From c345d76de09e32e3ff3a7b125aaf77996d6accd3 Mon Sep 17 00:00:00 2001
From: Grant Sanderson <grant@3blue1brown.com>
Date: Thu, 8 Aug 2024 11:36:28 -0500
Subject: [PATCH] Patch for glitches associated with non-flat stroke when
 tangency direction lines up with camera view

---
 .../shaders/quadratic_bezier_stroke/geom.glsl | 30 ++++++++++++++-----
 1 file changed, 22 insertions(+), 8 deletions(-)

diff --git a/manimlib/shaders/quadratic_bezier_stroke/geom.glsl b/manimlib/shaders/quadratic_bezier_stroke/geom.glsl
index 9e9117b6..f9c093ec 100644
--- a/manimlib/shaders/quadratic_bezier_stroke/geom.glsl
+++ b/manimlib/shaders/quadratic_bezier_stroke/geom.glsl
@@ -85,33 +85,47 @@ vec3 inverse_vector_product(vec3 vect, vec3 cross_product, float dot_product){
 }
 
 
-vec3 step_to_corner(vec3 point, vec3 tangent, vec3 unit_normal, vec4 joint_product, bool inner_joint){
+vec3 step_to_corner(vec3 point, vec3 tangent, vec3 unit_normal, vec4 joint_product, bool inside_curve){
     /*
     Step the the left of a curve.
     First a perpendicular direction is calculated, then it is adjusted
     so as to make a joint.
     */
     vec3 unit_tan = normalize(flat_stroke == 0.0 ? project(tangent, unit_normal) : tangent);
-    vec4 unit_jp = unit_joint_product(joint_product);
-    float cos_angle = unit_jp.w;
 
     // Step to stroke width bound should be perpendicular
     // both to the tangent and the normal direction
     vec3 step = normalize(cross(unit_normal, unit_tan));
 
-    // Conditions where no joint needs to be created
-    if (inner_joint || int(joint_type) == NO_JOINT || cos_angle > COS_THRESHOLD) return step;
+    // For non-flat stroke, there can be glitches when the tangent direction
+    // lines up very closely with the direction to the camera, treated here
+    // as the unit normal. To avoid those, this smoothly transitions to a step
+    // direction perpendicular to the true curve normal.
+    float alignment = abs(dot(normalize(tangent), unit_normal));
+    float alignment_threshold = 0.97;  // This could maybe be chosen in a more principled way based on stroke width
+    if (alignment > alignment_threshold) {
+        vec3 perp = normalize(cross(get_joint_unit_normal(joint_product), tangent));
+        step = mix(step, project(step, perp), smoothstep(alignment_threshold, 1.0, alignment));
+    }
 
+    if (inside_curve || int(joint_type) == NO_JOINT) return step;
+
+    vec4 unit_jp = unit_joint_product(joint_product);
+    float cos_angle = unit_jp.w;
+
+    if (cos_angle > COS_THRESHOLD) return step;
+
+    // Below here, figure out the adjustment to bevel or miter a joint
     if (flat_stroke == 0){
         // Figure out what joint product would be for everything projected onto
         // the plane perpendicular to the normal direction (which here would be to_camera)
+        step = normalize(cross(unit_normal, unit_tan));  // Back to original step
         vec3 adj_tan = inverse_vector_product(tangent, unit_jp.xyz, unit_jp.w);
         adj_tan = project(adj_tan, unit_normal);
         vec4 flat_jp = get_joint_product(unit_tan, adj_tan);
         cos_angle = unit_joint_product(flat_jp).w;
     }
 
-    // Adjust based on the joint.
     // If joint type is auto, it will bevel for cos(angle) > -0.7,
     // and smoothly transition to miter for those with sharper angles
     float miter_factor;
@@ -132,7 +146,7 @@ void emit_point_with_width(
     vec4 joint_product,
     float width,
     vec4 joint_color,
-    bool inner_joint
+    bool inside_curve
 ){
     // Find unit normal
     vec3 to_camera = camera_position - point;
@@ -146,7 +160,7 @@ void emit_point_with_width(
 
     // Figure out the step from the point to the corners of the
     // triangle strip around the polyline
-    vec3 step = step_to_corner(point, tangent, unit_normal, joint_product, inner_joint);
+    vec3 step = step_to_corner(point, tangent, unit_normal, joint_product, inside_curve);
 
     // TODO, this gives a potentially nice effect that's like a ribbon mostly with its
     // broad side to the camera. Currently hard to access via VMobject