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new projections based on cartography

This commit is contained in:
Zeno Rogue 2020-09-15 19:17:07 +02:00
parent a6482d00ab
commit 2e47adef1c
5 changed files with 197 additions and 8 deletions
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18
classes.cpp
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@ -940,6 +940,7 @@ namespace mf {
static const flagtype equivolume = 1024;
static const flagtype twopoint = 2048;
static const flagtype uses_bandshift = 4096;
static const flagtype broken = 8192; /* in spherical case, these are broken along the meridian 180 deg */
static const flagtype band = (cylindrical | pseudocylindrical | uses_bandshift);
static const flagtype pseudoband = (pseudocylindrical | uses_bandshift);
@ -972,9 +973,13 @@ enum eModel : int {
mdRotatedHyperboles, mdSpiral, mdPerspective,
// 20..24
mdEquivolume, mdCentralInversion, mdSimulatedPerspective, mdTwoHybrid, mdGeodesic,
// 25
mdMollweide, mdCentralCyl, mdCollignon, mdHorocyclic, mdQuadrant, mdAxial, mdAntiAxial,
// 32..
// 25..27
mdMollweide, mdCentralCyl, mdCollignon,
// 28..31
mdHorocyclic, mdQuadrant, mdAxial, mdAntiAxial,
// 32..38
mdWerner, mdAitoff, mdHammer, mdLoximuthal, mdMiller, mdGallStereographic, mdWinkelTripel,
// 39..
mdGUARD, mdPixel, mdHyperboloidFlat, mdPolynomial, mdManual
};
#endif
@ -1019,6 +1024,13 @@ EX vector<modelinfo> mdinf = {
{X3("quadrant coordinates"), mf::euc_boring, DEFAULTS},
{X3("axial coordinates"), mf::euc_boring, DEFAULTS},
{X3("anti-axial coordinates"), mf::euc_boring, DEFAULTS},
{X3("Werner projection"), mf::euc_boring | mf::broken, DEFAULTS}, // keep distances from pole, and distances along parallels
{X3("Aitoff projection"), mf::euc_boring | mf::broken, DEFAULTS}, // halve longitudes, do azequid, double x
{X3("Hammer projection"), mf::euc_boring | mf::broken, DEFAULTS}, // halve longitudes, do azequia, double x
{X3("loximuthal projection"), mf::euc_boring | mf::broken, DEFAULTS}, // map loxodromes azimuthally and equidistantly
{X3("Miller projection"), mf::euc_boring | mf::band, DEFAULTS}, // scale latitude 4/5 -> Mercator -> 5/4
{X3("Gall stereographic"), mf::euc_boring | mf::band, DEFAULTS}, // like central cylindrical but stereographic
{X3("Winkel tripel"), mf::euc_boring | mf::broken, DEFAULTS}, // mean of equirec and Aitoff
{X3("guard"), 0, DEFAULTS},
{X3("polynomial"), mf::conformal, DEFAULTS},
};

69
drawing.cpp
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@ -777,6 +777,7 @@ ld period_at(ld y) {
switch(pmodel) {
case mdBand:
case mdMiller:
return m * 4;
case mdSinusoidal:
return m * 2 * cos(y * M_PI);
@ -1544,7 +1545,75 @@ void dqi_poly::draw() {
cnt = i;
return;
}
int broken_coord = models::get_broken_coord(pmodel);
static bool in_broken = false;
if(broken_coord && !in_broken) {
int zcoord = broken_coord;
int ycoord = 3 - zcoord;
vector<hyperpoint> all;
for(int i=0; i<cnt; i++)
all.push_back(V.T * glhr::gltopoint((*tab)[offset+i]));
int fail = 0;
int last_fail;
for(int i=0; i<cnt-1; i++)
if(all[i][0] * all[i+1][0] <= 0 && (all[i][0] * all[i+1][zcoord] - all[i+1][0] * all[i][zcoord]) * (all[i][0] - all[i+1][0]) < 0)
last_fail = i, fail++;
vector<glvertex> v;
dqi_poly p = *this;
p.tab = &v;
p.offset = 0;
p.V.T = Id;
if(fail) {
dynamicval<bool> ib(in_broken, true);
ld part = ilerp(all[last_fail][0], all[last_fail+1][0], 0);
hyperpoint initial = normalize(lerp(all[last_fail], all[last_fail+1], 1 - (1-part) * .99));
bool have_initial = true;
v.push_back(glhr::pointtogl(initial));
last_fail++;
int at = last_fail;
do {
v.push_back(glhr::pointtogl(all[at]));
if(at == cnt-1 && all[at] != all[0]) {
p.cnt = isize(v); p.draw(); v.clear(); at = 0;
have_initial = false;
}
int next = at+1;
if(next == cnt) next = 0;
if(all[at][0] * all[next][0] <= 0 && (all[at][0] * all[next][zcoord] - all[next][0] * all[at][zcoord]) * (all[at][0] - all[next][0]) < 0) {
ld part = ilerp(all[at][0], all[next][0], 0);
if(part > .999 || part < .001) { in_broken = false; return; }
hyperpoint final = normalize(lerp(all[at], all[next], part * .99));
v.push_back(glhr::pointtogl(final));
if(have_initial) {
int max = 4 << vid.linequality;
if(final[0] * initial[0] > 0) {
for(int i=1; i<=max; i++)
v.push_back(glhr::pointtogl(lerp(final, initial, i * 1. / max)));
}
else {
hyperpoint end = Hypc;
end[ycoord] = final[ycoord] > 0 ? 1 : -1;
for(int i=1; i<=max; i++)
v.push_back(glhr::pointtogl(lerp(final, end, i * 1. / max)));
for(int i=1; i<=max; i++)
v.push_back(glhr::pointtogl(lerp(end, initial, i * 1. / max)));
}
}
p.cnt = isize(v); p.draw(); v.clear();
initial = normalize(lerp(all[at], all[next], 1 - (1-part) * .99));
have_initial = true;
v.push_back(glhr::pointtogl(initial));
}
at = next;
}
while(at != last_fail);
return;
}
}
if(sphere && pmodel == mdTwoPoint && !in_twopoint) {
#define MAX_PHASE 4
vector<glvertex> phases[MAX_PHASE];

5
hyper.h
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@ -241,6 +241,7 @@ struct projection_configuration {
ld clip_min, clip_max;
ld model_orientation, halfplane_scale, model_orientation_yz;
ld collignon_parameter;
ld aitoff_parameter, miller_parameter, loximuthal_parameter, winkel_parameter;
bool collignon_reflected;
string formula;
eModel basic_model;
@ -267,6 +268,10 @@ struct projection_configuration {
spiral_cone = 360;
use_atan = false;
product_z_scale = 1;
aitoff_parameter = .5;
miller_parameter = .8;
loximuthal_parameter = 0;
winkel_parameter = .5;
}
};

103
hypgraph.cpp
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@ -364,10 +364,14 @@ EX void apply_nil_rotation(hyperpoint& H) {
}
EX void applymodel(shiftpoint H_orig, hyperpoint& ret) {
apply_other_model(H_orig, ret, pmodel);
}
EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
hyperpoint H = H_orig.h;
if(models::product_model(pmodel)) {
if(models::product_model(md)) {
ld zlev = zlevel(H_orig.h);
H_orig.h /= exp(zlev);
hybrid::in_underlying_geometry([&] { applymodel(H_orig, ret); });
@ -376,7 +380,7 @@ EX void applymodel(shiftpoint H_orig, hyperpoint& ret) {
return;
}
switch(pmodel) {
switch(md) {
case mdPerspective: {
if(prod) H = product::inverse_exp(H);
apply_nil_rotation(H);
@ -832,6 +836,25 @@ EX void applymodel(shiftpoint H_orig, hyperpoint& ret) {
else
makeband(H_orig, ret, band_conformal);
break;
case mdMiller:
makeband(H_orig, ret, [] (ld& x, ld& y) {
// y *= pconf.miller_parameter;
band_conformal(x, y);
// y /= pconf.miller_parameter;
});
break;
case mdLoximuthal:
makeband(H_orig, ret, [] (ld&x, ld &y) {
ld orig_y = y;
band_conformal(x, y);
y -= pconf.loximuthal_parameter;
orig_y -= pconf.loximuthal_parameter;
if(y) x = x * orig_y / y;
y = orig_y;
});
break;
case mdTwoPoint:
makeband(H_orig, ret, make_twopoint);
@ -861,6 +884,59 @@ EX void applymodel(shiftpoint H_orig, hyperpoint& ret) {
makeband(H_orig, ret, [] (ld& x, ld& y) { y = tan_auto(y); ld top = vid.yres * M_PI / current_display->radius; if(y>top) y=top; if(y<-top) y=-top; });
break;
case mdGallStereographic:
makeband(H_orig, ret, [] (ld& x, ld& y) {
y = 2 * sin_auto(y) / (1 + cos_auto(y));
ld top = vid.yres * M_PI / current_display->radius; if(y>top) y=top; if(y<-top) y=-top;
});
break;
case mdAitoff: case mdHammer: case mdWinkelTripel:
makeband(H_orig, ret, [&] (ld& x, ld& y) {
ld ox = x, oy = y;
x *= pconf.aitoff_parameter;
ld x0 = sin_auto(x) * cos_auto(y);
ld y0 = cos_auto(x) * cos_auto(y);
ld z0 = sin_auto(y);
ld d = acos_auto(y0);
ld d0 = hypot(x0, z0);
if(md == mdAitoff || md == mdWinkelTripel) ;
else if(sphere) d = sqrt(2*(1 - cos(d))) * M_PI / 2;
else d = sqrt(2*(cosh(d) - 1)) / 1.5;
x = x0 * d / d0 / pconf.aitoff_parameter, y = z0 * d / d0;
if(md == mdWinkelTripel)
x = lerp(x, ox, pconf.model_transition),
y = lerp(y, oy, pconf.model_transition);
});
break;
case mdWerner: {
models::apply_orientation_yz(H[1], H[2]);
models::apply_orientation(H[0], H[1]);
find_zlev(H); // ignored for now
ld r = hdist0(H);
if(r == 0) { ret = H; return; }
ld angle = atan2(H[0], H[1]);
angle *= sin_auto(r) / r;
ret[0] = sin(angle) * r;
ret[1] = cos(angle) * r;
ret[2] = 0;
ret[3] = 1;
models::apply_orientation(ret[1], ret[0]);
models::apply_orientation_yz(ret[2], ret[1]);
break;
}
case mdCollignon:
find_zlev(H_orig.h);
makeband(H_orig, ret, [] (ld& x, ld& y) {
@ -1953,6 +2029,23 @@ EX void draw_boundary(int w) {
if(elliptic && !among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdMollweide, mdCollignon))
circle_around_center(M_PI/2, periodcolor, 0, PPR::CIRCLE);
int broken_coord = models::get_broken_coord(pmodel);
if(broken_coord) {
int unbroken_coord = 3 - broken_coord;
const ld eps = 1e-3;
const ld rem = sqrt(1-eps*eps);
for(int s: {-1, 1}) {
for(int a=1; a<180; a++) {
hyperpoint h = Hypc;
h[broken_coord] = -sin_auto(a*degree) * rem;
h[0] = sin_auto(a*degree) * eps * s;
h[unbroken_coord] = cos_auto(a*degree);
curvepoint(h);
}
queuecurve(shiftless(Id), periodcolor, 0, PPR::CIRCLE).flags |= POLY_FORCEWIDE;
}
}
switch(pmodel) {
case mdTwoPoint: {
@ -1979,10 +2072,12 @@ EX void draw_boundary(int w) {
return;
}
case mdBand: case mdBandEquidistant: case mdBandEquiarea: case mdSinusoidal: case mdMollweide: case mdCentralCyl: case mdCollignon: {
case mdBand: case mdBandEquidistant: case mdBandEquiarea: case mdSinusoidal: case mdMollweide: case mdCentralCyl: case mdCollignon:
case mdGallStereographic: case mdMiller:
{
if(GDIM == 3) return;
if(pmodel == mdBand && pconf.model_transition != 1) return;
bool bndband = (among(pmodel, mdBand, mdCentralCyl) ? hyperbolic : sphere);
bool bndband = (among(pmodel, mdBand, mdMiller, mdGallStereographic, mdCentralCyl) ? hyperbolic : sphere);
transmatrix T = spin(-pconf.model_orientation * degree);
ld right = M_PI/2 - 1e-5;
if(bndband)

10
models.cpp
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@ -207,7 +207,15 @@ EX namespace models {
if(m == mdHorocyclic)
return hyperbolic;
return
among(m, mdHalfplane, mdPolynomial, mdPolygonal, mdTwoPoint, mdJoukowsky, mdJoukowskyInverted, mdSpiral, mdSimulatedPerspective, mdTwoHybrid, mdHorocyclic, mdAxial, mdAntiAxial, mdQuadrant) || mdBandAny();
among(m, mdHalfplane, mdPolynomial, mdPolygonal, mdTwoPoint, mdJoukowsky, mdJoukowskyInverted, mdSpiral, mdSimulatedPerspective, mdTwoHybrid, mdHorocyclic, mdAxial, mdAntiAxial, mdQuadrant,
mdWerner, mdAitoff, mdHammer, mdLoximuthal, mdWinkelTripel) || mdBandAny();
}
/** @brief returns the broken coordinate, or zero */
EX int get_broken_coord(eModel m) {
if(m == mdWerner) return 1;
if(sphere) return (mdinf[m].flags & mf::broken) ? 2 : 0;
return 0;
}
EX bool is_perspective(eModel m) {