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relativistic projections added

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Zeno Rogue 2022-10-14 00:56:48 +02:00
parent 7a6df6f060
commit a7ca4c2902
5 changed files with 137 additions and 6 deletions
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8
classes.cpp
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@ -1007,9 +1007,9 @@ enum eModel : int {
mdHorocyclic, mdQuadrant, mdAxial, mdAntiAxial,
// 32..38
mdWerner, mdAitoff, mdHammer, mdLoximuthal, mdMiller, mdGallStereographic, mdWinkelTripel,
// 39..
mdPoorMan, mdPanini, mdRetroCraig, mdRetroLittrow, mdRetroHammer, mdThreePoint, mdLiePerspective, mdLieOrthogonal,
// 47..
// 39..48
mdPoorMan, mdPanini, mdRetroCraig, mdRetroLittrow, mdRetroHammer, mdThreePoint, mdLiePerspective, mdLieOrthogonal, mdRelPerspective, mdRelOrthogonal,
// 49..
mdGUARD, mdPixel, mdHyperboloidFlat, mdPolynomial, mdManual
};
#endif
@ -1069,6 +1069,8 @@ EX vector<modelinfo> mdinf = {
{X3("three-point equidistant"), mf::euc_boring, DEFAULTS},
{X3("Lie perspective"), mf::euc_boring, DEFAULTS},
{X3("Lie orthogonal"), mf::euc_boring, DEFAULTS},
{X3("relativistic perspective"), mf::euc_boring, DEFAULTS},
{X3("relativistic orthogonal"), mf::euc_boring, DEFAULTS},
{X3("guard"), mf::technical, DEFAULTS},
{X3("pixel"), mf::technical, DEFAULTS},
{X3("hypflat"), mf::technical, DEFAULTS},

2
drawing.cpp
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@ -483,6 +483,8 @@ bool behind3(shiftpoint h) {
return lp_apply(inverse_exp(h))[2] < 0;
if(pmodel == mdLiePerspective)
return lp_apply(lie_log(unshift(h)))[2] < 0;
if(pmodel == mdRelPerspective)
return lp_apply(rel_log(h))[2] < 0;
return h[2] < 0;
}

78
hypgraph.cpp
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@ -551,6 +551,13 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
return;
}
case mdRelPerspective: {
auto S = rel_log(H_orig); S[3] = 1;
S = lp_apply(S);
apply_perspective(S, ret);
return;
}
case mdPixel:
ret = H / current_display->radius;
return;
@ -796,6 +803,16 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
break;
}
case mdRelOrthogonal: {
ret = rel_log(H_orig);
ret *= .5;
ret[LDIM] = 1;
if(nonisotropic && !vrhr::rendering()) ret = lp_apply(ret);
break;
}
case mdHemisphere: {
#if CAP_VR
@ -2354,6 +2371,30 @@ EX void draw_model_elements() {
dynamicval<ld> lw(vid.linewidth, vid.linewidth * vid.multiplier_ring);
switch(pmodel) {
case mdRelOrthogonal:
case mdRelPerspective: {
constexpr ld cc = 3;
if(sl2) for(ld dist: {-0.1, 0.1}) {
transmatrix Lorentz = Id;
Lorentz[0][0] = Lorentz[2][2] = cosh(cc);
Lorentz[0][2] = Lorentz[2][0] = sinh(cc);
hyperpoint h = Lorentz * cspin(3, 2, dist) * C0;
for(int s=0; s<=360; s++)
curvepoint(spin(s*degree) * h);
queuecurve(shiftless(Id), ringcolor, 0, PPR::CIRCLE);
}
if(hyperbolic) for(ld dist: {-0.1, 0.1}) {
transmatrix Lorentz = Id;
Lorentz[0][0] = Lorentz[3][3] = cosh(cc);
Lorentz[0][3] = Lorentz[3][0] = sinh(cc);
hyperpoint h = Lorentz * hyperpoint(0, 0, cosh(dist), sinh(dist));
for(int s=0; s<=360; s++)
curvepoint(spin(s*degree) * h);
queuecurve(shiftless(Id), ringcolor, 0, PPR::CIRCLE);
}
return;
}
case mdRotatedHyperboles: {
queuestr(current_display->xcenter, current_display->ycenter + current_display->radius * pconf.alpha, 0, vid.fsize, "X", ringcolor, 1, 8);
return;
@ -3055,6 +3096,43 @@ EX hyperpoint lie_exp(hyperpoint h) {
return h;
}
EX hyperpoint rel_log(shiftpoint h) {
if(sl2) {
optimize_shift(h);
ld cycles = floor(h.shift / (2*M_PI) + .5);
hyperpoint h1 = unshift(h);
ld choice = h1[2] * h1[2] - h1[0] * h1[0] - h1[1] * h1[1];
ld r, z;
if(choice > 0) {
ld r = sqrt(choice);
ld z = asin_clamp(r);
if(h1[3] < 0) z = M_PI - z;
z += cycles * 2 * M_PI;
}
else if(cycles || h1[3] < -1 || choice == 0) {
/* impossible, or light-like */
r = 1; z = 0;
}
else {
r = sqrt(-choice);
z = asinh(r);
}
h1 = h1 * z / r;
h1[3] = 0;
return h1;
}
if(hyperbolic && GDIM == 3) {
hyperpoint h1 = h.h;
ld choice = h1[3] * h1[3] - h1[0] * h1[0] - h1[1] * h1[1];
ld r, z;
if(choice > 0) { r = sqrt(choice); z = asinh(r); }
else { r = sqrt(-choice); z = asin_clamp(r); if(h1[2] < 0) z = M_PI - z; }
h1 = h1 * z / r; h1[2] = h1[3]; h1[3] = 0;
return h1;
}
throw hr_exception("rel_log in wrong geometry");
}
EX hyperpoint lie_log(hyperpoint h) {
if(nil) {
h[3] = 0;

6
models.cpp
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@ -192,7 +192,7 @@ EX namespace models {
if(among(pm, mdBall, mdHemisphere)) return false;
return PIU(model_available(pm));
}
if(sl2) return among(pm, mdGeodesic, mdEquidistant, mdHorocyclic, mdPerspective);
if(sl2) return among(pm, mdGeodesic, mdEquidistant, mdRelPerspective, mdRelOrthogonal, mdHorocyclic, mdPerspective);
if(nonisotropic) return among(pm, mdDisk, mdPerspective, mdHorocyclic, mdGeodesic, mdEquidistant, mdFisheye, mdLiePerspective, mdLieOrthogonal);
if(sphere && (pm == mdHalfplane || pm == mdBall))
return false;
@ -230,7 +230,7 @@ EX namespace models {
}
EX bool is_perspective(eModel m) {
return among(m, mdPerspective, mdGeodesic, mdLiePerspective);
return among(m, mdPerspective, mdGeodesic, mdLiePerspective, mdRelPerspective);
}
EX bool is_3d(const projection_configuration& p) {
@ -258,7 +258,7 @@ EX namespace models {
if(m == mdHorocyclic && !sol) return XLAT("simple model: projection");
if(m == mdPerspective) return XLAT("simple model: perspective");
if(m == mdGeodesic) return XLAT("native perspective");
if(among(m, mdEquidistant, mdFisheye, mdHorocyclic, mdLiePerspective, mdLieOrthogonal)) return XLAT(mdinf[m].name_hyperbolic);
if(among(m, mdEquidistant, mdFisheye, mdHorocyclic, mdLiePerspective, mdLieOrthogonal, mdRelPerspective, mdRelOrthogonal)) return XLAT(mdinf[m].name_hyperbolic);
}
if(m == mdDisk && GDIM == 3) return XLAT("perspective in 4D");
if(m == mdHalfplane && GDIM == 3 && hyperbolic) return XLAT("half-space");

49
shaders.cpp
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@ -110,6 +110,49 @@ EX string shader_lie_log() {
}
}
EX string shader_rel_log() {
if(sl2) return
"uniform mediump float uIndexSL;\n"
"vec4 rel_log(vec4 h) {\n"
"float shift = uIndexSL + atan2(h[2], h[3]); \n"
"float ca = cos(uIndexSL); float sa = -sin(uIndexSL);\n"
"vec4 h1 = h;\n"
"h[2] = h1[2] * ca - h1[3] * sa; h[3] = h1[3] * ca + h1[2] * sa;\n"
"h[0] = h1[0] * ca - h1[1] * sa; h[1] = h1[1] * ca + h1[0] * sa;\n"
"h1 = h;"
"if(h1[3] <= 1. && h1[3] >= -1.) {\n"
"float r = sqrt(h1[2]*h1[2] - h1[0]*h1[0] - h1[1]*h1[1]);\n"
"float z = asin_clamp(r);\n"
"if(h1[3] < 0.) z = PI - z;\n"
"z += floor(shift / 2. / PI + .5) * 2. * PI;\n"
"float scale = z/r;\n"
"h1 = h1 * scale; h1[3] = 1.;\n"
"} else if(shift > PI || shift < -PI || h1[3] < -1.) { return vec4(0,0,0,1); } else {\n"
"float r = sqrt(h1[0]*h1[0] + h1[1]*h1[1] - h1[2]*h1[2]);\n"
"float z = asinh(r);\n"
"float scale = z/r;\n"
"h1 = h1 * scale; h1[3] = 1.;\n"
"}\n"
"return h1;\n"
"}\n";
if(hyperbolic && GDIM == 3) return
"vec4 rel_log(vec4 h) {\n"
" float choice = h[3] * h[3] - h[0] * h[0] - h[1] * h[1];\n"
" float z, r;\n"
" if(choice > 0.) { r = sqrt(choice); z = asinh(r); }\n"
" else { r = sqrt(-choice); z = asin_clamp(r); if(h[2] < 0.) z = PI - z; }\n"
" h = h * z / r; h[2] = h[3]; h[3] = 1.;\n"
" return h;\n"
" }\n";
println(hlog, "geometry is: ", geometry);
throw hr_exception("shader_rel_log in wrong geometry");
}
shared_ptr<glhr::GLprogram> write_shader(flagtype shader_flags) {
string varying, vsh, fsh, vmain = "void main() {\n", fmain = "void main() {\n";
@ -270,6 +313,12 @@ shared_ptr<glhr::GLprogram> write_shader(flagtype shader_flags) {
distfun = "length(t.xyz)";
vsh += shader_lie_log();
}
else if(pmodel == mdRelPerspective) {
shader_flags |= SF_PERS3 | SF_DIRECT;
coordinator += "t = rel_log(t);\n";
distfun = "length(t.xyz)";
vsh += shader_rel_log();
}
else if(pmodel == mdGeodesic) {
shader_flags |= SF_PERS3 | SF_DIRECT;
coordinator += "t = inverse_exp(t);\n";