diff options
Diffstat (limited to 'tooner_lighting.cginc')
| -rw-r--r-- | tooner_lighting.cginc | 28 |
1 files changed, 19 insertions, 9 deletions
diff --git a/tooner_lighting.cginc b/tooner_lighting.cginc index e088c17..adf7890 100644 --- a/tooner_lighting.cginc +++ b/tooner_lighting.cginc @@ -137,9 +137,8 @@ v2f vert(appdata v) #if defined(_TROCHOID) { - float theta = v.uv0.x * TAU; - float r0 = length(v.vertex.xyz); - v.vertex.xyz = trochoid_map(theta, r0, v.vertex.z); + o.objPos_pre_trochoid = v.vertex.xyz; + v.vertex.xyz = cyl2_to_troch_map(cyl_to_cyl2_map(cart_to_cyl_map(v.vertex.xyz))); } #endif #if defined(_FACE_ME_WORLD_Y) @@ -1598,12 +1597,23 @@ float4 effect(inout v2f i, out float depth) #if defined(_TROCHOID) { - i.normal = trochoid_normal(i.objPos.xyz, i.uv0); - - float theta = i.uv0.x * TAU; - float r0 = length(i.objPos.xyz); - float z = i.objPos.z; - i.objPos.xyz = trochoid_map(theta, r0, z); + // Let h(v) be the trochoid of the cartesian coordinates v. + // We evaluate h(v) by first mapping it to cylindrical coordinates, then applying a trochoid function defined on those coordinates: + // h(v) = h_cyl(g(v)) + // g(v) maps v to cylindrical coordinates. + // h_cyl(v) evaluates the trochoid function on cylindrical coordinates. + // We want to compute h'(v), i.e. its Jacobian. + // By the chain rule: + // h'(v) = h_cyl'(g(v)) * g'(v) + // The reality is a little more complex: we also apply a distortion to the cylindrical coordinates: + // h(v) = h_cyl(f(g(v))) + // where f(v) is that distortion. + // Again, by the chain rule: + // h'(v) = h_cyl'(f(g(v))) * f'(g(v)) * g'(v) + float3x3 j0 = cart_to_cyl_jacobian(i.objPos_pre_trochoid); + float3x3 j1 = cyl_to_cyl2_jacobian(cart_to_cyl_map(i.objPos_pre_trochoid)); + float3x3 j2 = cyl2_to_troch_jacobian(cyl_to_cyl2_map(cart_to_cyl_map(i.objPos_pre_trochoid))); + i.normal = normalize(mul(transpose(invert(mul(j0, mul(j1, j2)))), i.normal)); } #endif |