diff options
Diffstat (limited to 'trochoid_math.cginc')
| -rw-r--r-- | trochoid_math.cginc | 43 |
1 files changed, 27 insertions, 16 deletions
diff --git a/trochoid_math.cginc b/trochoid_math.cginc index 3a5107e..82daf9c 100644 --- a/trochoid_math.cginc +++ b/trochoid_math.cginc @@ -17,16 +17,22 @@ float3 cyl2_to_troch_map(float3 v) const float d = _Trochoid_d; const float rrrr = (R - r) * R / r; + float rr_gcd = gcd(round(R), round(r)); + float rr_lcm = (R * r) / rr_gcd; + float rr_lcm_factor = rr_lcm / R; + float toff = _Time[0] * _Trochoid_Speed; + float x = - cos(v.x * R) * v.y * (R - r) * TROCH_POSITION_SCALE + - cos(v.x * rrrr) * v.y * d * TROCH_POSITION_SCALE; + cos(v.x * rr_lcm_factor * R + toff * 2.3 + toff) * v.y * (R - r) * TROCH_POSITION_SCALE + + cos(v.x * rr_lcm_factor * rrrr - toff * 2.9 + toff) * v.y * d * TROCH_POSITION_SCALE; float y = - sin(v.x * R) * v.y * (R - r) * TROCH_POSITION_SCALE - - sin(v.x * rrrr) * v.y * d * TROCH_POSITION_SCALE; + sin(v.x * rr_lcm_factor * R - toff * 3.1 + toff) * v.y * (R - r) * TROCH_POSITION_SCALE - + sin(v.x * rr_lcm_factor * rrrr + toff * 3.7 + toff) * v.y * d * TROCH_POSITION_SCALE; float z = - (v.x * v.y * R * TROCH_Z_THETA_SCALE + - cos(v.x * R * 5) * v.y * TROCH_POSITION_SCALE + - v.y * v.z); + (v.x * v.y * rr_lcm_factor * R * TROCH_Z_THETA_SCALE + + cos(v.x * rr_lcm_factor * R * 5 + toff * 4.1 + toff) * v.y * TROCH_POSITION_SCALE + + //v.y * v.z); + v.z); return float3(x, y, z); } @@ -63,25 +69,30 @@ float3x3 cyl2_to_troch_jacobian(float3 v) const float d = _Trochoid_d; const float rrrr = (R - r) * R / r; + float rr_gcd = gcd(round(R), round(r)); + float rr_lcm = (R * r) / rr_gcd; + float rr_lcm_factor = rr_lcm / R; + float toff = _Time[0] * _Trochoid_Speed; + #if 1 float3 df_dt = float3( - -R * sin(v.x * R) * v.y * (R - r) * TROCH_POSITION_SCALE + - -rrrr * sin(v.x * rrrr) * v.y * d * TROCH_POSITION_SCALE, + -R * rr_lcm_factor * sin(v.x * rr_lcm_factor * R + toff * 2.3 + toff) * v.y * (R - r) * TROCH_POSITION_SCALE + + -rrrr * rr_lcm_factor * sin(v.x * rr_lcm_factor * rrrr - toff * 2.9 + toff) * v.y * d * TROCH_POSITION_SCALE, - R * cos(v.x * R) * v.y * (R - r) * TROCH_POSITION_SCALE - - rrrr * cos(v.x * rrrr) * v.y * d * TROCH_POSITION_SCALE, + R * rr_lcm_factor * cos(v.x * rr_lcm_factor * R - toff * 3.1 + toff) * v.y * (R - r) * TROCH_POSITION_SCALE - + rrrr * rr_lcm_factor * cos(v.x * rr_lcm_factor * rrrr + toff * 3.7 + toff) * v.y * d * TROCH_POSITION_SCALE, v.y * R * TROCH_Z_THETA_SCALE - - R * 5 * sin(v.x * R * 5) * v.y * TROCH_POSITION_SCALE); + R * rr_lcm_factor *5 * sin(v.x * rr_lcm_factor * R * 5 + toff * 4.1 + toff) * v.y * TROCH_POSITION_SCALE); #else float3 df_dt = (cyl2_to_troch_map(v + float3(TROCH_EPSILON, 0, 0)) - cyl2_to_troch_map(v - float3(TROCH_EPSILON, 0, 0))) / (2 * TROCH_EPSILON); #endif #if 1 float3 df_dr = float3( - ((R - r) * cos(v.x * R) + d * cos((R - r) * v.x * R / r)) * TROCH_POSITION_SCALE, - ((R - r) * sin(v.x * R) - d * sin((R - r) * v.x * R / r)) * TROCH_POSITION_SCALE, - cos(v.x * R * 5) * TROCH_POSITION_SCALE); + ((R - r) * rr_lcm_factor * cos(v.x * rr_lcm_factor * R + toff * 2.3) + d * rr_lcm_factor * cos((R - r) * v.x * rr_lcm_factor * R / r + toff * 2.9)) * TROCH_POSITION_SCALE, + ((R - r) * rr_lcm_factor * sin(v.x * rr_lcm_factor * R + toff * 3.1) - d * rr_lcm_factor * sin((R - r) * v.x * rr_lcm_factor * R / r + toff * 3.7)) * TROCH_POSITION_SCALE, + rr_lcm_factor * cos(v.x * rr_lcm_factor * R * 5 + toff * 4.1) * TROCH_POSITION_SCALE); #else float3 df_dr = (cyl2_to_troch_map(v + float3(0, TROCH_EPSILON, 0)) - cyl2_to_troch_map(v - float3(0, TROCH_EPSILON, 0))) / (2 * TROCH_EPSILON); #endif @@ -90,7 +101,7 @@ float3x3 cyl2_to_troch_jacobian(float3 v) float3 df_dz = float3( 0, 0, - v.y); + 1); #else float3 df_dz = (cyl2_to_troch_map(v + float3(0, 0, TROCH_EPSILON)) - cyl2_to_troch_map(v - float3(0, 0, TROCH_EPSILON))) / (2 * TROCH_EPSILON); #endif |