diff options
Diffstat (limited to 'custom31.slang')
| -rw-r--r-- | custom31.slang | 92 |
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 |