CAJ | 학술논문

网格切割在图形处理领域有着广泛的应用,为了更加有效和简单地得到同胚于圆盘的开网格,提出一种基于泊松标量场的三角网格切割算法.对于给定的任意网格,通过求解泊松方程构造标量场来选取临界点,并采用最速下降法给出临界点到边界或者初始点的切割路径;对于亏格不为零的网格,基于Morse理论,通过构造一个调和标量场来得到鞍点,并将它们连接到边界.该方法把任意亏格网格切割成与圆盘同胚的单边界网格,减小了在网格展开过程中产生的扭曲.实验结果表明,在给定临界点的情况下,采用文中算法得到的切割路径能很好地逼近最短路径,而且不受网格限制,适用于任意亏格的开或闭网格.
망격절할재도형처리영역유착엄범적응용,위료경가유효화간단지득도동배우원반적개망격,제출일충기우박송표량장적삼각망격절할산법.대우급정적임의망격,통과구해박송방정구조표량장래선취림계점,병채용최속하강법급출림계점도변계혹자초시점적절할로경;대우우격불위령적망격,기우Morse이론,통과구조일개조화표량장래득도안점,병장타문련접도변계.해방법파임의우격망격절할성여원반동배적단변계망격,감소료재망격전개과정중산생적뉴곡.실험결과표명,재급정림계점적정황하,채용문중산법득도적절할로경능흔호지핍근최단로경,이차불수망격한제,괄용우임의우격적개혹폐망격.
Mesh cutting is widely used in graphics. We present a more efficient and simple method based on Poisson scalar field for cutting an arbitrary genus surface mesh into a disc-like mesh. Given a mesh, we first solve a Poisson equation to construct a scalar field and use it to generate some critical points. The cutting paths between the critical points and the boundaries are solved in the Poisson scalar field using the deepest descent method. For meshes with nonzero-genus, we construct a Harmonic scalar field, and connect the saddle points with the boundaries based on the Morse theory. Our cutting cross a set of edges of the mesh including the boundaries if any, generating a single topological disc. We also reduce the distortion during mesh flattening. Our experiments show that the cutting path in this paper well approximate the shortest path given the critical points, and the proposed method is applicable to arbitrary genus meshes.