utils: added circular shaping functions from flong (Equation of a Circle From 3 Points and Joining Two Lines with a Circular Arc Fillet still missing)

utilities/flong.glsl

@@ -265,3 +265,53 @@ float cubic_bezier_through(float x, vec2 a, vec2 b) {
   return clamp(y, 0., 1.);
 }
 // cubic bezier through points end
+
+// Circular shaping
+
+float circ_ease_in (float x){
+  return 1. - sqrt(1. - x*x);
+}
+
+float circ_ease_out (float x){
+  return sqrt(1. - pow(1. - x, 2.));
+}
+
+float double_circ_seat(float x, float a) {
+  a = clamp(a, 0., 1.); 
+
+  if (x<=a){
+    return sqrt(pow(a, 2.) - pow(x-a, 2.));
+  }
+  return 1. - sqrt(pow(1.-a, 2.) - pow(x-a, 2.));
+}
+
+float double_circ_sigmoid(float x, float a) {
+  a = clamp(a, 0., 1.);
+
+  if (x<=a){
+    return a - sqrt(pow(a, 2.) - pow(x, 2.));
+  }
+  return a + sqrt(pow(1.-a, 2.) - pow(x-1., 2.));
+}
+
+float double_ellip_seat(float x, vec2 ab) {
+  float e = 0.00001;
+  float a = clamp(ab.x, 0.+e, 1.+e);
+  float b = clamp(ab.y, 0., 1.);
+
+  if (x<=a){
+    return (b/a) * sqrt(pow(a, 2.) - pow(x-a, 2.));
+  }
+  return 1.-((1.-b)/(1.-a))*sqrt(pow(1.-a, 2.)-pow(x-a,2.));
+}
+
+float double_ellip_sigmoid(float x, vec2 ab) {
+  float e = 0.00001;
+  float a = clamp(ab.x, 0.+e, 1.+e);
+  float b = clamp(ab.y, 0., 1.);
+
+  if (x<=a){
+    return b * (1. - (sqrt(pow(a, 2.) - pow(x, 2.))/a));
+  }
+  return b+((1.-b)/(1.-a))*sqrt(pow(1.-a,2.)-pow(x-1.,2.));
+}