add point align feature, aka inverse of axis align

1 files changed, 43 insertions, 1 deletions

diff --git a/vertex_deformation.slang b/vertex_deformation.slang
index 0846991..542281b 100644
--- a/vertex_deformation.slang
+++ b/vertex_deformation.slang
@@ -163,7 +163,7 @@ public float3 axis_align(float3 xyz, no_diff float3 po, no_diff float3 pp, no_di
   float3 sxr = cross(s, r);
 
   float3x3 to_rsrxs = float3x3(r, s, sxr);
-  // Inverse of orthonormal matrix is just the transpose.
+  // Inverse of orthonormal matrix is just the transpos.
   float3x3 to_cart  = transpose(to_rsrxs);
 
   // Move key vectors into (r, s, sxr) basis centered at `po`, per the derivation.
@@ -276,6 +276,48 @@ public void tube_to_plane_undeform_normal(
 }
 
 [Differentiable]
+public float3 point_align(float3 xyz, no_diff float3 po, no_diff float3 pp, no_diff float3 r, no_diff float t) {
+  // We assume that `s` is orthogonal to `r`, and that `r` is normalized.
+  float3 s = normalize(pp - po);
+  float3 sxr = cross(s, r);
+
+  float3x3 to_rsrxs = float3x3(r, s, sxr);
+  // Inverse of orthonormal matrix is just the transpose.
+  float3x3 to_cart  = transpose(to_rsrxs);
+
+  // Move key vectors into (r, s, sxr) basis centered at `po`, per the derivation.
+  float3 xyz_rsrxs = mul(to_rsrxs, xyz - po);
+  float3 pp_rsrxs  = mul(to_rsrxs, pp - po);
+
+  float2 v1 = xyz_rsrxs.xy;
+  float v1r = v1.x;
+  float v1s = v1.y;
+
+  float vs = v1.y;
+  float qs = pp_rsrxs.y;
+  float qr = v1.x;
+  float2 q = float2(qr, qs);
+  q *= vs / qs;
+
+  xyz_rsrxs.xy = q;
+
+  // Move back into cartesian space.
+  xyz = mul(to_cart, xyz_rsrxs) + po;
+
+  return xyz;
+}
+
+public void point_align_normal(inout float3 xyz, inout float3 normal, inout float3 tangent, float3 po, float3 pp, float3 r, float t) {
+  R3R3_NORMALS(xyz, normal, tangent, point_align, po, pp, r, t);
+}
+
+public void point_align_undeform_normal(float3 xyz, inout float3 normal, inout float3 tangent, float3 po, float3 pp, float3 r, float t) {
+  R3R3_DECLARE_BASIS_VECTORS(xyz);
+  R3R3_AUTODIFF_BASIS_VECTORS(point_align, po, pp, r, 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;
   float y = xyz.y;