This paper presents a new method for automatically generating texture atlases for polygonal models, called Least Squares Conformal Maps (LSCMs). The method is based on a least-squares approximation of the Cauchy-Riemann equations, which minimizes angle deformations and non-uniform scalings. The key properties of the method include the uniqueness of the solution, independence from similarity transformations and mesh resolution, and the preservation of triangle orientation, which prevents triangle flips. The method is robust and can parameterize large charts with complex borders. The paper also introduces segmentation methods to decompose the model into charts with natural shapes and a new packing algorithm to gather them in texture space. The segmentation algorithm uses feature detection and chart growing to create charts that correspond to meaningful geometric entities. The packing algorithm directly packs the charts rather than their bounding rectangles, leading to more efficient use of texture space. The results show that the LSCM method produces texture atlases with minimal artifacts and efficient use of texture space. The method is compared to existing methods like MIPS and shows similar performance in terms of stretch, but with mathematical guarantees. The method is also more efficient in computation and can be applied to both scanned and modeled data sets. The paper concludes that the LSCM method provides a complete and mathematically valid solution for parameterizing complex models, which is more efficient and robust than existing methods.This paper presents a new method for automatically generating texture atlases for polygonal models, called Least Squares Conformal Maps (LSCMs). The method is based on a least-squares approximation of the Cauchy-Riemann equations, which minimizes angle deformations and non-uniform scalings. The key properties of the method include the uniqueness of the solution, independence from similarity transformations and mesh resolution, and the preservation of triangle orientation, which prevents triangle flips. The method is robust and can parameterize large charts with complex borders. The paper also introduces segmentation methods to decompose the model into charts with natural shapes and a new packing algorithm to gather them in texture space. The segmentation algorithm uses feature detection and chart growing to create charts that correspond to meaningful geometric entities. The packing algorithm directly packs the charts rather than their bounding rectangles, leading to more efficient use of texture space. The results show that the LSCM method produces texture atlases with minimal artifacts and efficient use of texture space. The method is compared to existing methods like MIPS and shows similar performance in terms of stretch, but with mathematical guarantees. The method is also more efficient in computation and can be applied to both scanned and modeled data sets. The paper concludes that the LSCM method provides a complete and mathematically valid solution for parameterizing complex models, which is more efficient and robust than existing methods.