Least squares conformal maps for automatic texture atlas generation
Least squares conformal maps for automatic texture atlas generation
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DOI：
10.1145/566570.566590
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发表时间：
2002-07-01
影响因子：
6.2
通讯作者：
Maillot, J
中科院分区：
文献类型：
--
作者：
Lévy, B;Petitjean, S;Maillot, J
纹理图集是3D绘制系统的有效颜色表示。将待纹理模型分解为同胚于圆盘的图表，每个图表被参数化，展开的图表被打包在纹理空间中。现有的三角化曲面纹理图集方法存在一些局限性，需要生成大量具有简单边界的小图表。图之间的不连续会造成伪影，使得用规则图案绘制大区域变得困难。本文的主要贡献是基于柯西-黎曼方程的最小二乘逼近，提出了一种新的拟共形参数化方法。这样定义的目标函数最小化角度变形，我们证明了以下性质：最小值是唯一的，与纹理空间的相似性无关，与网格的分辨率无关，不能产生三角翻转。该函数在数值上表现良好，因此可以非常有效地最小化。该方法具有较强的健壮性，可以对边界复杂的大型图表进行参数化处理，并引入了分割方法将模型分解为具有自然形状的图表，并引入了一种新的填充算法在纹理空间中进行聚集。我们演示了我们的方法应用于绘制扫描和建模的数据集。
A Texture Atlas is an efficient color representation for 3D Paint Systems. The model to be textured is decomposed into charts homeomorphic to discs, each chart is parameterized, and the unfolded charts are packed in texture space. Existing texture atlas methods for triangulated surfaces suffer from several limitations, requiring them to generate a large number of small charts with simple borders. The discontinuities between the charts cause artifacts, and make it difficult to paint large areas with regular patterns.In this paper, our main contribution is a new quasi-conformal parameterization method, based on a least-squares approximation of the Cauchy-Riemann equations. The so-defined objective function minimizes angle deformations, and we prove the following properties: the minimum is unique, independent of a similarity in texture space, independent of the resolution of the mesh and cannot generate triangle flips. The function is numerically well behaved and can therefore be very efficiently minimized. Our approach is robust, and can parameterize large charts with complex borders.We also introduce segmentation methods to decompose the model into charts with natural shapes, and a new packing algorithm to gather them in texture space. We demonstrate our approach applied to paint both scanned and modeled data sets.