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raycasting:: Nil using geodesic formulas

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This commit is contained in:
Zeno Rogue 2019-10-23 23:09:49 +02:00
parent be9cea07b3
commit 0905117869
1 changed files with 58 additions and 2 deletions
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60
raycaster.cpp
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@ -218,12 +218,63 @@ void enable_raycaster() {
fmain +=
" dist = next < minstep ? 2.*next : next;\n";
fmain +=
if(nil) fsh +=
"vec4 translate(vec4 a, vec4 b) {\n"
"return vec4(a[0] + b[0], a[1] + b[1], a[2] + b[2] + a[0] * b[1], b[3]);\n"
"}\n"
"vec4 translatev(vec4 a, vec4 t) {\n"
"return vec4(t[0], t[1], t[2] + a[0] * t[1], 0.);\n"
"}\n"
"vec4 itranslate(vec4 a, vec4 b) {\n"
"return vec4(-a[0] + b[0], -a[1] + b[1], -a[2] + b[2] - a[0] * (b[1]-a[1]), b[3]);\n"
"}\n"
"vec4 itranslatev(vec4 a, vec4 t) {\n"
"return vec4(t[0], t[1], t[2] - a[0] * t[1], 0.);\n"
"}\n";
if(nil) fmain += "tangent = translate(position, itranslate(position, tangent));\n";
if(sol) fmain +=
"vec4 acc = christoffel(position, tangent, tangent);\n"
"vec4 pos2 = position + tangent * dist / 2.;\n"
"vec4 tan2 = tangent + acc * dist / 2.;\n"
"vec4 acc2 = christoffel(pos2, tan2, tan2);\n"
"vec4 nposition = position + tangent * dist + acc2 / 2. * dist * dist;\n";
if(nil) {
fmain +=
"vec4 xp, xt;\n"
"vec4 back = itranslatev(position, tangent);\n"
"if(back.x == 0. && back.y == 0.) {\n"
" xp = vec4(0., 0., back.z*dist, 1.);\n"
" xt = back;\n"
" }\n"
"else if(abs(back.z) == 0.) {\n"
" xp = vec4(back.x*dist, back.y*dist, back.x*back.y*dist*dist/2., 1.);\n"
" xt = vec4(back.x, back.y, dist*back.x*back.y, 0.);\n"
" }\n"
"else if(abs(back.z) < 1e-1) {\n"
// we use the midpoint method here, because the formulas below cause glitches due to float precision
" vec4 acc = christoffel(vec4(0,0,0,1), back, back);\n"
" vec4 pos2 = back * dist / 2.;\n"
" vec4 tan2 = back + acc * dist / 2.;\n"
" vec4 acc2 = christoffel(pos2, tan2, tan2);\n"
" xp = vec4(0,0,0,1) + back * dist + acc2 / 2. * dist * dist;\n"
" xt = back + acc * dist;\n"
" }\n"
"else {\n"
" float alpha = atan2(back.y, back.x);\n"
" float w = back.z * dist;\n"
" float c = length(back.xy) / back.z;\n"
" xp = vec4(2.*c*sin(w/2.) * cos(w/2.+alpha), 2.*c*sin(w/2.)*sin(w/2.+alpha), w*(1.+(c*c/2.)*((1.-sin(w)/w)+(1.-cos(w))/w * sin(w+2.*alpha))), 1.);\n"
" xt = back.z * vec4("
"c*cos(alpha+w),"
"c*sin(alpha+w),"
"1. + c*c*2.*sin(w/2.)*sin(alpha+w)*cos(alpha+w/2.),"
"0.);\n"
" }\n"
"vec4 nposition = translate(position, xp);\n";
}
if(nil) fmain +=
"float rz = (abs(nposition.x) > abs(nposition.y) ? -nposition.x*nposition.y : 0.) + nposition.z;\n";
@ -262,8 +313,13 @@ void enable_raycaster() {
"next = maxstep;\n"
"}\n";
if(nil) fmain +=
"tangent = translatev(position, xt);\n";
fmain +=
"position = nposition;\n"
"position = nposition;\n";
if(!nil) fmain +=
"tangent = tangent + acc * dist;\n";
}
else fmain +=