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Bijective Parameterization with Free Boundaries

机译:自由边界的双射参数化

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We present a fully automatic method for generating guaranteed bijectivernsurface parameterizations from triangulated 3D surfaces partitionedrninto charts. We do so by using a distortion metric that preventsrnlocal folds of triangles in the parameterization and a barrierrnfunction that prevents intersection of the chart boundaries. In addition,rnwe show how to modify the line search of an interior pointrnmethod to directly compute the singularities of the distortion metricrnand barrier functions to maintain a bijective map. By using anrnisometric metric that is efficient to compute and a spatial hash tornaccelerate the evaluation and gradient of the barrier function forrnthe boundary, we achieve fast optimization times. Unlike previousrnmethods, we do not require the boundary be constrained by thernuser to a non-intersecting shape to guarantee a bijection, and thernboundary of the parameterization is free to change shape during thernoptimization to minimize distortion.
机译:我们提出了一种全自动的方法,该方法可从划分为图表的三角3D曲面生成有保证的双射曲面参数化。通过使用可防止参数化中三角形的局部折叠的变形量度和可防止图表边界相交的屏障功能,可以做到这一点。另外,我们展示了如何修改内部点方法的线搜索以直接计算畸变度量和势垒函数的奇异性以维持双射图。通过使用有效计算的空间光度度量和空间散列来加速边界边界函数的求值和梯度,我们实现了快速的优化时间。与以前的方法不同,我们不要求用户将边界限制为不相交的形状以确保双射,并且参数化的边界在优化过程中可以自由更改形状以最小化失真。

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