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primitive rendering now implemented for stretched H2xE; removed the old implementation of SL(2,R)

This commit is contained in:
Zeno Rogue 2020-07-22 00:19:13 +02:00
parent 9ba448af94
commit 7e85f07458
7 changed files with 381 additions and 269 deletions
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1
drawing.cpp
View File

@ -2039,7 +2039,6 @@ EX void draw_main() {
if(ray::in_use && !ray::comparison_mode) {
ray::cast();
reset_projection();
if(stretch::in()) return; /*primitive not implemented */
}
DEBB(DF_GRAPH, ("outcircle"));

3
geom-exp.cpp
View File

@ -874,8 +874,7 @@ EX void showEuclideanMenu() {
dialog::editNumber(stretch::factor, -1, 9, 0.1, 0, XLAT("stretched geometry"),
XLAT(
"Stretch the metric along the fibers. This can currently be done in rotation spaces and in 8-cell, 24-cell and 120-cell. "
"Value of 0 means not stretched, -1 means S2xE or H2xE (works only in the limit). "
"Only the raycaster is implemented for stretched geometry, so you will see only walls. (Must be > -1)"
"Value of 0 means not stretched, -1 means S2xE or H2xE (works only in the limit). (Must be > -1)"
)
);
dialog::reaction = ray::reset_raycaster;

7
glhr.cpp
View File

@ -274,7 +274,7 @@ struct GLprogram {
GLuint vertShader, fragShader;
GLint uFog, uFogColor, uColor, tTexture, tInvExpTable, uMV, uProjection, uAlpha, uFogBase, uPP;
GLint uPRECX, uPRECY, uPRECZ, uIndexSL, uIterations, uLevelLines;
GLint uPRECX, uPRECY, uPRECZ, uIndexSL, uIterations, uLevelLines, uSV;
flagtype shader_flags;
@ -397,6 +397,7 @@ GLprogram::GLprogram(string vsh, string fsh) {
uPRECY = glGetUniformLocation(_program, "PRECY");
uPRECZ = glGetUniformLocation(_program, "PRECZ");
uIndexSL = glGetUniformLocation(_program, "uIndexSL");
uSV = glGetUniformLocation(_program, "uSV");
uIterations = glGetUniformLocation(_program, "uIterations");
uLevelLines = glGetUniformLocation(_program, "uLevelLines");
}
@ -411,6 +412,10 @@ EX void set_index_sl(ld x) {
glUniform1f(glhr::current_glprogram->uIndexSL, x);
}
EX void set_sv(ld x) {
glUniform1f(glhr::current_glprogram->uSV, x);
}
EX void set_sl_iterations(int steps) {
glUniform1i(glhr::current_glprogram->uIterations, steps);
}

11
hyperpoint.cpp
View File

@ -211,6 +211,7 @@ EX ld sin_auto(ld x) {
case gcHyperbolic: return sinh(x);
case gcSphere: return sin(x);
case gcProduct: return PIU(sin_auto(x));
case gcSL2: return sinh(x);
default: return x;
}
}
@ -221,6 +222,7 @@ EX ld asin_auto(ld x) {
case gcHyperbolic: return asinh(x);
case gcSphere: return asin(x);
case gcProduct: return PIU(asin_auto(x));
case gcSL2: return asinh(x);
default: return x;
}
}
@ -230,6 +232,7 @@ EX ld acos_auto(ld x) {
case gcHyperbolic: return acosh(x);
case gcSphere: return acos(x);
case gcProduct: return PIU(acos_auto(x));
case gcSL2: return acosh(x);
default: return x;
}
}
@ -266,6 +269,7 @@ EX ld asin_auto_clamp(ld x) {
switch(cgclass) {
case gcEuclid: return x;
case gcHyperbolic: return asinh(x);
case gcSL2: return asinh(x);
case gcSphere: return asin_clamp(x);
default: return x;
}
@ -274,6 +278,7 @@ EX ld asin_auto_clamp(ld x) {
EX ld acos_auto_clamp(ld x) {
switch(cgclass) {
case gcHyperbolic: return x < 1 ? 0 : acosh(x);
case gcSL2: return x < 1 ? 0 : acosh(x);
case gcSphere: return x > 1 ? 0 : x < -1 ? M_PI : acos(x);
case gcProduct: return PIU(acos_auto_clamp(x));
default: return x;
@ -284,6 +289,7 @@ EX ld cos_auto(ld x) {
switch(cgclass) {
case gcEuclid: return 1;
case gcHyperbolic: return cosh(x);
case gcSL2: return cosh(x);
case gcSphere: return cos(x);
case gcProduct: return PIU(cos_auto(x));
default: return 1;
@ -296,6 +302,7 @@ EX ld tan_auto(ld x) {
case gcHyperbolic: return tanh(x);
case gcSphere: return tan(x);
case gcProduct: return PIU(tan_auto(x));
case gcSL2: return tanh(x);
default: return 1;
}
}
@ -306,6 +313,7 @@ EX ld atan_auto(ld x) {
case gcHyperbolic: return atanh(x);
case gcSphere: return atan(x);
case gcProduct: return PIU(atan_auto(x));
case gcSL2: return atanh(x);
default: return x;
}
}
@ -314,6 +322,7 @@ EX ld atan2_auto(ld y, ld x) {
switch(cgclass) {
case gcEuclid: return y/x;
case gcHyperbolic: return atanh(y/x);
case gcSL2: return atanh(y/x);
case gcSphere: return atan2(y, x);
case gcProduct: return PIU(atan2_auto(y, x));
default: return y/x;
@ -1207,7 +1216,7 @@ EX hyperpoint tangent_length(hyperpoint dir, ld length) {
EX hyperpoint direct_exp(hyperpoint v) {
if(sn::in()) return nisot::numerical_exp(v);
if(nil) return nilv::formula_exp(v);
if(sl2) return slr::formula_exp(v);
if(sl2 || stretch::in()) return rots::formula_exp(v);
if(prod) return product::direct_exp(v);
ld d = hypot_d(GDIM, v);
if(d > 0) for(int i=0; i<GDIM; i++) v[i] = v[i] * sin_auto(d) / d;

625
nonisotropic.cpp
View File

@ -1586,70 +1586,9 @@ EX }
EX namespace slr {
/* This implementation is based on:
// https://pdfs.semanticscholar.org/bf46/824df892593a1b6d1c84a5f99e90eece7c54.pdf
// However, to make it consistent with the conventions in HyperRogue,
// coordinates 0<->2 and 1<->3 are swapped,
// then coordinates 2<->3 are swapped
*/
EX ld range_xy = 2;
EX int steps = 15;
EX hyperpoint from_phigans(hyperpoint h) {
ld r = asinh(hypot_d(2, h));
ld x = h[0];
ld y = h[1];
ld z = h[2];
return hyperpoint(x * cos(z) + y * sin(z), y * cos(z) - x * sin(z), cosh(r) * sin(z), cosh(r) * cos(z));
}
EX hyperpoint to_phigans(hyperpoint h) {
ld z = atan2(h[2], h[3]);
ld x = h[0];
ld y = h[1];
return point31(x * cos(z) - y * sin(z), y * cos(z) + x * sin(z), z);
}
/** in the 'phigans' model */
hyperpoint christoffel(const hyperpoint Position, const hyperpoint Velocity, const hyperpoint Transported) {
ld x = Position[0];
ld y = Position[1];
ld s = x*x + y*y + 1;
ld x2 = x * x;
ld y2 = y * y;
ld x4 = x2 * x2;
ld y4 = y2 * y2;
return point3(
+ Velocity[ 0 ] * Transported[ 0 ] * (x*(4*x2*y2 + 4*y4 + 9*y2 + 1))
+ Velocity[ 0 ] * Transported[ 1 ] * (-y*(4*x4 + 4*x2*y2 + 9*x2 + 2))
+ Velocity[ 0 ] * Transported[ 2 ] * (-x*y*(x2 + y2 + 2))
+ Velocity[ 1 ] * Transported[ 0 ] * (-y*(4*x4 + 4*x2*y2 + 9*x2 + 2))
+ Velocity[ 1 ] * Transported[ 1 ] * (x*(4*x4 + 4*x2*y2 + 9*x2 + 5))
+ Velocity[ 1 ] * Transported[ 2 ] * (x4 + x2*y2 + 2*x2 + 1)
+ Velocity[ 2 ] * Transported[ 0 ] * (-x*y*(x2 + y2 + 2))
+ Velocity[ 2 ] * Transported[ 1 ] * (x4 + x2*y2 + 2*x2 + 1),
+ Velocity[ 0 ] * Transported[ 0 ] * (y*(4*x2*y2 + 4*y4 + 9*y2 + 5))
+ Velocity[ 0 ] * Transported[ 1 ] * (-x*(4*x2*y2 + 4*y4 + 9*y2 + 2))
+ Velocity[ 0 ] * Transported[ 2 ] * (-x2*y2 - y4 - 2*y2 - 1)
+ Velocity[ 1 ] * Transported[ 0 ] * (-x*(4*x2*y2 + 4*y4 + 9*y2 + 2))
+ Velocity[ 1 ] * Transported[ 1 ] * (y*(4*x4 + 4*x2*y2 + 9*x2 + 1))
+ Velocity[ 1 ] * Transported[ 2 ] * (x*y*(x2 + y2 + 2))
+ Velocity[ 2 ] * Transported[ 0 ] * (-x2*y2 - y4 - 2*y2 - 1)
+ Velocity[ 2 ] * Transported[ 1 ] * (x*y*(x2 + y2 + 2)),
+ Velocity[ 0 ] * Transported[ 0 ] * (-4*x*y)
+ Velocity[ 0 ] * Transported[ 1 ] * (2*x2 - 2*y2)
+ Velocity[ 0 ] * Transported[ 2 ] * x
+ Velocity[ 1 ] * Transported[ 0 ] * (2*x2 - 2*y2)
+ Velocity[ 1 ] * Transported[ 1 ] * 4*x*y
+ Velocity[ 1 ] * Transported[ 2 ] * y
+ Velocity[ 2 ] * Transported[ 0 ] * x
+ Velocity[ 2 ] * Transported[ 1 ] * y
) / s;
}
EX transmatrix translate(hyperpoint h) {
return matrix4(
h[3], -h[2], h[1], h[0],
@ -1662,204 +1601,324 @@ EX namespace slr {
EX hyperpoint polar(ld r, ld theta, ld phi) {
return hyperpoint(sinh(r) * cos(theta-phi), sinh(r) * sin(theta-phi), cosh(r) * sin(phi), cosh(r) * cos(phi));
}
EX hyperpoint xyz_point(ld x, ld y, ld z) {
ld r = hypot(x, y);
ld f = r ? sinh(r) / r : 1;
return hyperpoint(x * f * cos(z) + y * f * sin(z), y * f * cos(z) - x * f * sin(z), cosh(r) * sin(z), cosh(r) * cos(z));
}
ld rootsin(ld square, ld s) {
if(square > 0) return sinh(sqrt(square) * s) / sqrt(square);
else if(square < 0) return sin(sqrt(-square) * s) / sqrt(-square);
else return s;
}
/** it==0 is standard asin, it==1 is the next solution (PI-asin) */
ld asin_it(ld z, int it) {
auto ans = asin(z);
if(it & 1) ans = M_PI - ans;
return ans;
}
ld arootsin(ld square, ld v, int it) {
if(square > 0) return asinh(v * sqrt(square)) / sqrt(square);
else if(square < 0) return asin_it(v * sqrt(-square), it) / sqrt(-square);
else return v;
}
ld roottan(ld square, ld s) {
if(square > 0) return tanh(sqrt(square) * s) / sqrt(square);
else if(square < 0) return tan(sqrt(-square) * s) / sqrt(-square);
else return s;
}
hyperpoint geodesic_polar(ld alpha, ld beta, ld s) {
auto c = cos(2*alpha);
ld t;
if(c > 0)
t = atan(sin(alpha) * tanh(sqrt(c) * s) / sqrt(c));
else if(c < 0) {
/* the formula in the paper is roughly atan(k*tan(s))
* however, atan is not always to be taken in [-PI/2,PI/2]:
* if s is in [kPI-PI/2, kPI+PI/2], we should also increase the result by kPI
*/
ld x = sqrt(-c) * s;
ld steps = floor(x/M_PI + 0.5);
t = atan(sin(alpha) * tan(sqrt(-c) * s) / sqrt(-c)) + M_PI * steps;
}
else t = atan(sin(alpha) * s);
return polar(
asinh(cos(alpha) * rootsin(c, s)),
beta - t,
2*sin(alpha)*s - t
);
}
EX hyperpoint formula_exp(hyperpoint h) {
ld s = hypot_d(3, h);
ld beta = atan2(h[1], h[0]);
ld alpha = asin(h[2] / s);
return geodesic_polar(alpha, beta, s);
}
void find_alpha(ld phi, ld r, ld theta, ld &alpha, ld &s, ld &beta) {
if(phi < 0) { find_alpha(-phi, r, -theta, alpha, s, beta); alpha = -alpha; beta = -beta; return; }
ld mina = 0, maxa = M_PI/2;
bool next_nan = true;
ld c;
for(int it=0; it<40; it++) {
alpha = (mina + maxa) / 2;
c = cos(2 * alpha);
s = arootsin(c, sinh(r) / cos(alpha), 0);
if(isnan(s)) { next_nan = true, maxa = alpha; continue; }
ld got_phi = 2*sin(alpha)*s - atan(sin(alpha) * roottan(c, s));
if(got_phi > phi) next_nan = false, maxa = alpha;
else mina = alpha;
}
if(next_nan) {
mina = M_PI/4;
for(int it=0; it<40; it++) {
alpha = (mina + maxa) / 2;
c = cos(2 * alpha);
s = arootsin(c, sinh(r) / cos(alpha), 1);
ld got_phi = 2*sin(alpha)*s - atan(sin(alpha) * roottan(c, s)) - M_PI;
if(got_phi < phi) maxa = alpha;
else mina = alpha;
}
beta = theta + atan(sin(alpha) * roottan(c, s)) + M_PI;
}
else beta = theta + atan(sin(alpha) * roottan(c, s));
}
EX hyperpoint get_inverse_exp(hyperpoint h, ld index IS(0)) {
if(sqhypot_d(2, h) < 1e-12) return point3(0, 0, atan2(h[2], h[3]) + index);
ld r = asinh(hypot_d(2, h));
ld xy = hypot_d(2, h);
ld phi = atan2(h[2], h[3]) + index;
ld theta = atan2(h[1], h[0]) + phi + index;
bool flipped = phi > 0;
if(flipped) phi = -phi, h[2] *= -1, h[0] *= -1;
ld alpha, s, beta;
find_alpha(phi, r, theta, alpha, s, beta);
ld SV = stretch::not_squared();
ld K = -1;
return point3(s * cos(beta) * cos(alpha), s * sin(beta) * cos(alpha), s * sin(alpha));
ld alpha = atan2(h[1], -h[0]);
hyperpoint res;
ld fiber_barrier = atan(1/SV);
ld flip_barrier = atan( 1 / tanh(asinh(xy)) / SV);
// test the side of the flip barrier
int part = -1;
if(1) {
ld kk = flip_barrier;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
ld r = atanh(rparam);
ld cr = cosh(r);
ld sr = sinh(r);
// sinh(r) = xy
// r = tanh(sinh(xy))
ld z = cr * (K - 1/SV/SV);
ld k = M_PI/2;
ld a = k / K;
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cos(k)) - u;
if(phi < phi1) part = 2;
}
if(part == -1) {
ld zw = xy;
ld u = xy * (K - 1/SV/SV) / K;
ld phi1 = atan2(zw, 1) - u;
if(phi > phi1) part = 0; else part = 1;
}
if(part == 2) {
ld min_k = fiber_barrier;
ld max_k = flip_barrier;
for(int it=0; it<30; it++) {
ld kk = (min_k + max_k) / 2;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
assert(rparam <= 1);
ld r = atanh(rparam);
ld cr = cosh(r);
ld sr = sinh(r);
ld z = cr * (K - 1/SV/SV);
ld k = M_PI - asin(xy / sr);
ld a = k / K;
ld len = a * hypot(sr, cr/SV);
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cos(k)) - u;
if(phi < phi1) max_k = kk;
else min_k = kk;
ld r_angle = alpha + u;
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
}
}
if(part == 0) {
ld min_k = 0;
ld max_k = fiber_barrier;
for(int it=0; it<30; it++) {
ld kk = (min_k + max_k) / 2;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
ld cr = 1 / sqrt(rparam*rparam - 1);
ld sr = rparam * cr;
ld z = cr * (K - 1/SV/SV);
ld k = asinh(xy / sr);
ld a = k / K;
ld len = a * hypot(sr, cr/SV);
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cosh(k)) - u;
if(phi > phi1) max_k = kk; else min_k = kk;
ld r_angle = alpha + u;
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
}
}
if(part == 1) {
ld min_k = fiber_barrier;
ld max_k = flip_barrier;
for(int it=0; it<30; it++) {
ld kk = (min_k + max_k) / 2;
ld x_part = cos(kk);
ld z_part = sin(kk);
ld rparam = x_part / z_part / SV;
ld r = atanh(rparam);
ld cr = cosh(r);
ld sr = sinh(r);
ld z = cr * (K - 1/SV/SV);
ld k = asin(xy / sr);
ld a = k / K;
ld len = a * hypot(sr, cr/SV);
ld zw = xy * cr / sr;
ld u = z * a;
ld phi1 = atan2(zw, cos(k)) - u;
if(isnan(phi1)) max_k = kk;
else if(phi > phi1) max_k = kk;
else min_k = kk;
ld r_angle = alpha + u;
res = point3(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len);
}
}
if(flipped) res[0] *= -1, res[2] *= -1;
return res;
}
#if ISWEB
#define ITERATE " for(int it=0; it<50; it++) { if(it >= uIterations) break; "
#else
#define ITERATE " for(int it=0; it<uIterations; it++) {"
#endif
EX string slshader =
"uniform mediump float uIndexSL;"
"uniform mediump int uIterations;"
"uniform mediump float uSV;"
"vec4 inverse_exp(vec4 h) {"
"if(h[0]*h[0] + h[1] * h[1] < 1e-6) return vec4(0, 0, atan2(h[2], h[3]) + uIndexSL, 1);"
"float r = asinh(sqrt(h[0] * h[0] + h[1] * h[1]));"
"float xy = length(h.xy);"
"float phi = atan2(h[2], h[3]) + uIndexSL;"
"float theta = atan2(h[1], h[0]) + phi + uIndexSL;"
"float alpha;"
"float s;"
"float beta;"
"float sgn = 1.;"
"float bound = .999;"
"if(phi < 0.) { phi = -phi; theta = -theta; sgn = -1.; }"
"float c;"
"s = sinh(r) / cos(PI/4.);"
"float gphi = 2.*sin(PI/4.)*s - atan(sin(PI/4.) * s);"
"float lo_gphi = gphi;"
"float lo_s = s;"
"float lo_alpha = PI/4.;"
"float lx_gphi = gphi;"
"float lx_s = s;"
"float lx_alpha = PI/4.;"
"float hi_gphi = gphi;"
"float hi_s = s;"
"float hi_alpha = PI/4.;"
"if(gphi > phi) {"
" float mina = 0.;"
" float maxa = PI/4.;"
" lo_gphi = 0.; lo_s = r; lo_alpha = 0.;"
#if ISWEB
" for(int it=0; it<50; it++) { if(it >= uIterations) break; "
#else
" for(int it=0; it<uIterations; it++) {"
#endif
" alpha = (mina + maxa) / 2.;"
" c = sqrt(cos(2. * alpha));"
" s = asinh(sinh(r) / cos(alpha) * c) / c;"
" gphi = 2.*sin(alpha)*s - atan(sin(alpha) * tanh(c * s) / c);"
" if(gphi > phi) { maxa = alpha; hi_alpha = alpha; hi_s = s; hi_gphi = gphi; }"
" else { mina = alpha; lo_alpha = alpha; lo_s = s; lo_gphi = gphi; }"
" }"
" }"
"else {"
" hi_gphi = phi; hi_s = phi; hi_alpha = 9.;"
" int next_nan = 1;"
" float mina = PI/4.;"
" float maxa = PI/2.;"
#if ISWEB
" for(int it=0; it<50; it++) { if(it >= uIterations) break; "
#else
" for(int it=0; it<uIterations; it++) {"
#endif
" alpha = (mina + maxa) / 2.;"
" c = sqrt(-cos(2. * alpha));"
" if(sinh(r) * c > bound * cos(alpha)) { next_nan = 1; maxa = alpha; continue; }"
" s = asin(sinh(r) * c / cos(alpha)) / c;"
" gphi = 2.*sin(alpha)*s - atan(sin(alpha) * tan(c*s) / c);"
" if(gphi > phi) { next_nan = 0; maxa = alpha; hi_gphi = gphi; hi_s = s; hi_alpha = alpha; }"
" else { mina = alpha; lx_gphi = lo_gphi; lx_s = lo_s; lx_alpha = lo_alpha; lo_gphi = gphi; lo_s = s; lo_alpha = alpha; }"
" }"
" if(next_nan != 0) {"
" mina = PI/4.; "
#if ISWEB
" for(int it=0; it<50; it++) { if(it >= uIterations) break; "
#else
" for(int it=0; it<uIterations; it++) {"
#endif
" alpha = (mina + maxa) / 2.;"
" c = sqrt(-cos(2. * alpha));"
" float z = sinh(r) * c / cos(alpha);"
" if(z>bound) { maxa = alpha; next_nan = 1; continue; }"
" float s1 = PI - asin(z);"
" s = s1 / c;"
" gphi = 2.*sin(alpha)*s - atan(sin(alpha) * tan(s1) / c) - PI;"
" if(gphi < phi) { next_nan = 0; maxa = alpha; hi_gphi = gphi; hi_s = s; hi_alpha = alpha; }"
" else { mina = alpha; lo_gphi = gphi; lo_s = s; lo_alpha = alpha; }"
" }"
" }"
" }"
"if(hi_alpha <= 9.) { hi_gphi = lx_gphi; hi_s = lx_s; hi_alpha = lx_alpha; } "
"float fr = (phi-lo_gphi) / (hi_gphi-lo_gphi);"
"alpha = lo_alpha + (hi_alpha-lo_alpha) * fr;"
"s = lo_s + (hi_s-lo_s) * fr;"
"beta = theta - phi + 2.*sin(alpha)*s;"
"alpha = alpha * sgn; beta = beta * sgn;"
"return vec4(s * cos(beta) * cos(alpha), s * sin(beta) * cos(alpha), s * sin(alpha), 1.);"
"vec4 res = vec4(sqrt(-1.),sqrt(-1.),sqrt(-1.),sqrt(-1.));"
"bool flipped = phi > 0.;"
"if(flipped) phi = -phi, h[2] *= -1, h[0] *= -1;"
"float alpha = atan2(h[1], -h[0]) + uIndexSL;"
"float fiber_barrier = atan(1./uSV);"
"float flip_barrier = atan(1. / tanh(asinh(xy)) / uSV);"
"int part = 0;"
"if(true) {"
"float x_part = cos(flip_barrier);"
"float z_part = sin(flip_barrier);"
"float rparam = x_part / z_part / uSV;"
"float r = atanh(rparam);"
"float cr = cosh(r);"
"float sr = sinh(r);"
"float z = cr * (-1.-1./uSV/uSV);"
"float k = PI/2.;"
"float a = -k;"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cos(k)) - u;"
"if(phi < phi1) part = 2;"
"}\n"
"if(part == 0) {"
"float zw = xy;"
"float u = xy * (1. + 1./uSV/uSV);"
"float phi1 = atan2(zw, 1.) - u;"
"if(phi > phi1) part = 0; else part = 1;"
"}\n"
"if(part == 2) {"
"float min_k = fiber_barrier;"
"float max_k = flip_barrier;"
ITERATE
"float kk = (min_k + max_k) / 2.;"
"float x_part = cos(kk);"
"float z_part = sin(kk);"
"float rparam = x_part / z_part / uSV;"
"float r = atanh(rparam);"
"float cr = cosh(r);"
"float sr = sinh(r);"
"float z = cr * (-1. - 1./uSV/uSV);"
"float k = PI - asin(xy / sr);"
"float a = -k;"
"float len = a * length(vec2(sr, cr/uSV));"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cos(k)) - u;"
"if(phi < phi1) max_k = kk; else min_k = kk;"
"float r_angle = alpha + u;"
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
"}"
"}\n"
"if(part == 0) {"
"float min_k = 0.;"
"float max_k = fiber_barrier;"
ITERATE
"float kk = (min_k + max_k) / 2.;"
"float x_part = cos(kk);"
"float z_part = sin(kk);"
"float rparam = x_part / z_part / uSV;"
"float cr = 1. / sqrt(rparam*rparam - 1.);"
"float sr = rparam * cr;"
"float z = cr * (-1. - 1./uSV/uSV);"
"float k = asinh(xy / sr);"
"float a = -k;"
"float len = a * length(vec2(sr, cr/uSV));"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cosh(k)) - u;"
"if(phi > phi1) max_k = kk; else min_k = kk;"
"float r_angle = alpha + u;"
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
"}"
"}\n"
"if(part == 1) {"
"float min_k = fiber_barrier;"
"float max_k = flip_barrier;"
ITERATE
"float kk = (min_k + max_k) / 2.;"
"float x_part = cos(kk);"
"float z_part = sin(kk);"
"float rparam = x_part / z_part / uSV;"
"float r = atanh(rparam);"
"float cr = cosh(r);"
"float sr = sinh(r);"
"float z = cr * (-1. - 1./uSV/uSV);"
"float k = asin(xy / sr);"
"float a = -k;"
"float len = a * length(vec2(sr, cr/uSV));"
"float zw = xy * cr / sr;"
"float u = z * a;"
"float phi1 = atan2(zw, cos(k)) - u;"
"if(phi > phi1) max_k = kk;"
"else min_k = kk;"
"float r_angle = alpha + u;"
"res = vec4(cos(r_angle) * x_part * len, -sin(r_angle) * x_part * len, z_part * len, 1);"
"}"
"}\n"
"if(flipped) res[0] *= -1., res[2] *= -1.;"
"return res;"
"}";
EX }
@ -2058,6 +2117,63 @@ EX namespace rots {
reset_projection(); current_display->set_all(0);
}
/** @brief exponential function for both slr and Berger sphere */
EX hyperpoint formula_exp(hyperpoint vel) {
bool sp = sphere;
ld K = sp ? 1 : -1;
ld len = hypot_d(3, vel);
if(vel[2] < 0) len = -len;
ld z_part = vel[2]/len;
ld x_part = sqrt(1 - z_part * z_part);
ld SV = stretch::not_squared();
ld rparam = x_part / z_part / SV;
ld beta = atan2(vel[1], vel[0]);
if(len < 0) beta += M_PI;
if(sl2 && rparam > 1) {
ld cr = 1 / sqrt(rparam*rparam - 1); // *i
ld sr = rparam * cr; // *i
ld z = cr * (K - 1/SV/SV); // *i
ld a = len / hypot(sr, cr/SV); // /i
ld k = K*a; // /i
ld u = z*a;
ld xy = sr * sinh(k);
ld zw = cr * sinh(k);
return hyperpoint(K*xy * cos(u+beta), K*xy * sin(u+beta), zw * cos(u) - cosh(k) * sin(u), zw * sin(u) + cosh(k)*cos(u));
}
else {
ld r = atan_auto(rparam);
ld cr = cos_auto(r);
ld sr = sin_auto(r);
ld z = cr * (K - 1/SV/SV);
ld a = len / hypot(sr, cr/SV);
ld k = K*a;
ld u = z*a;
ld xy = sr * sin(k);
ld zw = cr * sin(k);
return hyperpoint(K*xy * cos(u+beta), K*xy * sin(u+beta), zw * cos(u) - cos(k) * sin(u), zw * sin(u) + cos(k)*cos(u));
}
}
EX }
/** stretched rotation space (S3 or SLR) */
@ -2105,15 +2221,15 @@ EX namespace stretch {
return sqrt(squared());
}
hyperpoint isometric_to_actual(const hyperpoint at, const hyperpoint velocity) {
EX hyperpoint isometric_to_actual(const hyperpoint at, const hyperpoint velocity) {
return mulz(at, velocity, 1/not_squared());
}
hyperpoint actual_to_isometric(const hyperpoint at, const hyperpoint velocity) {
EX hyperpoint actual_to_isometric(const hyperpoint at, const hyperpoint velocity) {
return mulz(at, velocity, not_squared());
}
hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
EX hyperpoint christoffel(const hyperpoint at, const hyperpoint velocity, const hyperpoint transported) {
auto vel = itranslate(at) * velocity;
auto tra = itranslate(at) * transported;
@ -2147,8 +2263,7 @@ EX namespace nisot {
#if CAP_SOLV
else if(sn::in()) return sn::christoffel(at, velocity, transported);
#endif
else if(stretch::in()) return stretch::christoffel(at, velocity, transported);
else if(sl2) return slr::christoffel(at, velocity, transported);
else if(stretch::in() || sl2) return stretch::christoffel(at, velocity, transported);
else return point3(0, 0, 0);
}
@ -2186,22 +2301,13 @@ EX namespace nisot {
EX transmatrix parallel_transport_bare(transmatrix Pos, hyperpoint h) {
bool stretch = stretch::in();
bool stretch = stretch::in() || sl2;
h[3] = 0;
auto tPos = transpose(Pos);
const ld eps = 1e-4;
if(sl2 && !stretch) {
hyperpoint p = slr::to_phigans(tPos[3]);
for(int i=0; i<3; i++)
tPos[i] = (slr::to_phigans(tPos[3] + tPos[i] * eps) - p) / eps;
tPos[3] = p;
h = transpose(tPos) * h;
}
else h = Pos * h;
h = Pos * h;
int steps = rk_steps;
h /= steps;
@ -2266,13 +2372,6 @@ EX namespace nisot {
for(int i=0; i<3; i++) tPos[i] = stretch::actual_to_isometric(at, tPos[i]);
}
else if(sl2) {
hyperpoint p = slr::from_phigans(tPos[3]);
for(int i=0; i<3; i++)
tPos[i] = (slr::from_phigans(tPos[3] + tPos[i] * eps) - p) / eps;
tPos[3] = p;
}
return transpose(tPos);
}

2
raycaster.cpp
View File

@ -87,7 +87,7 @@ EX bool available() {
/** do we want to use the raycaster? */
EX bool requested() {
if(cgflags & qRAYONLY) return true;
if(stretch::in()) return true;
if(stretch::in() && sphere) return true;
if(!want_use) return false;
#if CAP_TEXTURE
if(texture::config.tstate == texture::tsActive) return false;

1
shaders.cpp
View File

@ -359,6 +359,7 @@ void display_data::set_projection(int ed) {
if(selected->uIterations != -1) {
glhr::set_index_sl(0);
glhr::set_sv(stretch::not_squared());
glhr::set_sl_iterations(slr::steps);
}