Make Chunk bounding polyhedron fully, but still not tightly, encapsulate the chunk

modules/globebrowsing/chunk/chunk.cpp

@@ -128,23 +128,44 @@ namespace openspace {
         BoundingHeights boundingHeight = getBoundingHeights();
 
         // assume worst case
-        double patchCenterRadius = ellipsoid.maximumRadius(); 
+        double patchCenterRadius = ellipsoid.maximumRadius();
+
+        double maxCenterRadius = patchCenterRadius + boundingHeight.max;
+        Geodetic2 halfSize = patch.halfSize();
 
         // As the patch is curved, the maximum height offsets at the corners must be long 
         // enough to cover large enough to cover a boundingHeight.max at the center of the 
-        // patch. 
-        double maxCenterRadius = patchCenterRadius + boundingHeight.max;
-        double maximumPatchSide = max(patch.halfSize().lat, patch.halfSize().lon);
-        double maxCornerHeight = maxCenterRadius / cos(maximumPatchSide) - patchCenterRadius;
+        // patch. Below this is done by an approximation.
+        double scaleToCoverCenter = 1 / cos(halfSize.lat) + 1 / cos(halfSize.lon) - 1; 
+        double maxCornerHeight = maxCenterRadius * scaleToCoverCenter - patchCenterRadius;
+
+        bool chunkIsNorthOfEquator = patch.isNorthern();
 
         // The minimum height offset, however, we can simply 
         double minCornerHeight = boundingHeight.min;
         std::vector<glm::dvec4> corners(8);
+        
+        Scalar latCloseToEquator = patch.edgeLatitudeNearestEquator();
+        Geodetic3 p1Geodetic = { { latCloseToEquator, patch.minLon() }, maxCornerHeight };
+        Geodetic3 p2Geodetic = { { latCloseToEquator, patch.maxLon() }, maxCornerHeight };
+        
+        glm::vec3 p1 = ellipsoid.cartesianPosition(p1Geodetic);
+        glm::vec3 p2 = ellipsoid.cartesianPosition(p2Geodetic);
+        glm::vec3 p = 0.5f * (p1 + p2);
+        Geodetic2 pGeodetic = ellipsoid.cartesianToGeodetic2(p);
+        Scalar latDiff = latCloseToEquator - pGeodetic.lat;
 
         for (size_t i = 0; i < 8; i++) {
             Quad q = (Quad)(i % 4);
             double cornerHeight = i < 4 ? minCornerHeight : maxCornerHeight;
-            const Geodetic3& cornerGeodetic = { patch.getCorner(q), cornerHeight };
+            Geodetic3 cornerGeodetic = { patch.getCorner(q), cornerHeight };
+            
+            bool cornerIsNorthern = i < 2;
+            bool cornerCloseToEquator = chunkIsNorthOfEquator ^ cornerIsNorthern;
+            if (cornerCloseToEquator) {
+                cornerGeodetic.geodetic2.lat += latDiff;
+            }
+
             corners[i] = dvec4(ellipsoid.cartesianPosition(cornerGeodetic), 1);
         }
         return corners;

modules/globebrowsing/chunk/chunkindex.h

@@ -42,6 +42,13 @@ enum Quad {
     SOUTH_EAST
 };
 
+enum CardinalDirection {
+    WEST = 0,
+    EAST,
+    NORTH,
+    SOUTH,
+};
+
 
 
 using HashKey = unsigned long;