diff --git a/manimlib/shaders/quadratic_bezier_fill/frag.glsl b/manimlib/shaders/quadratic_bezier_fill/frag.glsl
index 73d5c5e4..517da8ec 100644
--- a/manimlib/shaders/quadratic_bezier_fill/frag.glsl
+++ b/manimlib/shaders/quadratic_bezier_fill/frag.glsl
@@ -10,14 +10,11 @@ in vec3 xyz_coords;
 in float orientation;
 in vec2 uv_coords;
 in vec2 uv_b2;
+in vec2 simp_coords;
 in float bezier_degree;
 
 out vec4 frag_color;
 
-// Needed for quadratic_bezier_distance insertion below
-float modify_distance_for_endpoints(vec2 p, float dist, float t){
-    return dist;
-}
 
 #INSERT quadratic_bezier_distance.glsl
 
@@ -32,17 +29,10 @@ float sdf(){
     if(abs(v2 / u2) < 0.1 * uv_anti_alias_width){
         return abs(uv_coords[1]);
     }
-    // This converts uv_coords to yet another space where the bezier points sit on
-    // (0, 0), (1/2, 0) and (1, 1), so that the curve can be expressed implicityly
-    // as y = x^2.
-    mat2 to_simple_space = mat2(
-        v2, 0,
-        2 - u2, 4 * v2
-    );
-    vec2 p = to_simple_space * uv_coords;
+    vec2 p = simp_coords;
+    float Fp = (p.x * p.x - p.y);
     // Sign takes care of whether we should be filling the inside or outside of curve.
     float sgn = orientation * sign(v2);
-    float Fp = (p.x * p.x - p.y);
     if(sgn * Fp <= 0){
         return 0.0;
     }else{
diff --git a/manimlib/shaders/quadratic_bezier_fill/geom.glsl b/manimlib/shaders/quadratic_bezier_fill/geom.glsl
index 96ff1978..60ce7d1b 100644
--- a/manimlib/shaders/quadratic_bezier_fill/geom.glsl
+++ b/manimlib/shaders/quadratic_bezier_fill/geom.glsl
@@ -31,6 +31,7 @@ out float orientation;
 // uv space is where b0 = (0, 0), b1 = (1, 0), and transform is orthogonal
 out vec2 uv_coords;
 out vec2 uv_b2;
+out vec2 simp_coords;
 out float bezier_degree;
 
 vec3 unit_normal;
@@ -114,9 +115,18 @@ void emit_pentagon(vec3[3] points, vec3 normal){
     uv_b2 = (xyz_to_uv * vec4(p2, 1)).xy;
     uv_anti_alias_width = aaw / length(p1 - p0);
 
+    // Matrix from the uv space to an even simpler
+    // one where the curve is equal to y = x^2
+    mat2 to_simple_space = mat2(
+        uv_b2.y, 0,
+        2 - uv_b2.x, 4 * uv_b2.y
+    );
+    //
+
     for(int i = 0; i < 5; i++){
         vec3 corner = corners[i];
         uv_coords = (xyz_to_uv * vec4(corner, 1)).xy;
+        simp_coords = to_simple_space * uv_coords;
         int j = int(sign(i - 1) + 1);  // Maps i = [0, 1, 2, 3, 4] onto j = [0, 0, 1, 2, 2]
         emit_vertex_wrapper(corner, j);
     }