The parametrization of triangle meshes, in particular by means of computing a map onto the plane, is a key operation in computer graphics. Typically, a piecewise linear setting is assumed, i.e., the map is linear per triangle. We present a method for the efficient computation and optimization of piecewise nonlinear parametrizations, with higher-order polynomial maps per triangle. We describe how recent advances in piecewise linear parametrization, in particular efficient second-order optimization based on majorization, as well as practically important constraints, such as local injectivity, global injectivity, and seamlessness, can be generalized to this higher-order regime. Not surprisingly, parametrizations of higher quality, i.e., lower distortion, can be obtained that way, as we demonstrate on a variety of examples.

三角形网格的参数化，特别是通过计算平面上的贴图，是计算机图形学中的关键操作。通常，采用分段线性设置，即，每个三角形的贴图是线性的。我们提出了一种有效的计算和优化分段非线性参数化的方法，每个三角形具有更高阶的多项式映射。我们描述了分段线性参数化的最新进展，特别是基于主化的有效二阶优化，以及实际重要的约束（例如局部注入性，全局注入性和无缝性）如何可以推广到此高阶系统。毫不奇怪，正如我们在各种示例中所展示的，可以通过这种方式获得更高质量的参数化，即更低的失真。