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#ifndef __RAY_MARCHING_MAPS_INC
#define __RAY_MARCHING_MAPS_INC
#include "math.cginc"
#include "pema99.cginc"
// Macros for transforming normal and tangent using autodiff.
// r3r1 refers to "r3 to r1 transform", aka a mapping from a 3d real-valued
// space to a 1d space. This is intended for use with a ray marcher.
#define R3R1_DECLARE_BASIS_VECTORS(xyz) \
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 R3R1_AUTODIFF_BASIS_VECTORS(fun, ...) \
DifferentialPair<float> dp_x_out = fwd_diff(fun)(dp_x, __VA_ARGS__); \
DifferentialPair<float> dp_y_out = fwd_diff(fun)(dp_y, __VA_ARGS__); \
DifferentialPair<float> dp_z_out = fwd_diff(fun)(dp_z, __VA_ARGS__)
#define R3R1_DEFORM_NORMAL_AND_TANGENT(normal, tangent) \
{ \
float3 gradient = float3(dp_x_out.d, dp_y_out.d, dp_z_out.d); \
normal = normalize(gradient); \
float3 helper = abs(normal.z) < 0.999 ? float3(0, 0, 1) : float3(0, 1, 0); \
tangent = normalize(cross(helper, normal)); \
}
// Syntactic sugar - wraps the previous three macros.
#define R3R1_RAY_MARCH_NORMALS(xyz, normal, tangent, fun, ...) \
R3R1_DECLARE_BASIS_VECTORS(xyz); \
R3R1_AUTODIFF_BASIS_VECTORS(fun, __VA_ARGS__); \
R3R1_DEFORM_NORMAL_AND_TANGENT(normal, tangent)
[Differentiable]
public float map_ball(float3 p, no_diff float r) {
return length(p) - r;
}
public void map_ball_normal(float r, inout float3 xyz, inout float3 normal,
inout float3 tangent) {
R3R1_RAY_MARCH_NORMALS(xyz, normal, tangent, map_ball, r);
}
[Differentiable]
public float map_hexagon(float3 p, no_diff float2 h)
{
float3 q = abs(p);
const float3 k = float3(-0.8660254, 0.5, 0.57735);
p = abs(p);
p.xy -= 2.0*min(dot(k.xy, p.xy), 0.0)*k.xy;
float2 d = float2(
length(p.xy - float2(clamp(p.x, -k.z*h.x, k.z*h.x), h.x))*sign(p.y - h.x),
p.z-h.y );
return min(max(d.x,d.y),0.0) + length(max(d,0.0));
}
public void map_hexagon_normal(float2 h, inout float3 xyz, inout float3 normal,
inout float3 tangent) {
R3R1_RAY_MARCH_NORMALS(xyz, normal, tangent, map_hexagon, h);
}
#endif // __RAY_MARCHING_MAPS_INC
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