add plane<->tube deformation shader

1 files changed, 65 insertions, 27 deletions

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