Instead of tracking du and dv points on surface, track points off the surface in the normal direction

This means that surface shading will not necessarily work well for arbitrary transformations of the surface. But the existing solution was flimsy anyway, and caused annoying issues with singularity points.

manimlib/mobject/three_dimensions.py

@@ -106,6 +106,8 @@ class Sphere(Surface):
             resolution=resolution,
             **kwargs
         )
+        # Add bespoke normal specification to avoid issue at poles
+        self.data['d_normal_point'] = self.data['point'] * ((radius + self.normal_nudge) / radius)
 
     def uv_func(self, u: float, v: float) -> np.ndarray:
         return self.radius * np.array([

manimlib/mobject/types/surface.py

@@ -30,11 +30,10 @@ class Surface(Mobject):
     shader_folder: str = "surface"
     data_dtype: np.dtype = np.dtype([
         ('point', np.float32, (3,)),
-        ('du_point', np.float32, (3,)),
-        ('dv_point', np.float32, (3,)),
+        ('d_normal_point', np.float32, (3,)),
         ('rgba', np.float32, (4,)),
     ])
-    pointlike_data_keys = ['point', 'du_point', 'dv_point']
+    pointlike_data_keys = ['point', 'd_normal_point']
 
     def __init__(
         self,
@@ -48,9 +47,11 @@ class Surface(Mobject):
         # rows/columns of approximating squares
         resolution: Tuple[int, int] = (101, 101),
         prefered_creation_axis: int = 1,
-        # For du and dv steps.  Much smaller and numerical error
-        # can crop up in the shaders.
-        epsilon: float = 1e-4,
+        # For du and dv steps.
+        epsilon: float = 1e-3,
+        # Step off the surface to a new point which will
+        # be used to determine the normal direction
+        normal_nudge: float = 1e-3,
         **kwargs
     ):
         self.u_range = u_range
@@ -58,6 +59,7 @@ class Surface(Mobject):
         self.resolution = resolution
         self.prefered_creation_axis = prefered_creation_axis
         self.epsilon = epsilon
+        self.normal_nudge = normal_nudge
 
         super().__init__(
             **kwargs,
@@ -94,9 +96,11 @@ class Surface(Mobject):
             ).reshape((nu * nv, dim))
             for grid in (uv_grid, uv_plus_du, uv_plus_dv)
         ]
+        crosses = cross(du_points - points, dv_points - points)
+        normals = normalize_along_axis(crosses, 1)
+
         self.set_points(points)
-        self.data['du_point'][:] = du_points
-        self.data['dv_point'][:] = dv_points
+        self.data['d_normal_point'] = points + self.normal_nudge * normals
 
     def uv_to_point(self, u, v):
         nu, nv = self.resolution
@@ -152,12 +156,8 @@ class Surface(Mobject):
         return self.triangle_indices
 
     def get_unit_normals(self) -> Vect3Array:
-        points = self.get_points()
-        crosses = cross(
-            self.data['du_point'] - points,
-            self.data['dv_point'] - points,
-        )
-        return normalize_along_axis(crosses, 1)
+        # TOOD, I could try a more resiliant way to compute this using the neighboring grid values
+        return normalize_along_axis(self.data['d_normal_point'] - self.data['point'], 1)
 
     @Mobject.affects_data
     def pointwise_become_partial(
@@ -276,8 +276,7 @@ class TexturedSurface(Surface):
     shader_folder: str = "textured_surface"
     data_dtype: Sequence[Tuple[str, type, Tuple[int]]] = [
         ('point', np.float32, (3,)),
-        ('du_point', np.float32, (3,)),
-        ('dv_point', np.float32, (3,)),
+        ('d_normal_point', np.float32, (3,)),
         ('im_coords', np.float32, (2,)),
         ('opacity', np.float32, (1,)),
     ]
@@ -321,8 +320,7 @@ class TexturedSurface(Surface):
         self.resize_points(surf.get_num_points())
         self.resolution = surf.resolution
         self.data['point'][:] = surf.data['point']
-        self.data['du_point'][:] = surf.data['du_point']
-        self.data['dv_point'][:] = surf.data['dv_point']
+        self.data['d_normal_point'][:] = surf.data['d_normal_point']
         self.data['opacity'][:, 0] = surf.data["rgba"][:, 3]
         self.data["im_coords"] = np.array([
             [u, v]

manimlib/shaders/surface/vert.glsl

@@ -1,8 +1,7 @@
 #version 330
 
 in vec3 point;
-in vec3 du_point;
-in vec3 dv_point;
+in vec3 d_normal_point;
 in vec4 rgba;
 
 out vec4 v_color;
@@ -15,10 +14,6 @@ const float EPSILON = 1e-10;
 
 void main(){
     emit_gl_Position(point);
-    vec3 du = (du_point - point);
-    vec3 dv = (dv_point - point);
-    vec3 normal = cross(du, dv);
-    float mag = length(normal);
-    vec3 unit_normal = (mag < EPSILON) ? vec3(0, 0, sign(point.z)) : normal / mag;
+    vec3 unit_normal = normalize(d_normal_point - point);
     v_color = finalize_color(rgba, point, unit_normal);
 }

manimlib/shaders/textured_surface/vert.glsl

@@ -1,8 +1,7 @@
 #version 330
 
 in vec3 point;
-in vec3 du_point;
-in vec3 dv_point;
+in vec3 d_normal_point;
 in vec2 im_coords;
 in float opacity;
 
@@ -11,15 +10,17 @@ out vec3 v_unit_normal;
 out vec2 v_im_coords;
 out float v_opacity;
 
+uniform float is_sphere;
+uniform vec3 center;
+
 #INSERT emit_gl_Position.glsl
 #INSERT get_unit_normal.glsl
 
+const float EPSILON = 1e-10;
+
 void main(){
     v_point = point;
-    v_unit_normal = normalize(cross(
-        normalize(du_point - point),
-        normalize(dv_point - point)
-    ));
+    v_unit_normal = normalize(d_normal_point - point);;
     v_im_coords = im_coords;
     v_opacity = opacity;
     emit_gl_Position(point);