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rug:: using HyperRogue standard 3D geometry routines

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This commit is contained in:
Zeno Rogue
2020-04-14 16:44:56 +02:00
parent fef6894bbd
commit 9bf1a76a8b
2 changed files with 243 additions and 325 deletions
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79
surface.cpp
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@@ -11,6 +11,8 @@
#if CAP_SURFACE
namespace hr {
#define USING_NATIVE_GEOMETRY dynamicval<eGeometry> gw(geometry, hr::rug::gwhere)
EX namespace surface {
ld sech(ld d) { return 1 / cosh(d); }
@@ -24,7 +26,7 @@ string shape_name[] = { "hypersian rug", "tractricoid", "Dini's surface", "Kuen
EX eShape sh;
hyperpoint unit_vector[3] = {hpxyz(1,0,0), hpxyz(0,1,0), hpxyz(0,0,1)};
hyperpoint unit_vector[3] = {point3(1,0,0), point3(0,1,0), point3(0,0,1)};
ld last_int_of = 0, last_int = 0;
@@ -67,7 +69,7 @@ hyperpoint coord(hyperpoint h) {
ld r = 1 / cosh(t);
ld x = t - tanh(t);
return hpxyz( r * sin(v), r * cos(v), x );
return point31( r * sin(v), r * cos(v), x );
break;
}
@@ -77,7 +79,7 @@ hyperpoint coord(hyperpoint h) {
ld a = sqrt(1-dini_b*dini_b);
return hpxyz( a * sin(v) * sin(t), a * cos(v) * sin(t), a * (cos(t) + log(tan(t/2))) + dini_b * v );
return point31( a * sin(v) * sin(t), a * cos(v) * sin(t), a * (cos(t) + log(tan(t/2))) + dini_b * v );
break;
}
@@ -87,7 +89,7 @@ hyperpoint coord(hyperpoint h) {
ld deno = 1 / (1 + u * u * sin(v) * sin(v));
return hpxyz(
return point31(
2 * (cos(u) + u * sin(u)) * sin(v) * deno,
2 * (sin(u) - u * cos(u)) * sin(v) * deno,
log(tan(v/2)) + 2 * cos(v) * deno
@@ -101,7 +103,7 @@ hyperpoint coord(hyperpoint h) {
ld phi = hyper_b * cosh(v);
ld psi = integral(v);
return hpxyz( phi * cos(u), phi * sin(u), psi );
return point31( phi * cos(u), phi * sin(u), psi );
}
default:
@@ -122,10 +124,10 @@ hyperpoint coord_derivative(hyperpoint h, int cc) {
ld v = h[1];
if(cc == 0) {
ld phi = hyper_b * cosh(v);
return hpxyz( phi * -sin(u), phi * cos(u), 0 );
return point3( phi * -sin(u), phi * cos(u), 0 );
}
else {
return hpxyz( hyper_b * sinh(v) * cos(u), hyper_b * sinh(v) * sin(u), f(v) );
return point3( hyper_b * sinh(v) * cos(u), hyper_b * sinh(v) * sin(u), f(v) );
}
}
case dsKuen: {
@@ -134,12 +136,12 @@ hyperpoint coord_derivative(hyperpoint h, int cc) {
ld denom = pow(sin(v),2)*(u*u)+1;
ld denom2 = denom * denom;
if(cc == 1)
return hpxyz (
return point3(
2*sin(v)/denom*u*cos(u)+-4*(sin(u)*u+cos(u))*pow(sin(v),3)/denom2*u,
-4*pow(sin(v),3)*(sin(u)-u*cos(u))/denom2*u+2*sin(u)*sin(v)/denom*u,
-4*pow(sin(v),2)/denom2*u*cos(v)
);
else return hpxyz (
else return point3(
2*(sin(u)*u+cos(u))/denom*cos(v)+-4*(sin(u)*u+cos(u))*pow(sin(v),2)/denom2*(u*u)*cos(v),
2*(sin(u)-u*cos(u))/denom*cos(v)+-4*pow(sin(v),2)*(sin(u)-u*cos(u))/denom2*(u*u)*cos(v),
-4*sin(v)/denom2*(u*u)*pow(cos(v),2)+1/tan(v/2)*(pow(tan(v/2),2)+1)/2+-2*sin(v)/denom
@@ -166,13 +168,13 @@ ld compute_curvature(hyperpoint at) {
hyperpoint shape_origin() {
switch(sh) {
case dsDini:
return hpxyz(M_PI * .82, 0, 0);
return point31(M_PI * .82, 0, 0);
case dsTractricoid:
return hpxyz(1, 0, 0);
return point31(1, 0, 0);
case dsKuen:
return hpxyz(M_PI * .500001, M_PI * 1, 0);
return point31(M_PI * .500001, M_PI * 1, 0);
case dsHyperlike:
return hpxyz(0,0,0);
return point31(0,0,0);
default:
return Hypc;
}
@@ -284,7 +286,7 @@ transmatrix create_M_matrix(hyperpoint zero, hyperpoint v1) {
transmatrix T = build_matrix(Te0, Te1, Hypc, C03);
v1 = v1 / hypot_d(3, T*v1);
hyperpoint v2 = hpxyz(1e-3, 1e-4, 0);
hyperpoint v2 = point3(1e-3, 1e-4, 0);
v2 = v2 - v1 * ((T*v1) | (T*v2)) / hypot_d(3, T*v1);
v2 = v2 / hypot_d(3, T*v2);
@@ -307,9 +309,9 @@ dexp_origin at_zero(hyperpoint zero, transmatrix start) {
println(hlog, "zero = ", zero);
println(hlog, "curvature at zero = ", compute_curvature(zero));
println(hlog, "curvature at X1 = ", compute_curvature(zero + hpxyz(.3, 0, 0)));
println(hlog, "curvature at X2 = ", compute_curvature(zero + hpxyz(0, .3, 0)));
println(hlog, "curvature at X3 = ", compute_curvature(zero + hpxyz(.4, .3, 0)));
println(hlog, "curvature at X1 = ", compute_curvature(zero + point3(.3, 0, 0)));
println(hlog, "curvature at X2 = ", compute_curvature(zero + point3(0, .3, 0)));
println(hlog, "curvature at X3 = ", compute_curvature(zero + point3(.4, .3, 0)));
return {start, create_M_matrix(zero, unit_vector[0]), zero};
}
@@ -338,14 +340,14 @@ void addTriangleV(rug::rugpoint *t1, rug::rugpoint *t2, rug::rugpoint *t3, ld le
}
hyperpoint kuen_cross(ld v, ld u) {
auto du = coord_derivative(hpxyz(v,u,0), 0);
auto dv = coord_derivative(hpxyz(v,u,0), 1);
auto du = coord_derivative(point3(v,u,0), 0);
auto dv = coord_derivative(point3(v,u,0), 1);
return du^dv;
}
ld kuen_hypot(ld v, ld u) {
auto du = coord_derivative(hpxyz(v,u,0), 0);
auto dv = coord_derivative(hpxyz(v,u,0), 1);
auto du = coord_derivative(point3(v,u,0), 0);
auto dv = coord_derivative(point3(v,u,0), 1);
auto n = hypot_d(3, du^dv);
return n;
}
@@ -385,8 +387,8 @@ void draw_kuen_map() {
for(int h=0; h<512; h++) {
ld v = M_PI * (r+.5) / 512;
ld u = 2 * M_PI * (h+.5) / 512;
auto du = coord_derivative(hpxyz(v,u,0), 0);
auto dv = coord_derivative(hpxyz(v,u,0), 1);
auto du = coord_derivative(point3(v,u,0), 0);
auto dv = coord_derivative(point3(v,u,0), 1);
auto n = hypot_d(3, du^dv);
if(n > nmax) nmax = n;
@@ -459,7 +461,8 @@ void run_hyperlike() {
int sgn = y > 0 ? 1 : -1;
ld phi = hyper_b * cosh(y);
int pt = y * precision * sgn / hyperlike_bound();
p->flat = hpxyz(phi * cos(x), phi * sin(x), sgn * integral_table[pt]);
USING_NATIVE_GEOMETRY;
p->native = point31(phi * cos(x), phi * sin(x), sgn * integral_table[pt]);
p->valid = true;
}
}
@@ -520,7 +523,8 @@ void run_kuen() {
np->inqueue = false;
np->dist = 0;
np->h = p->h;
np->flat = coord(px.params);
USING_NATIVE_GEOMETRY;
np->native = coord(px.params);
np->surface_point = px;
np->dexp_id = p->dexp_id;
coverages[p->dexp_id] |= pid[part];
@@ -534,9 +538,11 @@ void run_kuen() {
for(int i=0; i<3; i++)
if(!r[i]) looks_good = false;
if(!looks_good) continue;
for(int i=0; i<3; i++)
if(hypot_d(3, r[i]->flat - r[(i+1)%3]->flat) > .2)
for(int i=0; i<3; i++) {
USING_NATIVE_GEOMETRY;
if(hypot_d(3, r[i]->native - r[(i+1)%3]->native) > .2)
looks_good = false;
}
if(looks_good)
addTriangleV(r[0], r[1], r[2]);
}
@@ -557,9 +563,11 @@ void run_kuen() {
template<class T> void run_function(T f) {
full_mesh();
for(auto p: rug::points)
p->flat = f(p->h),
for(auto p: rug::points) {
USING_NATIVE_GEOMETRY;
p->native = f(p->h),
p->valid = true;
}
}
void run_other() {
@@ -572,7 +580,10 @@ void run_other() {
auto h = p->h;
p->surface_point = map_to_surface(h, dp);
p->flat = coord(p->surface_point.params);
if(1) {
USING_NATIVE_GEOMETRY;
p->native = coord(p->surface_point.params);
}
history::progress(XLAT("solving the geodesics on: %1, %2/%3", XLAT(shape_name[sh]), its(it), its(isize(rug::points))));
if(p->surface_point.remaining_distance == 0)
coverage.emplace_back(h, rchar(it) + 256 * 7);
@@ -641,8 +652,8 @@ EX void run_shape(eShape s) {
ld minx = 1e9, maxx = -1e9;
for(auto p: rug::points) if(p->valid) {
minx = min(p->flat[2], minx);
maxx = max(p->flat[2], maxx);
minx = min(p->native[2], minx);
maxx = max(p->native[2], maxx);
rug::qvalid++;
}
@@ -650,7 +661,7 @@ EX void run_shape(eShape s) {
ld shift = -(minx + maxx) / 2;
for(auto p: rug::points) if(p->valid)
p->flat[2] += shift;
p->native[2] += shift;
}
rug::apply_rotation(crot);
@@ -747,7 +758,7 @@ EX void show_surfaces() {
}
else if(uni == 'x')
for(auto p: rug::points)
p->flat = p->surface_point.params;
p->native = p->surface_point.params;
else if(uni == '#')
dialog::editNumber(dini_b, -1, 1, .05, .15, XLAT("parameter"),
XLAT("The larger the number, the more twisted it is.")