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#ifndef __TROCHOID_MATH
#define __TROCHOID_MATH
#if defined(_TROCHOID)
#include "globals.cginc"
#define PI 3.14159265
#define TAU PI * 2.0
float3 _trochoid_map(float theta, float r0, float vert_z)
{
r0 = pow(r0, _Trochoid_r_Power);
r0 *= 100;
float R = _Trochoid_R;
float r = _Trochoid_r;
float d = _Trochoid_d;
theta *= max(R, r) * _Trochoid_theta_k;
float theta_t = theta + _Time[2] * _Trochoid_t_k;
float x = (R - r) * cos(theta_t) + d * cos((R - r) * theta_t / r);
float y = (R - r) * sin(theta_t) - d * sin((R - r) * theta_t / r);
float z = vert_z + cos(theta_t * 5) * .1 + theta * .0002;
float3 result = float3(x, y, z) * r0;
float3 trochoid_scale = float3(_Trochoid_X_Scale, _Trochoid_Y_Scale, _Trochoid_Z_Scale);
result *= trochoid_scale;
return result;
}
float3 trochoid_map(float3 pos)
{
float theta = atan2(pos.y, pos.x);
float r0 = length(pos.xy) * theta;
float z = pos.z;
float3 result = _trochoid_map(theta, r0, z);
return result;
}
float3 trochoid_normal(float3 pos)
{
// Parameters of the trochoid
float R = _Trochoid_R;
float r = _Trochoid_r;
float d = _Trochoid_d;
float theta_k = max(R, r) * _Trochoid_theta_k;
float t_k = _Trochoid_t_k;
float time = _Time[2];
float r_power = _Trochoid_r_Power;
// Intermediate variables based on input position
float r_orig = max(length(pos.xy), 1e-5); // Avoid division by zero
float theta = atan2(pos.y, pos.x);
float r0 = r_orig * theta;
float theta_scaled = theta * theta_k;
float theta_t = theta_scaled + time * t_k;
// Components of the trochoid function before final scaling
float C1 = cos(theta_t);
float S1 = sin(theta_t);
float common_factor = (R - r) / r;
float C2 = cos(common_factor * theta_t);
float S2 = sin(common_factor * theta_t);
float p_x = (R - r) * C1 + d * C2;
float p_y = (R - r) * S1 - d * S2;
float p_z = pos.z + cos(theta_t * 5.0) * 0.1 + theta * 0.0002;
// Partial derivatives of the components with respect to theta_t
float dp_x_dt = -(R - r) * S1 - d * common_factor * S2;
float dp_y_dt = (R - r) * C1 - d * common_factor * C2;
float dp_z_dt = -sin(theta_t * 5.0) * 5.0 * 0.1;
// Partial derivatives of intermediate variables w.r.t. pos.x and pos.y
float d_theta_dx = -pos.y / (r_orig * r_orig);
float d_theta_dy = pos.x / (r_orig * r_orig);
float d_r_orig_dx = pos.x / r_orig;
float d_r_orig_dy = pos.y / r_orig;
// The r0-dependent scaling factor and its derivative
float F = 100.0 * pow(r0, r_power);
float dF_dr0 = 100.0 * r_power * pow(r0, r_power - 1.0);
// Chain rule for tangents
// Tangent with respect to pos.x
float d_r0_dx = d_r_orig_dx * theta + r_orig * d_theta_dx;
float d_theta_t_dx = d_theta_dx * theta_k;
float dF_dx = dF_dr0 * d_r0_dx;
float dp_x_dx = dp_x_dt * d_theta_t_dx;
float dp_y_dx = dp_y_dt * d_theta_t_dx;
float dp_z_dx = dp_z_dt * d_theta_t_dx + 0.0002 * d_theta_dx;
float3 trochoid_scale = float3(_Trochoid_X_Scale, _Trochoid_Y_Scale, _Trochoid_Z_Scale);
float3 T_x = trochoid_scale * (dF_dx * float3(p_x, p_y, p_z) + F * float3(dp_x_dx, dp_y_dx, dp_z_dx));
// Tangent with respect to pos.y
float d_r0_dy = d_r_orig_dy * theta + r_orig * d_theta_dy;
float d_theta_t_dy = d_theta_dy * theta_k;
float dF_dy = dF_dr0 * d_r0_dy;
float dp_x_dy = dp_x_dt * d_theta_t_dy;
float dp_y_dy = dp_y_dt * d_theta_t_dy;
float dp_z_dy = dp_z_dt * d_theta_t_dy + 0.0002 * d_theta_dy;
float3 T_y = trochoid_scale * (dF_dy * float3(p_x, p_y, p_z) + F * float3(dp_x_dy, dp_y_dy, dp_z_dy));
return normalize(cross(T_x, T_y));
}
#endif // _TROCHOID
#endif // __TROCHOID_MATH
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