严格顶点约束的网格光顺算法

为了使网格光顺算法在优化网格顶点以消除噪声同时，保持原始数据的精度，避免模型细节当作噪声而去除，给出一种用于三角网格光顺的新算法,该算法保证光顺结果中每个顶点距离其原始位置不超过给定偏差范围.将此光顺问题转化为带有一组非线性约束的二次优化问题,并提出一种有效的迭代线性求解方法用于其优化.算法也可以通过在优化中结合特征约束来更好地保护模型的精细特征.在大量扫描模型和人工合成模型上进行了实验,结果显示：算法可以有效消除所有噪声,同时保持原始模型的特征．

Mesh smoothing with vertex tolerance constraints

In order to make the mesh smoothing algorithms preserve the data precision and avoid dealing with the details of the models as noises and removing them, while relocating the positions of the vertices to remove the noise, a novel approach was presented for smoothing triangular meshes which guarantees that each vertex in the result does not exceed a given distance tolerance from its original position. The problem was formulized as a quadratic optimization with a set of nonlinear constraints, and  a reliable iterative linear solution was proposed  to solve the optimization. The new algorithm can also preserve the sharp features in the result by integrating feature constraints in the optimization. Many experimental results on both scanned models and synthetic models showed  that the proposed algorithm can remove all the noise while preserving the features of the original model.