Area Preserving Parameterization

Area-preserving parameterization aims to map 3D surfaces onto 2D domains while minimizing geometric distortion, crucial for tasks like texture mapping and shape analysis. Current research focuses on developing novel parameterization methods, including those based on neural networks (e.g., using height fields or spherical harmonics) and piecewise linear functions (e.g., Delaunay triangulations), to improve accuracy and efficiency, particularly for complex shapes like anatomical surfaces and garments. These advancements enhance the representation and manipulation of 3D shapes in various fields, including computer graphics, medical imaging, and machine learning, by enabling more accurate and efficient processing of complex 3D data.