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Mollweide projection

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This commit is contained in:
Zeno Rogue 2019-08-14 08:23:09 +02:00
parent 843a53d07c
commit 10a8b8660b
5 changed files with 60 additions and 22 deletions
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4
classes.cpp
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@ -607,8 +607,8 @@ const modelinfo mdinf[int(mdPolynomial)+1] = {
{X3("central inversion"), mf::azimuthal | mf::conformal}, {X3("central inversion"), mf::azimuthal | mf::conformal},
{X3("two-point azimuthal"), mf::euc_boring | mf::twopoint}, {X3("two-point azimuthal"), mf::euc_boring | mf::twopoint},
{X3("two-point hybrid"), mf::euc_boring | mf::twopoint}, {X3("two-point hybrid"), mf::euc_boring | mf::twopoint},
{X3(""), 0}, {X3("geodesic"), 0},
{X3(""), 0}, {X3("Mollweide"), mf::euc_boring | mf::quasiband | mf::equiarea },
{X3(""), 0}, {X3(""), 0},
{X3("polynomial"), mf::conformal} {X3("polynomial"), mf::conformal}
}; };

4
classes.h
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@ -285,7 +285,9 @@ enum eModel {
mdRotatedHyperboles, mdSpiral, mdPerspective, mdRotatedHyperboles, mdSpiral, mdPerspective,
// 20..24 // 20..24
mdEquivolume, mdCentralInversion, mdSimulatedPerspective, mdTwoHybrid, mdGeodesic, mdEquivolume, mdCentralInversion, mdSimulatedPerspective, mdTwoHybrid, mdGeodesic,
// 25.. // 25
mdMollweide,
// 26..
mdGUARD, mdUnchanged, mdHyperboloidFlat, mdPolynomial, mdRug, mdFlatten mdGUARD, mdUnchanged, mdHyperboloidFlat, mdPolynomial, mdRug, mdFlatten
}; };

47
drawing.cpp
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@ -686,20 +686,34 @@ int mercator_coord;
int mercator_loop_min = 0, mercator_loop_max = 0; int mercator_loop_min = 0, mercator_loop_max = 0;
ld mercator_period; ld mercator_period;
ld period_at(ld y) {
ld m = current_display->radius;
y /= (m * vid.stretch);
switch(pmodel) {
case mdBand:
return m * 4;
case mdSinusoidal:
return m * 2 * cos(y * M_PI);
case mdMollweide:
return (abs(y) > .5-1e-6) ? m * 2 : m * 2 * sqrt(1 - y*y*4);
default:
return m * 2;
}
}
void fixMercator(bool tinf) { void fixMercator(bool tinf) {
if(pmodel == mdBand) mercator_period = period_at(0);
mercator_period = 4 * current_display->radius;
else
mercator_period = 2 * current_display->radius;
if(!models::model_straight) if(!models::model_straight)
for(auto& g: glcoords) for(auto& g: glcoords)
models::apply_orientation(g[0], g[1]); models::apply_orientation(g[0], g[1]);
if(pmodel == mdSinusoidal) if(among(pmodel, mdSinusoidal, mdMollweide))
for(int i = 0; i<isize(glcoords); i++) for(int i = 0; i<isize(glcoords); i++)
glcoords[i][mercator_coord] /= cos(glcoords[i][1] / current_display->radius / vid.stretch * M_PI); glcoords[i][mercator_coord] *= mercator_period / period_at(glcoords[i][1-mercator_coord]);
ld hperiod = mercator_period / 2; ld hperiod = mercator_period / 2;
@ -720,10 +734,10 @@ void fixMercator(bool tinf) {
if(pmodel == mdBandEquiarea) if(pmodel == mdBandEquiarea)
dmin = -vid.stretch * current_display->radius / M_PI, dmax = vid.stretch * current_display->radius / M_PI; dmin = -vid.stretch * current_display->radius / M_PI, dmax = vid.stretch * current_display->radius / M_PI;
for(int i = 0; i<isize(glcoords); i++) { // for(int i = 0; i<isize(glcoords); i++) {
while(glcoords[0][mercator_coord] < hperiod) glcoords[0][mercator_coord] += mercator_period; while(glcoords[0][mercator_coord] < hperiod) glcoords[0][mercator_coord] += mercator_period;
while(glcoords[0][mercator_coord] > hperiod) glcoords[0][mercator_coord] -= mercator_period; while(glcoords[0][mercator_coord] > hperiod) glcoords[0][mercator_coord] -= mercator_period;
} // }
ld first = glcoords[0][mercator_coord]; ld first = glcoords[0][mercator_coord];
ld next = first; ld next = first;
@ -754,9 +768,9 @@ void fixMercator(bool tinf) {
mercator_loop_min--, mincoord -= mercator_period; mercator_loop_min--, mincoord -= mercator_period;
while(maxcoord < cmax) while(maxcoord < cmax)
mercator_loop_max++, maxcoord += mercator_period; mercator_loop_max++, maxcoord += mercator_period;
if(pmodel == mdSinusoidal) if(among(pmodel, mdSinusoidal, mdMollweide))
for(int i = 0; i<isize(glcoords); i++) for(int i = 0; i<isize(glcoords); i++)
glcoords[i][mercator_coord] *= cos(glcoords[i][1] / current_display->radius / vid.stretch * M_PI); glcoords[i][mercator_coord] *= period_at(glcoords[i][1-mercator_coord]) / mercator_period;
if(!models::model_straight) if(!models::model_straight)
for(auto& g: glcoords) for(auto& g: glcoords)
models::apply_orientation(g[1], g[0]); models::apply_orientation(g[1], g[0]);
@ -784,9 +798,10 @@ void fixMercator(bool tinf) {
} }
minto += mercator_period; minto += mercator_period;
} }
if(pmodel == mdSinusoidal) if(among(pmodel, mdSinusoidal, mdMollweide))
for(int i = 0; i<isize(glcoords); i++) for(int i = 0; i<isize(glcoords); i++)
glcoords[i][mercator_coord] *= cos(glcoords[i][1] / current_display->radius / vid.stretch * M_PI); glcoords[i][mercator_coord] *= period_at(glcoords[i][1-mercator_coord]) / mercator_period;
glcoords.push_back(glcoords.back()); glcoords.push_back(glcoords.back());
glcoords.push_back(glcoords[0]); glcoords.push_back(glcoords[0]);
for(int u=1; u<=2; u++) { for(int u=1; u<=2; u++) {
@ -1092,10 +1107,10 @@ void dqi_poly::draw() {
if(l || lastl) { if(l || lastl) {
for(int i=0; i<isize(glcoords); i++) { for(int i=0; i<isize(glcoords); i++) {
if(pmodel == mdSinusoidal) { if(among(pmodel, mdSinusoidal, mdMollweide)) {
ld y = glcoords[i][1], x = glcoords[i][0]; ld y = glcoords[i][1], x = glcoords[i][0];
models::apply_orientation(x, y); models::apply_orientation(x, y);
mercator_period = 2 * current_display->radius * cos(y / current_display->radius / vid.stretch * M_PI); mercator_period = period_at(y);
} }
glcoords[i][mercator_coord] += models::ocos * mercator_period * (l - lastl); glcoords[i][mercator_coord] += models::ocos * mercator_period * (l - lastl);
glcoords[i][1-mercator_coord] += models::osin * mercator_period * (l - lastl); glcoords[i][1-mercator_coord] += models::osin * mercator_period * (l - lastl);

25
hypgraph.cpp
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@ -656,6 +656,27 @@ EX void applymodel(hyperpoint H, hyperpoint& ret) {
makeband(H, ret, make_twopoint); makeband(H, ret, make_twopoint);
break; break;
case mdMollweide:
makeband(H, ret, [] (ld& x, ld& y) {
ld theta =
hyperbolic ? min(y / 2 + 0.572365, y * 0.78509) :
euclid ? y :
y > 0 ? max(y * 0.012/0.015, M_PI/2 - (M_PI/2-y) * 0.066262/0.015708) :
min(y * 0.012/0.015, -M_PI/2 + (M_PI/2+y) * 0.066262/0.015708);
if(sphere && abs(theta) >= M_PI/2 - 1e-6) ;
else {
for(int it=0; it<4; it++) {
auto a = (sin_auto(2*theta) +2*theta - M_PI * sin_auto(y));
auto b = (2 + 2 * cos_auto(2*theta));
theta = theta - a / b;
// theta = theta - (sinh(2*theta) +2*K*theta - M_PI * sinh(y)) / (2 * K + 2 * cosh(2*theta));
} }
y = M_PI * sin_auto(theta) / 2;
x = x * cos_auto(theta);
});
break;
case mdBandEquiarea: case mdBandEquiarea:
makeband(H, ret, [] (ld& x, ld& y) { y = sin_auto(y); }); makeband(H, ret, [] (ld& x, ld& y) { y = sin_auto(y); });
break; break;
@ -1629,7 +1650,7 @@ EX void draw_boundary(int w) {
dynamicval<ld> dw(vid.linewidth, vid.linewidth * (svg::in ? svg::divby : 1)); dynamicval<ld> dw(vid.linewidth, vid.linewidth * (svg::in ? svg::divby : 1));
#endif #endif
if(elliptic && !among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal)) if(elliptic && !among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdMollweide))
circle_around_center(M_PI/2, periodcolor, 0, PPR::CIRCLE); circle_around_center(M_PI/2, periodcolor, 0, PPR::CIRCLE);
switch(pmodel) { switch(pmodel) {
@ -1658,7 +1679,7 @@ EX void draw_boundary(int w) {
return; return;
} }
case mdBand: case mdBandEquidistant: case mdBandEquiarea: case mdSinusoidal: { case mdBand: case mdBandEquidistant: case mdBandEquiarea: case mdSinusoidal: case mdMollweide: {
if(DIM == 3) return; if(DIM == 3) return;
if(pmodel == mdBand && models::model_transition != 1) return; if(pmodel == mdBand && models::model_transition != 1) return;
bool bndband = ((pmodel == mdBand) ? hyperbolic : sphere); bool bndband = ((pmodel == mdBand) ? hyperbolic : sphere);

2
models.cpp
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@ -108,7 +108,7 @@ EX namespace polygonal {
#if HDR #if HDR
inline bool mdAzimuthalEqui() { return among(pmodel, mdEquidistant, mdEquiarea, mdEquivolume); } inline bool mdAzimuthalEqui() { return among(pmodel, mdEquidistant, mdEquiarea, mdEquivolume); }
inline bool mdBandAny() { return among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal); } inline bool mdBandAny() { return among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdMollweide); }
#endif #endif
EX namespace models { EX namespace models {