This paper presents a method to generate high quality triangular or quadrilateral meshes that uses direction fields and a frontal point insertion strategy. Two types of direction fields are considered: asterisk fields and cross fields. With asterisk fields we generate high quality triangulations, while with cross fields we generate right-angled triangulations that are optimal for transformation to quadrilateral meshes. The input of our algorithm is an initial triangular mesh and a direction field calculated on it. The goal is to compute the vertices of the final mesh by an advancing front strategy along the direction field. We present an algorithm that enables to efficiently generate the points using solely information from the base mesh. A multi-threaded implementation of our algorithm is presented, allowing us to achieve significant speedup of the point generation. Regarding the quadrangulation process, we develop a quality criterion for right-angled triangles with respect to the local cross field and an optimization process based on it. Thus we are able to further improve the quality of the output quadrilaterals. The algorithm is demonstrated on the sphere and examples of high quality triangular and quadrilateral meshes of coastal domains are presented.
翻译:本文展示了一种方法来生成高质量的三角或四边三角间距, 使用方向字段和前点插入策略。 考虑了两种类型的方向字段: 星号字段和交叉字段。 有星号字段, 我们产生高质量的三角关系, 而有交叉字段, 我们生成了右三角三角关系, 最适宜转换成四边间距。 我们的算法输入是一个初始三角网格, 并以此为基础计算方向字段。 目标是通过在方向字段上推进前方战略, 计算最后网格的顶端。 我们展示了一种算法, 能够仅利用基网格中的信息有效生成点。 演示了多轨化的算法, 使我们能够大大加速点生成。 关于四边形进程, 我们为右三角三角三角间距与本地交叉场的优化进程制定了质量标准。 因此, 我们能够进一步提高产出四方间距的质量。 算法在高三角形和高三角形三角形三角形区域中展示了。