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nilv:: Nil shader, and improved geodesics

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Zeno Rogue
2019-08-06 20:55:41 +02:00
parent 9350053c49
commit 8ac64fc2a0
7 changed files with 68 additions and 35 deletions
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52
nonisotropic.cpp
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@@ -341,7 +341,7 @@ namespace nilv {
// v[1] = c sin alpha
// v[2] = w
if(v[0] == 0 && v[1] == 0) return v;
if(v[0] == 0 && v[1] == 0) return point31(v[0], v[1], v[2]);
if(v[2] == 0) return point31(v[0], v[1], v[0] * v[1] / 2);
@@ -361,7 +361,7 @@ namespace nilv {
ld side = h[2] - h[0] * h[1] / 2;
if(hypot_d(2, h) < 1e-6) return h;
if(hypot_d(2, h) < 1e-6) return point3(h[0], h[1], h[2]);
else if(side > 1e-6) {
wmin = 0, wmax = 2 * M_PI;
}
@@ -370,23 +370,23 @@ namespace nilv {
}
else return point3(h[0], h[1], 0);
ld alpha_total = atan2(h[1], h[0]);
ld alpha_total = h[0] ? atan(h[1] / h[0]) : M_PI/2;
ld cmul;
ld b;
if(abs(h[0]) > abs(h[1]))
cmul = h[0] / 2 / cos(alpha_total);
b = h[0] / 2 / cos(alpha_total);
else
cmul = h[1] / 2 / sin(alpha_total);
b = h[1] / 2 / sin(alpha_total);
ld sa = sin(2 * alpha_total);
ld s = sin(2 * alpha_total);
for(int it=0;; it++) {
ld w = (wmin + wmax) / 2;
ld c = cmul / sin(w/2);
ld z = w * (1 + (c*c/2) * ((1 - sin(w)/w) + (1-cos(w))/w * sa));
ld w = (wmin + wmax) / 2;
ld z = b * b * (s + (sin(w) - w)/(cos(w) - 1)) + w;
if(it == iterations) {
ld alpha = alpha_total - w/2;
ld c = b / sin(w/2);
return point3(c * w * cos(alpha), c * w * sin(alpha), w);
}
if(h[2] > z) wmin = w;
@@ -394,6 +394,36 @@ namespace nilv {
}
}
string nilshader =
"vec4 inverse_exp(vec4 h) {"
"float wmin, wmax;"
"float side = h[2] - h[0] * h[1] / 2.;"
"if(h[0]*h[0] + h[1]*h[1] < 1e-12) return vec4(h[0], h[1], h[2], 1);"
"if(side > 1e-6) { wmin = 0.; wmax = 2.*PI; }"
"else if(side < -1e-6) { wmin = -2.*PI; wmax = 0.; }"
"else return vec4(h[0], h[1], 0., 1.);"
"float at = h[0] != 0. ? atan(h[1] / h[0]) : PI/2.;"
"float b = abs(h[0]) > abs(h[1]) ? h[0] / 2. / cos(at) : h[1] / 2. / sin(at);"
"float s = sin(2. * at);"
"for(int it=0; it<50; it++) {"
"float w = (wmin + wmax) / 2.;"
"float z = b * b * (s + (sin(w) - w)/(cos(w) - 1.)) + w;"
"if(h[2] > z) wmin = w;"
"else wmax = w;"
"}"
"float w = (wmin + wmax) / 2.;"
"float alpha = at - w/2.;"
"float c = b / sin(w/2.);"
"return vec4(c*w*cos(alpha), c*w*sin(alpha), w, 1.);"
/* "float w = atan(side) * 4.;"
"float alpha = at - w/2.;"
"float c = b / sin(w/2.);"
"return vec4(c*w*cos(alpha), c*w*sin(alpha), w, 1.);" */
"}";
struct mvec : array<int, 3> {
mvec() { }