begin work on "un-tube" feature

essentially the inverse of the sheet -> tube transform.

1 files changed, 37 insertions, 2 deletions

diff --git a/vertex_deformation.slang b/vertex_deformation.slang
index 047f7d7..577b0d2 100644
--- a/vertex_deformation.slang
+++ b/vertex_deformation.slang
@@ -84,7 +84,7 @@ float3x3 inverse(float3x3 m, float det) {
   return inv;
 }
 
-// Takes map a 2x2 quad on the xy plane to a tube. The circular cross section
+// Maps a 2x2 quad on the xy plane to a tube. The circular cross section
 // is on the xz plane.
 [Differentiable]
 public float3 plane_to_tube(float3 xyz, no_diff float t) {
@@ -93,7 +93,8 @@ public float3 plane_to_tube(float3 xyz, no_diff float t) {
   float z0 = xyz.z;
 
   float theta = x0 * PI;
-  float phi   = z0 * PI;
+
+  // Equivalent to (1 / (|t| + eps)) * sign(t)
   float radius = 1.0f / (dabs(t) + 1e-4f) * sign(t);
 
   float x = sin(theta / radius) * (radius * PI_RCP - z0);
@@ -114,6 +115,40 @@ public void plane_to_tube_undeform_normal(float3 xyz, inout float3 normal,
   R3R3_UNDEFORM_NORMAL_AND_TANGENT(normal, tangent);
 }
 
+// Maps a tube with circular cross section on the xz plane to a quad on the xy
+// plane.
+[Differentiable]
+public float3 tube_to_plane(float3 xyz, no_diff float t) {
+  float x0 = xyz.x;
+  float y0 = xyz.y;
+  float z0 = xyz.z;
+
+  float theta = atan2(z0, x0) - PI;
+  float r = length(float2(x0, z0));
+  x0 = r * cos(theta);
+  z0 = r * sin(theta);
+
+  // Equivalent to (1 / (|t| + eps)) * sign(t)
+  float radius = 1.0f / (dabs(t) + 1e-4f) * sign(t);
+
+  float x = sin(theta / radius) * (radius * PI_RCP - z0);
+  float z = (1.0f - cos(theta / radius)) * (radius * PI_RCP) + cos(theta / radius) * z0;
+
+  return float3(x, y0, z);
+}
+
+public void tube_to_plane_normal(inout float3 xyz, inout float3 normal,
+    inout float3 tangent, float t) {
+  R3R3_NORMALS(xyz, normal, tangent, tube_to_plane, t);
+}
+
+public void tube_to_plane_undeform_normal(float3 xyz, inout float3 normal,
+    inout float3 tangent, float t) {
+  R3R3_DECLARE_BASIS_VECTORS(xyz);
+  R3R3_AUTODIFF_BASIS_VECTORS(tube_to_plane, t);
+  R3R3_UNDEFORM_NORMAL_AND_TANGENT(normal, tangent);
+}
+
 [Differentiable]
 public float3 seal(float3 xyz, no_diff float A, no_diff float k, no_diff float t) {
   float x = xyz.x;