Fixed the random-dimples-on-zeros bug while fixing up the fill shaders

manimlib/mobject/types/vectorized_mobject.py

@@ -64,7 +64,6 @@ class VMobject(Mobject):
             ('point', np.float32, (3,)),
             ('color', np.float32, (4,)),
             ('fill_all', np.float32, (1,)),
-            ('orientation', np.float32, (1,)),
         ],
         "stroke_dtype": [
             ("point", np.float32, (3,)),
@@ -984,16 +983,13 @@ class VMobject(Mobject):
 
         # Triangulate
         inner_verts = points[inner_vert_indices]
-        inner_tri_indices = inner_vert_indices[
-            earclip_triangulation(inner_verts, rings)
-        ]
+        inner_tri_indices = inner_vert_indices[earclip_triangulation(inner_verts, rings)]
 
         tri_indices = np.hstack([indices, inner_tri_indices])
         return tri_indices
 
     def get_fill_shader_data(self):
         points = self.points
-
         orientation = self.get_orientation()
         tri_indices = self.get_triangulation(orientation)
 
@@ -1007,8 +1003,9 @@ class VMobject(Mobject):
         # are on the boundary, and the rest are in the interior
         data["fill_all"][:len(points)] = 0
         data["fill_all"][len(points):] = 1
-        data["orientation"] = orientation
-
+        # Always send points in a positively oriented way
+        if orientation < 0:
+            data["point"][:len(points)] = points[::-1]
         return data
 
 

manimlib/shaders/quadratic_bezier_fill_frag.glsl

@@ -1,11 +1,10 @@
 #version 330
 
 in vec4 color;
-in float fill_type;
+in float fill_all;  // Either 0 or 1e
 in float uv_anti_alias_width;
 
 in vec2 uv_coords;
-in vec2 wz_coords;
 in vec2 uv_b2;
 in float bezier_degree;
 
@@ -16,7 +15,7 @@ const float FILL_OUTSIDE = 1;
 const float FILL_ALL = 2;
 
 
-// Needed for quadratic_bezier_distance
+// Needed for quadratic_bezier_distance insertion below
 float modify_distance_for_endpoints(vec2 p, float dist, float t){
     return dist;
 }
@@ -26,27 +25,36 @@ float modify_distance_for_endpoints(vec2 p, float dist, float t){
 // replaces this line with the contents of quadratic_bezier_sdf.glsl
 #INSERT quadratic_bezier_distance.glsl
 
-
-bool is_inside_curve(){
-    if(bezier_degree < 2) return false;
-
-    float value = wz_coords.x * wz_coords.x - wz_coords.y;
-    if(fill_type == FILL_INSIDE) return value < 0;
-    if(fill_type == FILL_OUTSIDE) return value > 0;
-    return false;
-}
-
-
 float sdf(){
-    if(is_inside_curve()) return -1.0;
+    // For really flat curves, just take the distance to the curve
+    if(bezier_degree < 2 || abs(uv_b2.y / uv_b2.x) < uv_anti_alias_width){
         return min_dist_to_curve(uv_coords, uv_b2, bezier_degree, false);
+    }
+    // This converts uv_coords to a 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.
+    float u2 = uv_b2.x;
+    float v2 = uv_b2.y;
+    mat2 to_simple_space = mat2(
+        v2, 0,
+        2 - u2, 4 * v2
+    );
+    vec2 p = to_simple_space * uv_coords;
+
+    float Fp = sign(v2) * (p.x * p.x - p.y);
+
+    vec2 grad = vec2(
+        - 2 * p.x * v2,  // del C / del u
+        4 * v2 - 4 * p.x * (2 - u2)  // del C / del v
+    );
+    return Fp / length(grad);
 }
 
 
 void main() {
     if (color.a == 0) discard;
     frag_color = color;
-    if (fill_type == FILL_ALL) return;
+    // TODO, Add shading based on normal vector, light position and gloss
+    if (fill_all == 1.0) return;
     frag_color.a *= smoothstep(1, 0, sdf() / uv_anti_alias_width);
-    // frag_color.a += 0.2;
 }

manimlib/shaders/quadratic_bezier_fill_geom.glsl

@@ -11,17 +11,13 @@ uniform vec3 frame_center;
 in vec3 bp[3];
 in vec4 v_color[3];
 in float v_fill_all[3];
-in float v_orientation[3];
 
 out vec4 color;
-out float fill_type;
+out float fill_all;
 out float uv_anti_alias_width;
-
 // uv space is where b0 = (0, 0), b1 = (1, 0), and transform is orthogonal
 out vec2 uv_coords;
 out vec2 uv_b2;
-// wz space is where b0 = (0, 0), b1 = (0.5, 0), b2 = (1, 1)
-out vec2 wz_coords;
 
 out float bezier_degree;
 
@@ -38,30 +34,6 @@ const float SQRT5 = 2.236068;
 #INSERT quadratic_bezier_geometry_functions.glsl
 #INSERT scale_and_shift_point_for_frame.glsl
 
-
-mat3 get_xy_to_wz(vec2 b0, vec2 b1, vec2 b2){
-    // If linear or null, this matrix is not needed
-    if(bezier_degree < 2) return mat3(1.0);
-
-    vec2 inv_col1 = 2 * (b1 - b0);
-    vec2 inv_col2 = b2 - 2 * b1 + b0;
-    float inv_det = cross(inv_col1, inv_col2);
-
-    mat3 transform = mat3(
-        inv_col2.y, -inv_col1.y, 0,
-        -inv_col2.x, inv_col1.x, 0,
-        0, 0, inv_det
-    ) / inv_det;
-
-    mat3 shift = mat3(
-        1, 0, 0,
-        0, 1, 0,
-        -b0.x, -b0.y, 1
-    );
-    return transform * shift;
-}
-
-
 void emit_simple_triangle(){
     for(int i = 0; i < 3; i++){
         color = v_color[i];
@@ -75,29 +47,17 @@ void emit_simple_triangle(){
 }
 
 
-void emit_pentagon(vec2 bp0, vec2 bp1, vec2 bp2, float orientation){
+void emit_pentagon(vec2 bp0, vec2 bp1, vec2 bp2){
     // Tangent vectors
     vec2 t01 = normalize(bp1 - bp0);
     vec2 t12 = normalize(bp2 - bp1);
-
-    // Inside and left turn -> rot right -> -1
-    // Outside and left turn -> rot left -> +1
-    // Inside and right turn -> rot left -> +1
-    // Outside and right turn -> rot right -> -1
-    float c_orient = (cross(t01, t12) > 0) ? 1 : -1;
-    c_orient *= orientation;
-
-    bool fill_in = (c_orient > 0);
-    fill_type = fill_in ? FILL_INSIDE : FILL_OUTSIDE;
-
-    // float orient = in_or_out * c_orient;
-
     // Normal vectors
     // Rotate tangent vector 90-degrees clockwise
-    // if the curve is positively oriented, otherwise
-    // rotate it 90-degrees counterclockwise
-    vec2 n01 = orientation * vec2(t01.y, -t01.x);
-    vec2 n12 = orientation * vec2(t12.y, -t12.x);
+    vec2 n01 = vec2(t01.y, -t01.x);
+    vec2 n12 = vec2(t12.y, -t12.x);
+
+    float c_orient = sign(cross(t01, t12));
+    bool fill_in = (c_orient > 0);
 
     float aaw = anti_alias_width;
     vec2 nudge1 = fill_in ? 0.5 * aaw * (n01 + n12) : vec2(0);
@@ -113,29 +73,19 @@ void emit_pentagon(vec2 bp0, vec2 bp1, vec2 bp2, float orientation){
     if(!fill_in) coords_index_map = int[5](1, 0, 2, 4, 3);
         
     mat3 xy_to_uv = get_xy_to_uv(bp0, bp1);
-    mat3 xy_to_wz = get_xy_to_wz(bp0, bp1, bp2);
     uv_b2 = (xy_to_uv * vec3(bp2, 1)).xy;
     uv_anti_alias_width = anti_alias_width / length(bp1 - bp0);
 
+    int nearest_bp_index_map[5] = int[5](0, 0, 1, 2, 2);
     for(int i = 0; i < 5; i++){
         vec2 corner = corners[coords_index_map[i]];
+        float z = bp[nearest_bp_index_map[i]].z;
         uv_coords = (xy_to_uv * vec3(corner, 1)).xy;
-        wz_coords = (xy_to_wz * vec3(corner, 1)).xy;
-        float z;
         // I haven't a clue why an index map doesn't work just
         // as well here, but for some reason it doesn't.
-        if(i < 2){
-            color = v_color[0];
-            z = bp[0].z;
-        }
-        else if(i == 2){
-            color = v_color[1];
-            z = bp[1].z;
-        }
-        else{
-            color = v_color[2];
-            z = bp[2].z;
-        }
+        if(i < 2)       color = v_color[0];
+        else if(i == 2) color = v_color[1];
+        else            color = v_color[2];
         gl_Position = vec4(
             scale_and_shift_point_for_frame(vec3(corner, z)),
             1.0
@@ -147,17 +97,16 @@ void emit_pentagon(vec2 bp0, vec2 bp1, vec2 bp2, float orientation){
 
 
 void main(){
-    float fill_all = v_fill_all[0];
+    fill_all = v_fill_all[0];
 
     if(fill_all == 1){
-        fill_type = FILL_ALL;
         emit_simple_triangle();
-    }else{
+        return;
+    }
+
     vec2 new_bp[3];
     int n = get_reduced_control_points(bp[0].xy, bp[1].xy, bp[2].xy, new_bp);
     bezier_degree = float(n);
-        float orientation = v_orientation[0];
-
     vec2 bp0, bp1, bp2;
     if(n == 0){
         return;  // Don't emit any vertices
@@ -172,7 +121,6 @@ void main(){
         bp2 = new_bp[2];
     }
 
-        emit_pentagon(bp0, bp1, bp2, orientation);
-    }
+    emit_pentagon(bp0, bp1, bp2);
 }
 

manimlib/shaders/quadratic_bezier_fill_vert.glsl

@@ -2,23 +2,16 @@
 
 in vec3 point;
 in vec4 color;
-// fill_all is 0 or 1
-in float fill_all;
-// orientation is +1 for counterclockwise curves, -1 otherwise
-in float orientation;
+in float fill_all;  // Either 0 or 1
 
 out vec3 bp;  // Bezier control point
 out vec4 v_color;
 out float v_fill_all;
-out float v_orientation;
-
 
 #INSERT rotate_point_for_frame.glsl
 
-
 void main(){
     bp = rotate_point_for_frame(point);
     v_color = color;
     v_fill_all = fill_all;
-    v_orientation = orientation;
 }

manimlib/shaders/quadratic_bezier_geometry_functions.glsl

@@ -30,25 +30,25 @@ mat3 get_xy_to_uv(vec2 b0, vec2 b1){
 // might change.  The idea is to inform the caller of the degree,
 // while also passing tangency information in the linear case.
 int get_reduced_control_points(vec2 b0, vec2 b1, vec2 b2, out vec2 new_points[3]){
-    float epsilon = 1e-6;
+    float length_threshold = 1e-6;
+    float angle_threshold = 1e-3;
     vec2 v01 = (b1 - b0);
     vec2 v12 = (b2 - b1);
-    bool distinct_01 = length(v01) > epsilon;  // v01 is considered nonzero
-    bool distinct_12 = length(v12) > epsilon;  // v12 is considered nonzero
+    // bool aligned = abs(cross(normalize(v01), normalize(v12))) < angle_threshold;
+    bool aligned = acos(dot(normalize(v01), normalize(v12))) < angle_threshold;
+    bool distinct_01 = length(v01) > length_threshold;  // v01 is considered nonzero
+    bool distinct_12 = length(v12) > length_threshold;  // v12 is considered nonzero
     int n_uniques = int(distinct_01) + int(distinct_12);
-    if(n_uniques == 2){
-        bool linear = dot(normalize(v01), normalize(v12)) > 1 - epsilon;
-        if(linear){
-            new_points[0] = b0;
-            new_points[1] = b2;
-            return 1;
-        }else{
+
+    bool quadratic = (n_uniques == 2) && !aligned;
+    bool linear = (n_uniques == 1) || ((n_uniques == 2) && aligned);
+    bool constant = (n_uniques == 0);
+    if(quadratic){
         new_points[0] = b0;
         new_points[1] = b1;
         new_points[2] = b2;
         return 2;
-        }
-    }else if(n_uniques == 1){
+    }else if(linear){
         new_points[0] = b0;
         new_points[1] = b2;
         return 1;