75a060a243
For polygon cell shapes (that are not triangles or quadrilaterals), interpolations are done by finding the center point and creating a triangle fan around that point. Previously, the gradient was computed in the same way as interpolation: identifying the correct triangle and computing the gradient for that triangle. The problem with that approach is that makes the gradient discontinuous at the boundaries of this implicit triangle fan. To make things worse, this discontinuity happens right at each vertex where gradient calculations happen frequently. This means that when you ask for the gradient at the vertex, you might get wildly different answers based on floating point imprecision. Get around this problem by creating a small triangle around the point in question, interpolating values to that triangle, and use that for the gradient. This makes for a smoother gradient transition around these internal boundaries.
975 B
Fix cell derivatives for polygon cell shape
For polygon cell shapes (that are not triangles or quadrilaterals), interpolations are done by finding the center point and creating a triangle fan around that point. Previously, the gradient was computed in the same way as interpolation: identifying the correct triangle and computing the gradient for that triangle.
The problem with that approach is that makes the gradient discontinuous at the boundaries of this implicit triangle fan. To make things worse, this discontinuity happens right at each vertex where gradient calculations happen frequently. This means that when you ask for the gradient at the vertex, you might get wildly different answers based on floating point imprecision.
Get around this problem by creating a small triangle around the point in question, interpolating values to that triangle, and use that for the gradient. This makes for a smoother gradient transition around these internal boundaries.