fix mitering bug with ground polylines over long distances

CHANGES.md

@@ -14,8 +14,9 @@ Change Log
 ##### Fixes :wrench:
 * Fixed an edge case where Cesium would provide ion access token credentials to non-ion servers if the actual asset entrypoint was being hosted by ion. [#7839](https://github.com/AnalyticalGraphicsInc/cesium/pull/7839)
 * Fixed a bug that caused Cesium to request non-existent tiles for terrain tilesets lacking tile availability, i.e. a `layer.json` file.
-* Fixed memory leak when removing entities that had a `HeightReference` of `CLAMP_TO_GROUND` or `RELATIVE_TO_GROUND`. This includes when removing a `DataSource`. 
+* Fixed memory leak when removing entities that had a `HeightReference` of `CLAMP_TO_GROUND` or `RELATIVE_TO_GROUND`. This includes when removing a `DataSource`.
 * Fixed 3D Tiles credits not being shown in the data attribution box. [#7877](https://github.com/AnalyticalGraphicsInc/cesium/pull/7877)
+* Fixed a bug that caused missing segments for ground polylines with coplanar points over large distances. [#7855](https://github.com/AnalyticalGraphicsInc/cesium/issues/7855)
 
 ### 1.57 - 2019-05-01
 

Source/Core/GroundPolylineGeometry.js

@@ -353,41 +353,42 @@ define([
         return result;
     }
 
+    function tangentDirection(target, origin, up, result) {
+        result = direction(target, origin, result);
+
+        // orthogonalize
+        result = Cartesian3.cross(result, up, result);
+        result = Cartesian3.normalize(result, result);
+        result = Cartesian3.cross(up, result, result);
+        return result;
+    }
+
     var toPreviousScratch = new Cartesian3();
     var toNextScratch = new Cartesian3();
     var forwardScratch = new Cartesian3();
-    var coplanarNormalScratch = new Cartesian3();
-    var coplanarPlaneScratch = new Plane(Cartesian3.UNIT_X, 0.0);
     var vertexUpScratch = new Cartesian3();
     var cosine90 = 0.0;
+    var cosine180 = -1.0;
     function computeVertexMiterNormal(previousBottom, vertexBottom, vertexTop, nextBottom, result) {
         var up = direction(vertexTop, vertexBottom, vertexUpScratch);
-        var toPrevious = direction(previousBottom, vertexBottom, toPreviousScratch);
-        var toNext = direction(nextBottom, vertexBottom, toNextScratch);
-
-        // Check if points are coplanar in a right-side-pointing plane that contains "up."
-        // This is roughly equivalent to the points being colinear in cartographic space.
-        var coplanarNormal = Cartesian3.cross(up, toPrevious, coplanarNormalScratch);
-        coplanarNormal = Cartesian3.normalize(coplanarNormal, coplanarNormal);
-        var coplanarPlane = Plane.fromPointNormal(vertexBottom, coplanarNormal, coplanarPlaneScratch);
-        var nextBottomDistance = Plane.getPointDistance(coplanarPlane, nextBottom);
-        if (CesiumMath.equalsEpsilon(nextBottomDistance, 0.0, CesiumMath.EPSILON7)) {
-            // If the points are coplanar, point the normal in the direction of the plane
-            Cartesian3.clone(coplanarNormal, result);
-            return result;
+
+        // Compute vectors pointing towards neighboring points but tangent to this point on the ellipsoid
+        var toPrevious = tangentDirection(previousBottom, vertexBottom, up, toPreviousScratch);
+        var toNext = tangentDirection(nextBottom, vertexBottom, up, toNextScratch);
+
+        // Check if tangents are almost opposite - if so, no need to miter.
+        if (CesiumMath.equalsEpsilon(Cartesian3.dot(toPrevious, toNext), cosine180, CesiumMath.EPSILON5)) {
+             result = Cartesian3.cross(up, toPrevious, result);
+             result = Cartesian3.normalize(result, result);
+             return result;
         }
 
-        // Average directions to previous and to next
+        // Average directions to previous and to next in the plane of Up
         result = Cartesian3.add(toNext, toPrevious, result);
         result = Cartesian3.normalize(result, result);
 
-        // Rotate this direction to be orthogonal to up
-        var forward = Cartesian3.cross(up, result, forwardScratch);
-        Cartesian3.normalize(forward, forward);
-        Cartesian3.cross(forward, up, result);
-        Cartesian3.normalize(result, result);
-
         // Flip the normal if it isn't pointing roughly bound right (aka if forward is pointing more "backwards")
+        var forward = Cartesian3.cross(up, result, forwardScratch);
         if (Cartesian3.dot(toNext, forward) < cosine90) {
             result = Cartesian3.negate(result, result);
         }

Specs/Core/GroundPolylineGeometrySpec.js

@@ -287,7 +287,7 @@ defineSuite([
             positions : Cartesian3.fromDegreesArray([
                 0.01, 0.0,
                 0.02, 0.0,
-                0.01, 0.0
+                0.01, CesiumMath.EPSILON7
             ]),
             granularity : 0.0
         });
@@ -299,11 +299,10 @@ defineSuite([
 
         var miteredStartNormal = Cartesian3.unpack(startNormalAndForwardOffsetZvalues, 32);
         var miteredEndNormal = Cartesian3.unpack(endNormalAndTextureCoordinateNormalizationXvalues, 0);
-        var reverseMiteredEndNormal = Cartesian3.multiplyByScalar(miteredEndNormal, -1.0, new Cartesian3());
 
-        expect(Cartesian3.equalsEpsilon(miteredStartNormal, reverseMiteredEndNormal, CesiumMath.EPSILON7)).toBe(true);
+        expect(Cartesian3.equalsEpsilon(miteredStartNormal, miteredEndNormal, CesiumMath.EPSILON7)).toBe(true);
 
-        var approximateExpectedMiterNormal = new Cartesian3(0.0, 1.0, 0.0);
+        var approximateExpectedMiterNormal = new Cartesian3(0.0, -1.0, 0.0);
 
         Cartesian3.normalize(approximateExpectedMiterNormal, approximateExpectedMiterNormal);
         expect(Cartesian3.equalsEpsilon(approximateExpectedMiterNormal, miteredStartNormal, CesiumMath.EPSILON2)).toBe(true);