add plane<->tube deformation shader

5 files changed, 74 insertions, 44 deletions

diff --git a/3ner.cginc b/3ner.cginc
index 4b98812..a1ab224 100644
--- a/3ner.cginc
+++ b/3ner.cginc
@@ -184,14 +184,15 @@ float4 frag(v2f i, uint facing : SV_IsFrontFace
   i.normal *= facing ? 1 : -1;
   i.normal = normalize(i.normal);
   i.tangent.xyz = normalize(i.tangent.xyz);
+
   Pbr pbr = getPbr(i);
 #if defined(_UNLIT)
   return pbr.albedo;
-#else
+#endif
+
   LightData light_data;
   GetLighting(i, pbr, light_data);
   return brdf(pbr, light_data);
-#endif
 }
 
 #endif  // __3NER_INC
diff --git a/3ner.shader b/3ner.shader
index 47d414b..b31e85f 100644
--- a/3ner.shader
+++ b/3ner.shader
@@ -48,9 +48,7 @@ Shader "yum_food/3ner"
           //ifex _Custom31_Tubes_Enabled==0
           [HideInInspector] m_start_Custom31_Tubes("Tubes", Float) = 0
             [ThryToggle(_CUSTOM31_TUBES)] _Custom31_Tubes_Enabled("Enable", Float) = 0
-            _Custom31_Tubes_A("A", Range(0,1)) = 0
-            _Custom31_Tubes_k("k", Range(0,8)) = 1
-            _Custom31_Tubes_tk("time factor", Range(0,10)) = 1
+            _Custom31_Tubes_t("t", Range(0,1)) = 1
           [HideInInspector] m_end_Custom31_Tubes("Tubes", Float) = 0
           //endex
 
diff --git a/custom31.slang b/custom31.slang
index 4b0e003..1254800 100644
--- a/custom31.slang
+++ b/custom31.slang
@@ -1,14 +1,44 @@
 #ifndef __CUSTOM31_INC
 #define __CUSTOM31_INC
 
-#define PI 3.14159265f
-
-float3x3 inverse(float3x3 m) {
-  float det =
-    m._11 * (m._22 * m._33 - m._23 * m._32) -
-    m._12 * (m._21 * m._33 - m._23 * m._31) +
-    m._13 * (m._21 * m._32 - m._22 * m._31);
-
+#define PI     3.14159265f
+#define PI_RCP 0.31830988f
+
+// Differentiable absolute value.
+#define dabs(x) length(float2(x, 1e-6))
+#define dlerp(x, y, t) ((x) * (1-t) + (y) * t)
+
+// Macros for transforming normal and tangent using autodiff.
+// r3r3 refers to "r3 to r3 transform", aka a mapping between 3d real-valued
+// spaces.
+#define R3R3_DECLARE_BASIS_VECTORS \
+  DifferentialPair<float3> dp_x = diffPair(xyz, float3(1, 0, 0)); \
+  DifferentialPair<float3> dp_y = diffPair(xyz, float3(0, 1, 0)); \
+  DifferentialPair<float3> dp_z = diffPair(xyz, float3(0, 0, 1))
+
+#define R3R3_AUTODIFF_BASIS_VECTORS(fun, ...) \
+  DifferentialPair<float3> dp_x_out = fwd_diff(fun)(dp_x, __VA_ARGS__); \
+  DifferentialPair<float3> dp_y_out = fwd_diff(fun)(dp_y, __VA_ARGS__); \
+  DifferentialPair<float3> dp_z_out = fwd_diff(fun)(dp_z, __VA_ARGS__)
+
+#define R3R3_DEFORM_NORMAL_AND_TANGENT(normal, tangent) \
+  float3x3 jacobian = float3x3(                           \
+    float3(dp_x_out.d.x, dp_y_out.d.x, dp_z_out.d.x),     \
+    float3(dp_x_out.d.y, dp_y_out.d.y, dp_z_out.d.y),     \
+    float3(dp_x_out.d.z, dp_y_out.d.z, dp_z_out.d.z)      \
+  );                                                      \
+  float jac_det = determinant(jacobian);                  \
+  float3x3 itjac = inverse(transpose(jacobian), jac_det); \
+  normal = normalize(mul(itjac, normal)) * sign(jac_det); \
+  tangent = normalize(mul(jacobian, tangent))
+
+// Syntactic sugar - wraps the previous three macros.
+#define R3R3_NORMALS(normal, tangent, fun, ...) \
+  R3R3_DECLARE_BASIS_VECTORS;   \
+  R3R3_AUTODIFF_BASIS_VECTORS(fun, __VA_ARGS__);  \
+  R3R3_DEFORM_NORMAL_AND_TANGENT(normal, tangent)
+
+float3x3 inverse(float3x3 m, float det) {
   if (abs(det) < 1e-6) {
     return float3x3(
         1,0,0,
@@ -53,26 +83,34 @@ public float3 c31_deform(float3 xyz, no_diff float A, no_diff float k, no_diff f
   );
 }
 
+
 // Deform a normal vector using the inverse transpose of the jacobian.
-public void c31_deform_normal(float3 xyz, inout float3 normal, inout float3 tangent, float A, float k, float t) {
-  // Compute jacobian using autodiff applied to basis vectors.
-  DifferentialPair<float3> dp_x = diffPair(xyz, float3(1, 0, 0));
-  DifferentialPair<float3> dp_y = diffPair(xyz, float3(0, 1, 0));
-  DifferentialPair<float3> dp_z = diffPair(xyz, float3(0, 0, 1));
-
-  DifferentialPair<float3> dp_x_out = fwd_diff(c31_deform)(dp_x, A, k, t);
-  DifferentialPair<float3> dp_y_out = fwd_diff(c31_deform)(dp_y, A, k, t);
-  DifferentialPair<float3> dp_z_out = fwd_diff(c31_deform)(dp_z, A, k, t);
-
-  // Transform normal and tangent using jacobian
-  float3x3 jacobian = float3x3(
-    float3(dp_x_out.d.x, dp_y_out.d.x, dp_z_out.d.x),
-    float3(dp_x_out.d.y, dp_y_out.d.y, dp_z_out.d.y),
-    float3(dp_x_out.d.z, dp_y_out.d.z, dp_z_out.d.z)
-  );
-  float3x3 itjac = inverse(transpose(jacobian));
-  normal = normalize(mul(itjac, normal));
-  tangent = normalize(mul(jacobian, tangent));
+public void c31_deform_normal(float3 xyz, inout float3 normal,
+    inout float3 tangent, float A, float k, float t) {
+  R3R3_NORMALS(normal, tangent, c31_deform, A, k, t);
+}
+
+// Takes map 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) {
+  float x0 = xyz.x;
+  float y0 = xyz.y;
+  float z0 = xyz.z;
+
+  float theta = x0 * PI;
+  float radius = min(1e3, (1.0f / (t * t)));
+
+  float x = sin(theta / radius) * radius * PI_RCP;
+  // The z0 term here is required to make the jacobian invertible.
+  float z = z0 + (1.0f - cos(theta / radius)) * radius * PI_RCP;
+
+  return float3(x, y0, z);
+}
+
+public void plane_to_tube_normal(float3 xyz, inout float3 normal,
+    inout float3 tangent, float t) {
+  R3R3_NORMALS(normal, tangent, plane_to_tube, t);
 }
 
 #endif  // __CUSTOM31_INC
diff --git a/globals.cginc b/globals.cginc
index f615136..38a1019 100644
--- a/globals.cginc
+++ b/globals.cginc
@@ -58,10 +58,7 @@ texture2D _Cloth_Sheen_DFG_LUT;
 #endif  // _CLOTH_SHEEN
 
 #if defined(_CUSTOM31_TUBES)
-float _Custom31_Tubes_Speed;
-float _Custom31_Tubes_A;
-float _Custom31_Tubes_k;
-float _Custom31_Tubes_tk;
+float _Custom31_Tubes_t;
 #endif  // _CUSTOM31_TUBES
 
 #endif  // __GLOBALS_INC
diff --git a/vertex.cginc b/vertex.cginc
index 0140ff2..fd08bbb 100644
--- a/vertex.cginc
+++ b/vertex.cginc
@@ -5,19 +5,15 @@
 
 void deform(inout float3 objPos) {
 #if defined(_CUSTOM31_TUBES)
-  float A = _Custom31_Tubes_A;
-  float k = _Custom31_Tubes_k;
-  float t = _Time[2] * _Custom31_Tubes_tk;
-  objPos = c31_deform(objPos, A, k, t);
+  float t = _Custom31_Tubes_t;
+  objPos = plane_to_tube(objPos, t);
 #endif  // _CUSTOM31_TUBES
 }
 
 void deform_normal(float3 objPos, inout float3 objNorm, inout float3 objTan) {
 #if defined(_CUSTOM31_TUBES)
-  float A = _Custom31_Tubes_A;
-  float k = _Custom31_Tubes_k;
-  float t = _Time[2] * _Custom31_Tubes_tk;
-  c31_deform_normal(objPos, objNorm, objTan, A, k, t);
+  float t = _Custom31_Tubes_t;
+  plane_to_tube_normal(objPos, objNorm, objTan, t);
 #endif  // _CUSTOM31_TUBES
 }