From b7ea24f9ea6d795d9c1d467e943988a5c6c98fec Mon Sep 17 00:00:00 2001
From: Grant Sanderson <grant@3blue1brown.com>
Date: Fri, 20 Jan 2023 10:09:58 -0800
Subject: [PATCH] Tweak stroke frag

---
 .../shaders/quadratic_bezier_stroke/frag.glsl | 22 ++++++++++---------
 1 file changed, 12 insertions(+), 10 deletions(-)

diff --git a/manimlib/shaders/quadratic_bezier_stroke/frag.glsl b/manimlib/shaders/quadratic_bezier_stroke/frag.glsl
index 54319965..2ad580e8 100644
--- a/manimlib/shaders/quadratic_bezier_stroke/frag.glsl
+++ b/manimlib/shaders/quadratic_bezier_stroke/frag.glsl
@@ -10,7 +10,7 @@ in float is_linear;
 
 out vec4 frag_color;
 
-const float QUICK_DIST_WIDTH = 0.2;
+const float QUICK_DIST_WIDTH = 0.4;
 
 float dist_to_curve(){
     // 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
     float x0 = uv_coords.x;
     float y0 = uv_coords.y;
-    if(uv_stroke_width < QUICK_DIST_WIDTH){
-        // This is a quick approximation for computing
-        // the distance to the curve.
-        // Evaluate F(x, y) = y - x^2
-        // divide by its gradient's magnitude
-        return abs((y0 - x0 * x0) / sqrt(1 + 4 * x0 * x0));
-    }
+    // This is a quick approximation for computing
+    // the distance to the curve.
+    // Evaluate F(x, y) = y - x^2
+    // divide by its gradient's magnitude
+    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.
     // 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
     //
     // 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 q = -0.5 * x0;
     for(int i = 0; i < 2; i++){
@@ -45,7 +47,7 @@ float dist_to_curve(){
         float dfx = 3 * x * x + p;
         x = x - fx / dfx;
     }
-    return distance(vec2(x0, y0), vec2(x, x * x));
+    return distance(uv_coords, vec2(x, x * x));
 }