标题： 用于单连通开曲面的密度均衡映射 显示英文标题

标题： Density-equalizing maps for simply-connected open surfaces

摘要： 在本文中，我们关注的是在$\mathbb{R}^3$中创建单连通开曲面的平坦映射的问题。 利用物理学中的密度扩散自然原理，我们提出了一种有效的算法，用于计算具有任何预定密度分布的密度相等平坦映射。 通过改变初始密度分布，可以实现具有不同特性的大量映射。 例如，单连通开曲面的面积保持参数化可以轻松计算。 实验结果被展示以证明我们所提出方法的有效性。 探讨了在数据可视化和曲面重网格化中的应用。 显示英文摘要

摘要： In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properties can be achieved. For instance, area-preserving parameterizations of simply-connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.