Clean up a few messes from previous commit

manimlib/shaders/inserts/quadratic_bezier_geometry_functions.glsl

@@ -59,8 +59,9 @@ mat3 map_point_pairs(vec2 src0, vec2 src1, vec2 dest0, vec2 dest1){
 }
 
 
-mat3 get_xy_to_uv(vec2 controls[3], float bezier_degree){
+mat3 get_xy_to_uv(vec2 controls[3], float bezier_degree, out float new_bezier_degree){
     vec2[2] dest;
+    new_bezier_degree = bezier_degree;
     if (bezier_degree == 1.0){
         dest[0] = vec2(0, 0);
         dest[1] = vec2(1, 0);
@@ -68,8 +69,15 @@ mat3 get_xy_to_uv(vec2 controls[3], float bezier_degree){
         vec2 xs = xs_on_clean_parabola(controls);
         float x0 = xs.x;
         float x2 = xs.y;
-        dest[0] = vec2(x0, x0 * x0);
-        dest[1] = vec2(x2, x2 * x2);
+        float thresh = 2.0;
+        if((x0 > thresh && x2 > thresh) || (x0 < -thresh && x2 < -thresh)){
+            dest[0] = vec2(0, 0);
+            dest[1] = vec2(1, 0);
+            new_bezier_degree = 1.0;
+        }else{
+            dest[0] = vec2(x0, x0 * x0);
+            dest[1] = vec2(x2, x2 * x2);
+        }
     }
     return map_point_pairs(
         controls[0], controls[2], dest[0], dest[1]

manimlib/shaders/quadratic_bezier_stroke/frag.glsl

@@ -12,7 +12,7 @@ in float bezier_degree;
 
 out vec4 frag_color;
 
-const float QUICK_DIST_WIDTH = 0.1;
+const float QUICK_DIST_WIDTH = 0.2;
 
 
 float cube_root(float x){
@@ -23,17 +23,18 @@ float cube_root(float x){
 // Distance from (x0, y0) to the curve y = x^2
 float dist_to_curve(float x0, float y0){
     if(bezier_degree == 1.0){
+        // In this case, the curve will actually have
+        // been set to equal the x axis
         return y0;
     }
-    if(false && uv_stroke_width < QUICK_DIST_WIDTH){
+    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 (y0 - x0 * x0) / sqrt(1 + 4 * x0 * x0);
     }
-    // Otherwise, explicit solve for the minmal distance using the cubic formula
-    //
+    // Otherwise, solve for the minimal distance.
     // The distance squared between (x0, y0) and a point (x, x^2) looks like
     //
     // (x0 - x)^2 + (y0 - x^2)^2 = x^4 + (1 - 2y0)x^2 - 2x0 * x + (x0^2 + y0^2)
@@ -42,12 +43,7 @@ float dist_to_curve(float x0, float y0){
     // 
     // x^3 + (0.5 - y0) * x - 0.5 * x0 = 0
     //
-    // float p = 0.5 - y0;
-    // float mhq = 0.25 * x0;  // negative half of q
-    // float sqrt_disc = sqrt(mhq * mhq + p * p * p / 27.0);
-    // float x = cube_root(mhq + sqrt_disc) + cube_root(mhq - sqrt_disc);
-    // return distance(uv_coords, vec2(x, x * x));
-
+    // Use two rounds of Newton's method
     float x = x0;
     float p = (0.5 - y0);
     float q = -0.5 * x0;
@@ -69,6 +65,5 @@ void main() {
     float signed_dist = abs(dist_to_curve(x0, y0)) - 0.5 * uv_stroke_width;
 
     frag_color = color;
-    // if(uv_stroke_width > QUICK_DIST_WIDTH) frag_color = vec4(1, 0, 0, 1);
     frag_color.a *= smoothstep(0.5, -0.5, signed_dist / uv_anti_alias_width);
 }

manimlib/shaders/quadratic_bezier_stroke/geom.glsl

@@ -131,7 +131,6 @@ int get_corners(
 void main() {
     if (distance(verts[0], verts[1]) == 0 && distance(verts[1], verts[2]) == 0) return;
 
-    bezier_degree = (abs(v_joint_angle[1]) < ANGLE_THRESHOLD) ? 1.0 : 2.0;
     vec3 unit_normal = camera_rotation * vec3(0.0, 0.0, 1.0); // TODO, track true unit normal globally
 
     // Control points are projected to the xy plane before drawing, which in turn
@@ -150,10 +149,6 @@ void main() {
         scaled_strokes[i] = v_stroke_width[i] * sf;
     }
 
-    // If the curve is flat, put the middle control in the midpoint
-    if (bezier_degree == 1.0){
-        flat_controls[1] = 0.5 * (flat_controls[0] + flat_controls[2]);
-    }
 
     // Set joint information
     float angle_from_prev = v_joint_angle[0];
@@ -167,6 +162,24 @@ void main() {
         angle_to_next = 0.0;
     }
 
+    // We want to change the coordinates to a space where the curve
+    // coincides with y = x^2, between some values x0 and x2. Or, in
+    // the case of a linear curve (bezier degree 1), just put it on
+    // the segment from (0, 0) to (1, 0)
+    bezier_degree = (abs(v_joint_angle[1]) < ANGLE_THRESHOLD) ? 1.0 : 2.0;
+
+    float new_bezier_degree;
+    mat3 xy_to_uv = get_xy_to_uv(flat_controls, bezier_degree, new_bezier_degree);
+    bezier_degree = new_bezier_degree;
+
+    float scale_factor = length(xy_to_uv[0].xy);
+    uv_anti_alias_width = scale_factor * anti_alias_width * (frame_shape.y / pixel_shape.y);
+
+    // If the curve is flat, put the middle control in the midpoint
+    if (bezier_degree == 1.0){
+        flat_controls[1] = 0.5 * (flat_controls[0] + flat_controls[2]);
+    }
+
     // Corners of a bounding region around curve
     vec2 corners[5];
     int n_corners = get_corners(
@@ -178,11 +191,6 @@ void main() {
     int index_map[5] = int[5](0, 0, 1, 2, 2);
     if(n_corners == 4) index_map[2] = 2;
 
-    // Find uv conversion
-    mat3 xy_to_uv = get_xy_to_uv(flat_controls, bezier_degree);
-    float scale_factor = length(xy_to_uv[0].xy);
-    uv_anti_alias_width = scale_factor * anti_alias_width * (frame_shape.y / pixel_shape.y);
-
     // Emit each corner
     for(int i = 0; i < n_corners; i++){
         uv_coords = (xy_to_uv * vec3(corners[i], 1.0)).xy;