We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from point and curve sources using piecewise-quadratic elements, exactly reproducing flat distances regardless of mesh quality while improving accuracy over existing approaches on curved meshes. The formulation naturally supports sources placed anywhere on the mesh, not just at vertices.

翻译：我们提出了一种新颖的离散测地线表示与优化框架，用于三角形网格，该框架减少了线性方法在非均匀和粗糙离散化上产生的伪影。我们的方法使用分段二次元计算来自点和曲线源的平方测地线距离，无论网格质量如何都能精确再现平面距离，同时在弯曲网格上相比现有方法提高了精度。该公式自然地支持源放置在网格上的任意位置，而不仅限于顶点。