Mesh Distortion Based On Laplacian Coordinates

Mesh deformation refers to modify the shape of the 3D mesh model through a certain way, which has been widely used in 3D animation, film special effects,3D games and other fields. In recent years, with the rapid development of the 3D scanner, computer and other technologies, more and more 3D models have been applied into various fields, which led to the larger demand of 3Dmodel deformation technology. Therefore, the mesh deformation technology has attracted more and more attention of the scholars at home and abroad. At present, it belongs to one of the important research direction in computer graphics.The initial deformation technology can be traced back the free-form deformation appeared in the 1980’s. Its main idea is to surround the model with a box, through the change of box’s space to change the model itself. This method is more suitable for the smooth surface deformation. The multi-resolution deformation technology comes to appear later, and then the skeleton sub-space deformation technology and the mesh deformation based on differential coordinates and other technologies appeared. The 3D mesh deformation based on differential coordinates is simple to implement, has the better deformation effect, and can keep the local detail features of the deformed portion unchanging. Therefore, the mesh deformation based on differential coordinates has drawn much of researchers’ attention. This paper made some related researches on the mesh deformation technology based on differential coordinates. The following is the main contents of this paper and some views that proposed in this paper.This paper introduced the deformation technology based on differential coordinates and the detailed process of mesh deformation, and pointed out the shortcomings of the differential coordinates itself, namely the rotational invariance of model local vector in deformation process. According to its shortcomings, the paper introduced the 3D mesh deformation method in Laplace coordinates based on the value coordinates in the projection plane. Compared with the method to solve the rotational invariance of local vector, this method is simple and the time complexity of the algorithm is low.This paper put forward the free-controlling vertex method by selecting the vertices in Bezier curve. Mesh model can be divided into three parts in the deformation process:including, the controlling vertex part, the required part, and unchanged part. The deformation process is accomplished by moving the free-controlling vertex part to a certain spatial position, and then obtained the rest of the model position through a certain way. Therefore, how well the selection of free-controlling vertex has a certain relationship with the deformation results. At present, general most of them selected the vertices in a rectangle as the free-controlling vertices. However, the region shape selected by this method is fixed. And sometimes the selected region shape is not necessarily the ideal. The paper proposed that the region shape of the free-controlling vertex selected by the free-controlling vertex method can be changed freely, which can freely select the vertices what the user wanted.In the model whole deformation process, some local features of the model might change.This paper put forward a deformation technology to keep the local features unchanging in the global deformation. In the overall deformation process of the model on the differential coordinates, the car’s tires will become the ellipse when elongated the car. The method proposed in this paper can ensure car’s tires still keep the round in the process of elongating the car, but the position of the car’s tires will change with the elongation of the car, so as to ensure the distorted model look like distortion-less.