more tube-plane simplifications

5 files changed, 47 insertions, 352 deletions

diff --git a/3ner.shader b/3ner.shader
index 0819f3d..d260aff 100644
--- a/3ner.shader
+++ b/3ner.shader
@@ -204,34 +204,14 @@ Shader "yum_food/3ner"
             [HideInInspector] m_end_Vertex_Deformation_XY_Untube("XY Untube", Float) = 0
             //endex
 
-            //ifex _Vertex_Deformation_XZ_Tube_Enabled==0
-            [HideInInspector] m_start_Vertex_Deformation_XZ_Tube("XZ Tube", Float) = 0
-              [ThryToggle(_VERTEX_DEFORMATION_XZ_TUBE)] _Vertex_Deformation_XZ_Tube_Enabled("Enable", Float) = 0
-              _Vertex_Deformation_XZ_Tube_p("p", Vector) = (0, 0, 1)
-              _Vertex_Deformation_XZ_Tube_r("r", Vector) = (0, 0, -1)
-              _Vertex_Deformation_XZ_Tube_s("s", Vector) = (0, 0, -1)
-              _Vertex_Deformation_XZ_Tube_t("t", Range(-1,4)) = 0
-            [HideInInspector] m_end_Vertex_Deformation_XZ_Tube("XZ Tube", Float) = 0
-            //endex
-
-            //ifex _Vertex_Deformation_YZ_Tube_Enabled==0
-            [HideInInspector] m_start_Vertex_Deformation_YZ_Tube("YZ Tube", Float) = 0
-              [ThryToggle(_VERTEX_DEFORMATION_YZ_TUBE)] _Vertex_Deformation_YZ_Tube_Enabled("Enable", Float) = 0
-              _Vertex_Deformation_YZ_Tube_p("p", Vector) = (0, 0, 1)
-              _Vertex_Deformation_YZ_Tube_r("r", Vector) = (0, 0, -1)
-              _Vertex_Deformation_YZ_Tube_s("s", Vector) = (0, 0, -1)
-              _Vertex_Deformation_YZ_Tube_t("t", Range(-1,4)) = 0
-            [HideInInspector] m_end_Vertex_Deformation_YZ_Tube("YZ Tube", Float) = 0
-            //endex
-
-            //ifex _Vertex_Deformation_XY_Tube_Enabled==0
-            [HideInInspector] m_start_Vertex_Deformation_XY_Tube("XY Tube", Float) = 0
-              [ThryToggle(_VERTEX_DEFORMATION_XY_TUBE)] _Vertex_Deformation_XY_Tube_Enabled("Enable", Float) = 0
-              _Vertex_Deformation_XY_Tube_p("p", Vector) = (0, 0, 1)
-              _Vertex_Deformation_XY_Tube_r("r", Vector) = (0, 0, -1)
-              _Vertex_Deformation_XY_Tube_s("s", Vector) = (0, 0, -1)
-              _Vertex_Deformation_XY_Tube_t("t", Range(-1,4)) = 0
-            [HideInInspector] m_end_Vertex_Deformation_XY_Tube("XY Tube", Float) = 0
+            //ifex _Vertex_Deformation_Tube_Enabled==0
+            [HideInInspector] m_start_Vertex_Deformation_Plane_To_Tube("Plane to Tube", Float) = 0
+              [ThryToggle(_VERTEX_DEFORMATION_PLANE_TO_TUBE)] _Vertex_Deformation_Plane_To_Tube_Enabled("Enable", Float) = 0
+              _Vertex_Deformation_Plane_To_Tube_p("p", Vector) = (0, 0, 1)
+              _Vertex_Deformation_Plane_To_Tube_r("r", Vector) = (0, 0, -1)
+              _Vertex_Deformation_Plane_To_Tube_s("s", Vector) = (0, 0, -1)
+              _Vertex_Deformation_Plane_To_Tube_t("t", Range(-1,1)) = 0
+            [HideInInspector] m_end_Vertex_Deformation_Plane_To_Tube("Plane to Tube", Float) = 0
             //endex
           [HideInInspector] m_end_Vertex_Deformation_Tubes("Tubes", Float) = 0
           //endex
diff --git a/features.cginc b/features.cginc
index af52b18..5644d37 100644
--- a/features.cginc
+++ b/features.cginc
@@ -42,9 +42,7 @@
 #pragma shader_feature_local _VERTEX_DEFORMATION_XZ_UNTUBE
 #pragma shader_feature_local _VERTEX_DEFORMATION_YZ_UNTUBE
 #pragma shader_feature_local _VERTEX_DEFORMATION_XY_UNTUBE
-#pragma shader_feature_local _VERTEX_DEFORMATION_XZ_TUBE
-#pragma shader_feature_local _VERTEX_DEFORMATION_YZ_TUBE
-#pragma shader_feature_local _VERTEX_DEFORMATION_XY_TUBE
+#pragma shader_feature_local _VERTEX_DEFORMATION_PLANE_TO_TUBE
 //endex
 
 //ifex _Vertex_Deformation_L2_L1_Enabled==0
diff --git a/globals.cginc b/globals.cginc
index c838091..54f58f2 100644
--- a/globals.cginc
+++ b/globals.cginc
@@ -85,24 +85,12 @@ float _Vertex_Deformation_XZ_Untube_t;
 float _Vertex_Deformation_YZ_Untube_t;
 #endif  // _VERTEX_DEFORMATION_YZ_UNTUBE
 
-#if defined(_VERTEX_DEFORMATION_XY_TUBE)
-float3 _Vertex_Deformation_XY_Tube_p;
-float3 _Vertex_Deformation_XY_Tube_r;
-float3 _Vertex_Deformation_XY_Tube_s;
-float _Vertex_Deformation_XY_Tube_t;
-#endif  // _VERTEX_DEFORMATION_XY_TUBE
-#if defined(_VERTEX_DEFORMATION_XZ_TUBE)
-float3 _Vertex_Deformation_XZ_Tube_p;
-float3 _Vertex_Deformation_XZ_Tube_r;
-float3 _Vertex_Deformation_XZ_Tube_s;
-float _Vertex_Deformation_XZ_Tube_t;
-#endif  // _VERTEX_DEFORMATION_XZ_TUBE
-#if defined(_VERTEX_DEFORMATION_YZ_TUBE)
-float3 _Vertex_Deformation_YZ_Tube_p;
-float3 _Vertex_Deformation_YZ_Tube_r;
-float3 _Vertex_Deformation_YZ_Tube_s;
-float _Vertex_Deformation_YZ_Tube_t;
-#endif  // _VERTEX_DEFORMATION_YZ_TUBE
+#if defined(_VERTEX_DEFORMATION_PLANE_TO_TUBE)
+float3 _Vertex_Deformation_Plane_To_Tube_p;
+float3 _Vertex_Deformation_Plane_To_Tube_r;
+float3 _Vertex_Deformation_Plane_To_Tube_s;
+float _Vertex_Deformation_Plane_To_Tube_t;
+#endif  // _VERTEX_DEFORMATION_PLANE_TO_TUBE
 
 #if defined(_VERTEX_DEFORMATION_NORM_CONVERSION)
 float _Vertex_Deformation_Norm_Conversion_Input_k;
diff --git a/vertex.cginc b/vertex.cginc
index daa5ce0..a5770f2 100644
--- a/vertex.cginc
+++ b/vertex.cginc
@@ -59,67 +59,21 @@
 #define VERTEX_DEFORM_XY_UNTUBE_NORM
 #endif  // VERTEX_DEFORMATION_XY_UNTUBE
 
-#if defined(_VERTEX_DEFORMATION_XZ_TUBE)
-#define VERTEX_DEFORM_XZ_TUBE_PREAMBLE                    \
-  float3 p = _Vertex_Deformation_XZ_Tube_p;               \
-  float3 r = _Vertex_Deformation_XZ_Tube_r;               \
-  float3 s = _Vertex_Deformation_XZ_Tube_s;               \
-  float t = _Vertex_Deformation_XZ_Tube_t
-#define VERTEX_DEFORM_XZ_TUBE_POS                         \
+#if defined(_VERTEX_DEFORMATION_PLANE_TO_TUBE)
+#define VERTEX_DEFORM_PLANE_TO_TUBE_PREAMBLE                    \
+  float3 p = _Vertex_Deformation_Plane_To_Tube_p;               \
+  float3 r = _Vertex_Deformation_Plane_To_Tube_r;               \
+  float3 s = _Vertex_Deformation_Plane_To_Tube_s;               \
+  float t = _Vertex_Deformation_Plane_To_Tube_t
+#define VERTEX_DEFORM_PLANE_TO_TUBE_POS                         \
   objPos = plane_to_tube(objPos.xyz, p, r, s, t)
-#define VERTEX_DEFORM_XZ_TUBE_NORM                        \
+#define VERTEX_DEFORM_PLANE_TO_TUBE_NORM                        \
   plane_to_tube_normal(objPos.xyz, objNorm, objTan, p, r, s, t)
 #else
-#define VERTEX_DEFORM_XZ_TUBE_PREAMBLE
-#define VERTEX_DEFORM_XZ_TUBE_POS
-#define VERTEX_DEFORM_XZ_TUBE_NORM
-#endif  // VERTEX_DEFORMATION_XZ_TUBE
-
-#if defined(_VERTEX_DEFORMATION_YZ_TUBE)
-#define VERTEX_DEFORM_YZ_TUBE_PREAMBLE                    \
-  float3 p = _Vertex_Deformation_YZ_Tube_p;               \
-  float3 r = _Vertex_Deformation_YZ_Tube_r;               \
-  float3 s = _Vertex_Deformation_YZ_Tube_s;               \
-  float t = _Vertex_Deformation_YZ_Tube_t
-#define VERTEX_DEFORM_YZ_TUBE_POS                         \
-  objPos = plane_to_tube(objPos.yxz, p, r, s, t);            \
-  objPos = objPos.yxz
-#define VERTEX_DEFORM_YZ_TUBE_NORM                        \
-  float3 yzPos = objPos.yxz;                              \
-  float3 yzNorm = objNorm.yxz;                            \
-  float3 yzTan = objTan.yxz;                              \
-  plane_to_tube_normal(yzPos, yzNorm, yzTan, p, r, s, t);    \
-  objPos = yzPos.yxz;                                     \
-  objNorm = yzNorm.yxz;                                   \
-  objTan = yzTan.yxz
-#else
-#define VERTEX_DEFORM_YZ_TUBE_PREAMBLE
-#define VERTEX_DEFORM_YZ_TUBE_POS
-#define VERTEX_DEFORM_YZ_TUBE_NORM
-#endif  // VERTEX_DEFORMATION_YZ_TUBE
-
-#if defined(_VERTEX_DEFORMATION_XY_TUBE)
-#define VERTEX_DEFORM_XY_TUBE_PREAMBLE                    \
-  float3 p = _Vertex_Deformation_XY_Tube_p;               \
-  float3 r = _Vertex_Deformation_XY_Tube_r;               \
-  float3 s = _Vertex_Deformation_XY_Tube_s;               \
-  float t = _Vertex_Deformation_XY_Tube_t
-#define VERTEX_DEFORM_XY_TUBE_POS                         \
-  objPos = plane_to_tube(objPos.xzy, p, r, s, t);            \
-  objPos = objPos.xzy
-#define VERTEX_DEFORM_XY_TUBE_NORM                        \
-  float3 xyPos = objPos.xzy;                              \
-  float3 xyNorm = objNorm.xzy;                            \
-  float3 xyTan = objTan.xzy;                              \
-  plane_to_tube_normal(xyPos, xyNorm, xyTan, p, r, s, t);    \
-  objPos = xyPos.xzy;                                     \
-  objNorm = xyNorm.xzy;                                   \
-  objTan = xyTan.xzy
-#else
-#define VERTEX_DEFORM_XY_TUBE_PREAMBLE
-#define VERTEX_DEFORM_XY_TUBE_POS
-#define VERTEX_DEFORM_XY_TUBE_NORM
-#endif  // VERTEX_DEFORMATION_XY_TUBE
+#define VERTEX_DEFORM_PLANE_TO_TUBE_PREAMBLE
+#define VERTEX_DEFORM_PLANE_TO_TUBE_POS
+#define VERTEX_DEFORM_PLANE_TO_TUBE_NORM
+#endif  // VERTEX_DEFORMATION_PLANE_TO_TUBE
 
 #if defined(_VERTEX_DEFORMATION_NORM_CONVERSION)
 #define VERTEX_DEFORM_NORM_CONVERSION_PREAMBLE                    \
@@ -202,16 +156,8 @@ void deform(inout float3 objPos) {
     VERTEX_DEFORM_XY_UNTUBE_POS;
   }
   {
-    VERTEX_DEFORM_XZ_TUBE_PREAMBLE;
-    VERTEX_DEFORM_XZ_TUBE_POS;
-  }
-  {
-    VERTEX_DEFORM_YZ_TUBE_PREAMBLE;
-    VERTEX_DEFORM_YZ_TUBE_POS;
-  }
-  {
-    VERTEX_DEFORM_XY_TUBE_PREAMBLE;
-    VERTEX_DEFORM_XY_TUBE_POS;
+    VERTEX_DEFORM_PLANE_TO_TUBE_PREAMBLE;
+    VERTEX_DEFORM_PLANE_TO_TUBE_POS;
   }
   {
     VERTEX_DEFORM_NORM_CONVERSION_PREAMBLE;
@@ -246,16 +192,8 @@ void deform_normal(inout float3 objPos, inout float3 objNorm, inout float3 objTa
     VERTEX_DEFORM_XY_UNTUBE_NORM;
   }
   {
-    VERTEX_DEFORM_XZ_TUBE_PREAMBLE;
-    VERTEX_DEFORM_XZ_TUBE_NORM;
-  }
-  {
-    VERTEX_DEFORM_YZ_TUBE_PREAMBLE;
-    VERTEX_DEFORM_YZ_TUBE_NORM;
-  }
-  {
-    VERTEX_DEFORM_XY_TUBE_PREAMBLE;
-    VERTEX_DEFORM_XY_TUBE_NORM;
+    VERTEX_DEFORM_PLANE_TO_TUBE_PREAMBLE;
+    VERTEX_DEFORM_PLANE_TO_TUBE_NORM;
   }
   {
     VERTEX_DEFORM_NORM_CONVERSION_PREAMBLE;
@@ -275,217 +213,6 @@ void deform_normal(inout float3 objPos, inout float3 objNorm, inout float3 objTa
   }
 }
 
-// `objPos` is in the un-deformed coordinate system, while `objNorm` and
-// `objTan` are in the deformed coordinate system. The task is to map `objNorm`
-// and `objTan` to the un-deformed coordinate system.
-// We do this, coarsely, as follows:
-//  1. Map objPos into the deformed coordinate system through stepwise
-//     transformations, like `deform`. We remember each position along the way.
-//  2. Map objNorm and objTan back one step using the deformed final position.
-//     For the first iteration, we use the last (deformed) `objPos` that we
-//     remembered from step 1.
-//  3. Repeat step 2 until we're back in the un-deforme coordinate system. At
-//     each step, we use the cached objPos from the forward pass (step 1), so
-//     that we evaluate the normal deformation at the correct point in space.
-void undeform_normal(inout float3 objPos, inout float3 objNorm, inout float3 objTan) {
-  const float t = getTime();
-  const int kMaxDeformations = 32;
-  // Cache each intermediate position so we can undo stages in reverse order.
-  float3 posHistory[kMaxDeformations + 1];
-  int posCount = 0;
-  posHistory[posCount++] = objPos;
-
-#if defined(_VERTEX_DEFORMATION_XZ_UNTUBE)
-  {
-    VERTEX_DEFORM_XZ_UNTUBE_PREAMBLE;
-    VERTEX_DEFORM_XZ_UNTUBE_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_YZ_UNTUBE)
-  {
-    VERTEX_DEFORM_YZ_UNTUBE_PREAMBLE;
-    VERTEX_DEFORM_YZ_UNTUBE_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_XY_UNTUBE)
-  {
-    VERTEX_DEFORM_XY_UNTUBE_PREAMBLE;
-    VERTEX_DEFORM_XY_UNTUBE_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_XZ_TUBE)
-  {
-    VERTEX_DEFORM_XZ_TUBE_PREAMBLE;
-    VERTEX_DEFORM_XZ_TUBE_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_YZ_TUBE)
-  {
-    VERTEX_DEFORM_YZ_TUBE_PREAMBLE;
-    VERTEX_DEFORM_YZ_TUBE_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_XY_TUBE)
-  {
-    VERTEX_DEFORM_XY_TUBE_PREAMBLE;
-    VERTEX_DEFORM_XY_TUBE_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_NORM_CONVERSION)
-  {
-    VERTEX_DEFORM_NORM_CONVERSION_PREAMBLE;
-    VERTEX_DEFORM_NORM_CONVERSION_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_SEAL)
-  {
-    VERTEX_DEFORM_SEAL_PREAMBLE;
-    VERTEX_DEFORM_SEAL_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_SINE_WAVES)
-  {
-    VERTEX_DEFORM_SINE_WAVES_PREAMBLE;
-    VERTEX_DEFORM_SINE_WAVES_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_FBM)
-  {
-    VERTEX_DEFORM_FBM_PREAMBLE;
-    VERTEX_DEFORM_FBM_POS;
-    posHistory[posCount++] = objPos;
-  }
-#endif
-  float3 objPos_deformed = objPos;
-
-  int cursor = posCount - 1;
-  objPos = posHistory[cursor];
-
-#if defined(_VERTEX_DEFORMATION_FBM)
-  if (cursor > 0) {
-    VERTEX_DEFORM_FBM_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    fbm_undeform_normal(stageInput, st, amplitude, gain, lacunarity, scale,
-        octaves, velocity, objNorm, objTan);
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_SINE_WAVES)
-  if (cursor > 0) {
-    VERTEX_DEFORM_SINE_WAVES_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    sine_wave_undeform_normal(stageInput, objNorm, objTan, amplitude, direction,
-        k, omega, st);
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_SEAL)
-  if (cursor > 0) {
-    VERTEX_DEFORM_SEAL_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    seal_undeform_normal(stageInput, objNorm, objTan, A, k, st);
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_NORM_CONVERSION)
-  if (cursor > 0) {
-    VERTEX_DEFORM_NORM_CONVERSION_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    norm_conversion_undeform_normal(stageInput, objNorm, objTan, input_k, output_k, t);
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_XY_TUBE)
-  if (cursor > 0) {
-    VERTEX_DEFORM_XY_TUBE_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    float3 xyPos = stageInput.xzy;
-    float3 xyNorm = objNorm.xzy;
-    float3 xyTan = objTan.xzy;
-    plane_to_tube_undeform_normal(xyPos, xyNorm, xyTan, p, r, s, t);
-    objNorm = xyNorm.xzy;
-    objTan = xyTan.xzy;
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_YZ_TUBE)
-  if (cursor > 0) {
-    VERTEX_DEFORM_YZ_TUBE_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    float3 yzPos = stageInput.yxz;
-    float3 yzNorm = objNorm.yxz;
-    float3 yzTan = objTan.yxz;
-    plane_to_tube_undeform_normal(yzPos, yzNorm, yzTan, p, r, s, t);
-    objNorm = yzNorm.yxz;
-    objTan = yzTan.yxz;
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_XZ_TUBE)
-  if (cursor > 0) {
-    VERTEX_DEFORM_XZ_TUBE_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    plane_to_tube_undeform_normal(stageInput, objNorm, objTan, p, r, s, t);
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_XY_UNTUBE)
-  if (cursor > 0) {
-    VERTEX_DEFORM_XY_UNTUBE_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    float3 xyPos = stageInput.xzy;
-    float3 xyNorm = objNorm.xzy;
-    float3 xyTan = objTan.xzy;
-    tube_to_plane_undeform_normal(xyPos, xyNorm, xyTan, t);
-    objNorm = xyNorm.xzy;
-    objTan = xyTan.xzy;
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_YZ_UNTUBE)
-  if (cursor > 0) {
-    VERTEX_DEFORM_YZ_UNTUBE_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    float3 yzPos = stageInput.yxz;
-    float3 yzNorm = objNorm.yxz;
-    float3 yzTan = objTan.yxz;
-    tube_to_plane_undeform_normal(yzPos, yzNorm, yzTan, t);
-    objNorm = yzNorm.yxz;
-    objTan = yzTan.yxz;
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-#if defined(_VERTEX_DEFORMATION_XZ_UNTUBE)
-  if (cursor > 0) {
-    VERTEX_DEFORM_XZ_UNTUBE_PREAMBLE;
-    float3 stageInput = posHistory[cursor - 1];
-    tube_to_plane_undeform_normal(stageInput, objNorm, objTan, t);
-    objPos = stageInput;
-    cursor -= 1;
-  }
-#endif
-
-  objPos = objPos_deformed;
-}
-
 void propagateObjPos(inout v2f i) {
   i.worldPos = mul(unity_ObjectToWorld, float4(i.objPos, 1));
   i.pos = UnityObjectToClipPos(i.objPos);
diff --git a/vertex_deformation.slang b/vertex_deformation.slang
index c193889..3118394 100644
--- a/vertex_deformation.slang
+++ b/vertex_deformation.slang
@@ -91,8 +91,10 @@ float2 project_x_onto_y(float2 x, float2 y) {
   return (dot(x, y) / dot(y, y)) * y;
 }
 
-// Maps a 2x2 quad on the xy plane to a tube. The circular cross section
-// is on the xz plane.
+// Maps a 2x2 quad to a tube.
+// `s_cart` is the axis along which the tube is rolled.
+// `r_cart` is an axis along which points are not transformed. It is assumed to
+// be orthogonal `s_cart`.
 [Differentiable]
 public float3 plane_to_tube(float3 xyz,
     no_diff float3 p, no_diff float3 r_cart, no_diff float3 s_cart, no_diff float t) {
@@ -102,7 +104,7 @@ public float3 plane_to_tube(float3 xyz,
   r_cart = normalize(r_cart);
   s_cart = normalize(s_cart);
   float3 rxs_cart = cross(s_cart, r_cart);
-  float3x3 to_rsrxs = transpose(float3x3(r_cart, s_cart, rxs_cart));
+  float3x3 to_rsrxs = float3x3(r_cart, s_cart, rxs_cart);
   float3x3 to_cart  = inverse(to_rsrxs, determinant(to_rsrxs));
 
   // Translate origin to `p` then change into (r, s, r x s) basis.
@@ -118,23 +120,23 @@ public float3 plane_to_tube(float3 xyz,
   //  v0: vector of length ||Lr + Lv0|| at angle atan2(Lv0, Lr)
   //  v1: vector of length ||Lr|| at angle ||Lv0|| / ||Lr||
   // Interpolate in polar coordinates to make it wrap nicely.
-  float radius_src = length(float2(r, rxs));
-  float radius_dst = max(abs(r), epsilon);
+  float r0 = length(float2(r, rxs));
+  float r1 = max(abs(r), epsilon);
 
-  float angle_src = atan2(rxs, r);
-  float angle_dst = rxs / radius_dst;
+  float theta0 = atan2(rxs, r);
+  float theta1 = rxs / r1;
 
-  float delta = angle_dst - angle_src;
-  float angle = angle_src + t * delta;
+  // Interpolate polar coordinates.
+  float radius = dlerp(r0, r1, t);
+  float theta = dlerp(theta0, theta1, t);
 
-  // Radial interpolation per derivation.
-  float radius = dlerp(radius_src, radius_dst, t);
-  float2 nb_t = float2(cos(angle), sin(angle)) * radius;
+  // Map into (r, rxs) basis.
+  float2 nb_t = float2(cos(theta), sin(theta)) * radius;
 
-  // Reconstruct with preserved axial component.
+  // Un-project from (r, rxs) plane to full (r, s, rxs) basis.
   xyz = float3(nb_t.x, s, nb_t.y);
 
-  // Move back into cartesian basis.
+  // Map back to cartesian basis.
   xyz = mul(to_cart, xyz) + p;
 
   return xyz;