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new Conformal Square projection (with transition and shader and Euclidean form)

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Zeno Rogue
2023-03-19 12:21:05 +01:00
parent 02f0b1e714
commit 1b7f4b869e
4 changed files with 206 additions and 10 deletions
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68
shaders.cpp
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@@ -276,10 +276,15 @@ shared_ptr<glhr::GLprogram> write_shader(flagtype shader_flags) {
}
else if(pmodel == mdDisk && GDIM == 3 && !spherespecial && !nonisotropic && !gproduct) {
coordinator += "t /= (t[3] + uAlpha);\n";
vsh += "uniform mediump float uAlpha;";
vsh += "uniform mediump float uAlpha;\n";
shader_flags |= SF_DIRECT | SF_BOX | SF_ZFOG;
treset = true;
}
else if(pmodel == mdConformalSquare && pconf.model_transition == 1) {
shader_flags |= SF_ORIENT | SF_DIRECT;
coordinator += "t = uPP * t;", vsh += "uniform mediump mat4 uPP;";
coordinator += "t = to_square(t);";
}
else if(pmodel == mdBand && hyperbolic) {
shader_flags |= SF_BAND | SF_ORIENT | SF_BOX | SF_DIRECT;
coordinator += "t = uPP * t;", vsh += "uniform mediump mat4 uPP;";
@@ -848,6 +853,67 @@ EX void add_if(string& shader, const string& seek, const string& function) {
EX void add_fixed_functions(string& shader) {
/* from the most complex to the simplest */
add_if(shader, "to_square",
"mediump vec4 to_square(mediump vec4 h) {\n"
"float d = length(h.xy);\n"
"float x = d / (h.z + 1.);\n"
"float cos_phiosqrt2 = sqrt(2.) / (x + 1./x);\n"
"float cos_lambda = -h.y / d;\n"
"float sin_lambda = h.x / d;\n"
"float cos_a = cos_phiosqrt2 * (sin_lambda + cos_lambda);\n"
"float cos_b = cos_phiosqrt2 * (sin_lambda - cos_lambda);\n"
"float sin_a = sqrt(1. - cos_a * cos_a);\n"
"float sin_b = sqrt(1. - cos_b * cos_b);\n"
"float cos_a_cos_b = cos_a * cos_b;\n"
"float sin_a_sin_b = sin_a * sin_b;\n"
"float sin2_m = 1.0 + cos_a_cos_b - sin_a_sin_b;\n"
"float sin2_n = 1.0 - cos_a_cos_b - sin_a_sin_b;\n"
"float sin_m = sqrt_clamp(sin2_m);\n"
"float cos_m = sqrt_clamp(1. - sin2_m);\n"
"if(sin_lambda < 0.) sin_m = -sin_m;\n"
"float sin_n = sqrt_clamp(sin2_n);\n"
"float cos_n = sqrt_clamp(1.0 - sin2_n);\n"
"if(cos_lambda > 0.0) sin_n = -sin_n;\n"
"#define divby 0.53935260118837935472\n"
"vec4 res = vec4(ellFaux(cos_m,sin_m,sqrt(2.)/2.) * divby, ellFaux(cos_n,sin_n,sqrt(2.)/2.) * divby, 0, 1);\n"
"if(x > 1.) {\n"
" if(abs(res[0]) > abs(res[1])) {\n"
" if(res[0] > 0.) res[0] = 2. - res[0]; else res[0] = -2. - res[0];\n"
" }\n"
" else {\n"
" if(res[1] > 0.) res[1] = 2. - res[1]; else res[1] = -2. - res[1];\n"
" }\n"
" }\n"
"return res;\n"
"}\n");
add_if(shader, "sqrt_clamp", "mediump float sqrt_clamp(mediump float x) { return x >= 0. ? sqrt(x) : 0.; }\n");
add_if(shader, "ellFaux", "mediump float ellFaux(mediump float cos_phi, mediump float sin_phi, mediump float k) {\n"
"return sin_phi * ellRF(cos_phi * cos_phi, 1. - k * k * sin_phi * sin_phi, 1.);\n"
"}\n");
add_if(shader, "ellRF", "mediump float ellRF(mediump float x, mediump float y, mediump float z) {\n"
"float delx = 1., dely = 1., delz = 1.;\n"
"const float eps = 0.0025;\n"
"float mean;\n"
"while(abs(delx) > eps || abs(dely) > eps || abs(delz) > eps) {\n"
" float sx = sqrt(x);\n"
" float sy = sqrt(y);\n"
" float sz = sqrt(z);\n"
" float len = sx * (sy+sz) + sy * sz;\n"
" float x = .25 * (x+len);\n"
" float y = .25 * (y+len);\n"
" float z = .25 * (z+len);\n"
" mean = (x+y+z)/3.;\n"
" delx = (mean-x) / mean;\n"
" dely = (mean-y) / mean;\n"
" delz = (mean-z) / mean;\n"
" }\n"
"float e2 = delx * dely - delz * delz;\n"
"float e3 = delx * dely * delz;\n"
"return ((1.0 + (e2 / 24.0 - 0.1 - 3.0 * e3 / 44.0) * e2+ e3 / 14.) / sqrt(mean));\n"
"}\n");
add_if(shader, "tanh", "mediump float tanh(mediump float x) { return sinh(x) / cosh(x); }\n");
add_if(shader, "sinh", "mediump float sinh(mediump float x) { return (exp(x) - exp(-x)) / 2.0; }\n");
add_if(shader, "asin_clamp", "mediump float asin_clamp(mediump float x) { return x > 1. ? PI/2. : x < -1. ? -PI/2. : asin(x); }\n");