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fixes to Lie log/exp in SL2

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Zeno Rogue
2022-12-29 21:19:08 +01:00
parent 78fb0cca20
commit 7068b41d28
2 changed files with 25 additions and 13 deletions
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35
hypgraph.cpp
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@@ -3087,7 +3087,9 @@ EX void rotate_view(transmatrix T) {
if(!gproduct && !rug::rugged) current_display->which_copy = T * current_display->which_copy;
}
EX hyperpoint lie_exp(hyperpoint h) {
EX shiftpoint lie_exp(hyperpoint h1) {
shiftpoint sh = shiftless(h1);
auto& h = sh.h;
if(nil) {
h[3] = 1;
h[2] += h[0] * h[1] / 2;
@@ -3120,16 +3122,21 @@ EX hyperpoint lie_exp(hyperpoint h) {
else if(sl2) {
h[3] = 0;
ld v = h[0] * h[0] + h[1] * h[1] - h[2] * h[2];
if(v > 0) {
h *= sin(v) / sqrt(v);
println(hlog, "v = ", v);
if(v < 0) {
v = sqrt(-v);
h *= sin(v) / v;
h[3] += cos(v);
ld cycles = floor(v / TAU + .5);
sh.shift += TAU * cycles * (h[2] > 0 ? 1 : -1);
}
else if(v < 0) {
h *= sinh(v) / sqrt(-v);
else if(v > 0) {
v = sqrt(v);
h *= sinh(v) / v;
h[3] += cosh(v);
}
else h[3]++;
return h;
return sh;
}
else {
/* not implemented -- approximate for now */
@@ -3141,11 +3148,10 @@ EX hyperpoint lie_exp(hyperpoint h) {
for(int i=0; i<16; i++) T = T * T;
h = tC0(T);
}
return h;
return sh;
}
/** With relativistic_length off, compute the Lie logarithm in SL(2,R) or de Sitter space.
* With relativistic_length on, this corresponds to a geodesic in AdS/dS, so make it as long as the length of the geodesic in AdS/dS space.
/** Compute the Lie logarithm in SL(2,R), which corresponds to a geodesic in AdS; or a geodesic in de Sitter space.
**/
EX hyperpoint rel_log(shiftpoint h, bool relativistic_length) {
@@ -3161,7 +3167,11 @@ EX hyperpoint rel_log(shiftpoint h, bool relativistic_length) {
if(h1[3] < 0) z = M_PI - z;
z += cycles * TAU;
}
else if(cycles || h1[3] < -1 || choice == 0) {
else if(cycles || h1[3] < -1) {
/* impossible, or light-like */
r = 1; z = 0;
}
else if(choice == 0) {
if(!relativistic_length) return h1 - C0;
/* impossible, or light-like */
r = 1; z = 0;
@@ -3170,7 +3180,6 @@ EX hyperpoint rel_log(shiftpoint h, bool relativistic_length) {
r = sqrt(-choice);
z = asinh(r);
}
if(!relativistic_length) r = sqhypot_d(3, h1);
h1 = h1 * z / r;
h1[3] = 0;
return h1;
@@ -3255,7 +3264,7 @@ EX hyperpoint lie_log_correct(const shiftpoint H_orig, hyperpoint& H) {
return lie_log(H_orig);
}
/** shift the view according to the given tangent vector */
/** Shift the view according to the given tangent vector. NOTE: known bug when // note: possible error when lie_exp includes a shift!*/
EX transmatrix get_shift_view_of(const hyperpoint H, const transmatrix V, eShiftMethod sm IS(shift_method(smaManualCamera))) {
switch(sm) {
case smProduct:
@@ -3268,7 +3277,7 @@ EX transmatrix get_shift_view_of(const hyperpoint H, const transmatrix V, eShift
transmatrix IV = view_inverse(View);
transmatrix view_shift = eupush( tC0(IV) );
transmatrix rot = V * view_shift;
hyperpoint tH = lie_exp(inverse(rot) * H);
hyperpoint tH = lie_exp(inverse(rot) * H).h;
return rot * eupush(tH) * inverse(view_shift);
}
case smGeodesic:

3
shaders.cpp
View File

@@ -105,6 +105,9 @@ EX string shader_lie_log() {
else if(hyperbolic) {
return "vec4 lie_log(vec4 v) { v = deparabolic13(v); v[3] = 1.; /* if(abs(v[0]) > 1e-6) { float m = v[0] / (exp(v[0]) - 1.); v[1] *= m; v[2] *= m; } */ return v; }\n";
}
else if(sl2) {
return shader_rel_log() + "vec4 lie_log(vec4 h) { return rel_log(h); }\n";
}
else {
return "vec4 lie_log(vec4 v) { return v; }\n";
}