3 + m2*n2;
float g = m + m*n2;
float co;
if(d < 0.0)
{
float p = acos(q/c3)/3.0;
float s = cos(p);
float t = sin(p)*sqrt(3.0);
float rx = sqrt( -c*(s + t + 2.0) + m2 );
float ry = sqrt( -c*(s - t + 2.0) + m2 );
co = ( ry + sign(l)*rx + abs(g)/(rx*ry) - m)/2.0;
}
else
{
float h = 2.0*m*n*sqrt( d );
float s = sign(q+h)*pow( abs(q+h), 1.0/3.0 );
float u = sign(q-h)*pow( abs(q-h), 1.0/3.0 );
float rx = -s - u - c*4.0 + 2.0*m2;
float ry = (s - u)*sqrt(3.0);
float rm = sqrt( rx*rx + ry*ry );
float p = ry/sqrt(rm-rx);
co = (p + 2.0*g/rm - m)/2.0;
}
float si = sqrt(1.0 - co*co);
vec2 closestPoint = vec2(ab.x*co, ab.y*si);
return length(closestPoint - p ) * sign(p.y-closestPoint.y);
*/
}
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