From 2b61413a8149073a3cc8954ee8173bdf925aad3f Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Sat, 30 Mar 2019 17:45:56 +0100
Subject: [PATCH] azimuthal equivolume projection

---
 classes.cpp    | 1 +
 classes.h      | 2 ++
 conformal.cpp  | 1 +
 hyper.h        | 4 ++--
 hyperpoint.cpp | 9 +++++++++
 hypgraph.cpp   | 6 ++++--
 6 files changed, 19 insertions(+), 4 deletions(-)

diff --git a/classes.cpp b/classes.cpp
index 8d4b092b..2880853d 100644
--- a/classes.cpp
+++ b/classes.cpp
@@ -585,6 +585,7 @@ const modelinfo models[int(mdPolynomial)+1] = {
   {X3("rotated hyperboles"), mf::hyper_only},  
   {X3("spiral"), mf::hyper_or_torus | mf::quasiband},
   {X3("native perspective"), 0},
+  {X3("azimuthal equi-volume"), mf::azimuthal | mf::equivolume | mf::euc_boring},
   {X3(""), 0},
   {X3(""), 0},
   {X3(""), 0},
diff --git a/classes.h b/classes.h
index b9a14f5e..b22e9d4f 100644
--- a/classes.h
+++ b/classes.h
@@ -258,6 +258,7 @@ enum eModel {
   mdHemisphere, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdTwoPoint, 
   mdFisheye, mdJoukowsky, mdJoukowskyInverted,
   mdRotatedHyperboles, mdSpiral, mdPerspective,
+  mdEquivolume, 
   mdGUARD, mdUnchanged, mdHyperboloidFlat, mdPolynomial
   };
 
@@ -274,6 +275,7 @@ namespace mf {
   static const flagtype hyper_only = 128;
   static const flagtype hyper_or_torus = 256;
   static const flagtype quasiband = 512;
+  static const flagtype equivolume = 1024;
   };
   
 struct modelinfo {
diff --git a/conformal.cpp b/conformal.cpp
index db70f978..5eb00d82 100644
--- a/conformal.cpp
+++ b/conformal.cpp
@@ -609,6 +609,7 @@ namespace conformal {
     if(sphere && (pm == mdHalfplane || pm == mdBall))
       return false;
     if(DIM == 2 && pm == mdPerspective) return false;
+    if(DIM == 2 && pm == mdEquivolume) return false;
     if(DIM == 3 && among(pm, mdBall, mdHyperboloid, mdFormula, mdPolygonal, mdRotatedHyperboles, mdSpiral, mdHemisphere)) return false;
     return true;
     }    
diff --git a/hyper.h b/hyper.h
index 4fef44d5..124e50da 100644
--- a/hyper.h
+++ b/hyper.h
@@ -2232,9 +2232,9 @@ void drawShape(pair<ld,ld>* coords, int qty, color_t color);
 
 extern eModel pmodel;
 
-inline bool mdAzimuthalEqui() { return pmodel == mdEquidistant || pmodel == mdEquiarea; }
+inline bool mdAzimuthalEqui() { return among(pmodel, mdEquidistant, mdEquiarea, mdEquivolume); }
 
-inline bool mdBandAny() { return pmodel == mdBand || pmodel == mdBandEquidistant || pmodel == mdBandEquiarea || pmodel == mdSinusoidal; }
+inline bool mdBandAny() { return among(pmodel, mdBand, mdBandEquidistant, mdBandEquiarea, mdSinusoidal); }
 
 color_t darkena(color_t c, int lev, int a);
 
diff --git a/hyperpoint.cpp b/hyperpoint.cpp
index f5793be6..51795bdd 100644
--- a/hyperpoint.cpp
+++ b/hyperpoint.cpp
@@ -67,6 +67,15 @@ ld asin_auto(ld x) {
     }
   }
 
+ld volume_auto(ld r) {
+  switch(cgclass) {
+    case gcEuclid: return 4 * r * r * r / 3 * M_PI;
+    case gcHyperbolic: return M_PI * (sinh(2*r) - 2 * r);
+    case gcSphere: return M_PI * (2 * r - sin(2*r));
+    default: return 0;
+    }
+  }
+
 ld asin_auto_clamp(ld x) {
   switch(cgclass) {
     case gcEuclid: return x;
diff --git a/hypgraph.cpp b/hypgraph.cpp
index d62d6402..2ad5290f 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -557,7 +557,7 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
       makeband(H, ret, [] (ld& x, ld& y) { x *= cos_auto(y); });
       break;
     
-    case mdEquidistant: case mdEquiarea: {
+    case mdEquidistant: case mdEquiarea: case mdEquivolume: {
       ld zlev = find_zlev(H);
 
       ld rad = hypot_d(DIM, H);
@@ -568,7 +568,9 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
       
       // 4 pi / 2pi = M_PI 
       
-      if(pmodel == mdEquiarea && sphere)
+      if(pmodel == mdEquivolume)
+        d = pow(volume_auto(d), 1/3.) * pow(M_PI / 2, 1/3.);
+      else if(pmodel == mdEquiarea && sphere)
         d = sqrt(2*(1 - cos(d))) * M_PI / 2;
       else if(pmodel == mdEquiarea && hyperbolic)
         d = sqrt(2*(cosh(d) - 1)) / 1.5;