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Tweak stroke frag

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This commit is contained in:
Grant Sanderson 2023-01-20 10:09:58 -08:00
parent 7df6efb55f
commit b7ea24f9ea
1 changed files with 12 additions and 10 deletions
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14
manimlib/shaders/quadratic_bezier_stroke/frag.glsl
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@ -10,7 +10,7 @@ in float is_linear;
out vec4 frag_color; out vec4 frag_color;
const float QUICK_DIST_WIDTH = 0.2; const float QUICK_DIST_WIDTH = 0.4;
float dist_to_curve(){ float dist_to_curve(){
// In the linear case, the curve will have // In the linear case, the curve will have
@ -20,13 +20,15 @@ float dist_to_curve(){
// Returns distance from uv_coords to the curve v = u^2 // Returns distance from uv_coords to the curve v = u^2
float x0 = uv_coords.x; float x0 = uv_coords.x;
float y0 = uv_coords.y; float y0 = uv_coords.y;
if(uv_stroke_width < QUICK_DIST_WIDTH){
// This is a quick approximation for computing // This is a quick approximation for computing
// the distance to the curve. // the distance to the curve.
// Evaluate F(x, y) = y - x^2 // Evaluate F(x, y) = y - x^2
// divide by its gradient's magnitude // divide by its gradient's magnitude
return abs((y0 - x0 * x0) / sqrt(1 + 4 * x0 * x0)); float Fxy = y0 - x0 * x0;
} float grad_sq = 1 + 4 * x0 * x0;
float approx_dist = abs(Fxy) / sqrt(grad_sq);
if(approx_dist < QUICK_DIST_WIDTH) return approx_dist;
// Otherwise, solve for the minimal distance. // Otherwise, solve for the minimal distance.
// The distance squared between (x0, y0) and a point (x, x^2) looks like // The distance squared between (x0, y0) and a point (x, x^2) looks like
// //
@ -37,7 +39,7 @@ float dist_to_curve(){
// x^3 + (0.5 - y0) * x - 0.5 * x0 = 0 // x^3 + (0.5 - y0) * x - 0.5 * x0 = 0
// //
// Use two rounds of Newton's method // Use two rounds of Newton's method
float x = x0; float x = x0 + 2 * x0 * Fxy / grad_sq; // Seed with a step along the gradient vector
float p = (0.5 - y0); float p = (0.5 - y0);
float q = -0.5 * x0; float q = -0.5 * x0;
for(int i = 0; i < 2; i++){ for(int i = 0; i < 2; i++){
@ -45,7 +47,7 @@ float dist_to_curve(){
float dfx = 3 * x * x + p; float dfx = 3 * x * x + p;
x = x - fx / dfx; x = x - fx / dfx;
} }
return distance(vec2(x0, y0), vec2(x, x * x)); return distance(uv_coords, vec2(x, x * x));
} }