基于微分坐标的网格morphing

发布时间：2018-08-16 17:26

【摘要】：随着计算机图形学和硬件技术的高速发展,计算机动画作为一种新兴的产业已经渗透到了人们生活的各个角落,如商业广告,电影特技、动画片、几何造型、工业设计等领域。作为计算机动画的主要手段,morphing属于变形的一种,它是指从一个物体(初始物体)到另一个物体(目标物体)的连续、光滑、自然的过渡。设计者们可以通过该技术产生新的中间物体“填满”两个给定的物体,并通过原有的几何形状融合出新的几何形状。随着需求的增长激发了大量的三维物体morphing的工作。这里的物体可以是数字图象、多边形、多面体、网格曲面、点云数据等。本文主要针对三维网格曲面morphing展开相关研究。一般情况下,网格曲面的morphing过程可以分为两个阶段：1.网格配准；2.形状插值。本文对微分坐标的相关知识和三维网格morphing技术的发展进行了深入的研究、分类和总结。针对三维网格morphing中存在的问题并结合微分坐标的性质,本文提出了一套基于微分坐标系统三维网格的morphing算法。在网格配准阶段,我们首先对初始网格和目标网格做带约束的最小二乘网格,实质上是在最小二乘意义下通过修改网格顶点的微分坐标得出新的顶点位置,使其达到初始对齐；其次,最小化双向最近点距离；最后我们构造法向投影算子完成网格配准。在形状插值阶段,直接插值配准阶段求得的始末网格微分坐标,并补充在差值过程中丢失的微分信息,进而重建“关键帧”网格。与传统的办法相比,配准阶段,该算法可以在任意亏格的同胚网格模型之间进行,并且对输入网格的点数没有过多的要求,直接利用起始网格的链接关系重构目标网格。不需要借助共同参数域,也不用先将网格进行分割再融合技术,避免了由此带来的很多问题。扩大了实用性,化简了算法的流程,提高了运算速度。在形状插值部分中,本文很好的利用在配准过程中已经计算好的微分坐标,有效的防止了形状插值的体积收缩,并且的到了较好的视觉效果。此外,本文提出的morphing技术还具有用户交互少的特点,在用户给定初始配准点对集之后,算法可以自动生成有效的morphing序列。
[Abstract]:With the rapid development of computer graphics and hardware technology, computer animation as a new industry has penetrated into every corner of people's lives, such as commercial advertising, film stunts, animation, geometric modeling, industrial design and other fields. Morphing, as the main means of computer animation, is a kind of deformation, which refers to the continuous, smooth and natural transition from one object (initial object) to another (target object). Through this technique, designers can produce a new intermediate object to "fill" two given objects, and fuse new geometric shapes through the original geometry. As demand grows, a large number of three-dimensional objects morphing work. The objects here can be digital images, polygons, polyhedrons, grid surfaces, point cloud data, etc. This paper mainly focuses on the research of three-dimensional mesh surface morphing. In general, the morphing process of a mesh surface can be divided into two stages: 1. Grid registration 2. Shape interpolation. In this paper, the related knowledge of differential coordinates and the development of 3D grid morphing technology are deeply studied, classified and summarized. Aiming at the existing problems in 3D grid morphing and combining the properties of differential coordinates, a set of morphing algorithm based on differential coordinate system is proposed in this paper. In the stage of grid registration, we first make the constrained least square grid for the initial mesh and the target grid. In essence, we can get the new vertex position by modifying the differential coordinates of the grid vertex in the sense of least square, so that the initial alignment can be achieved. Secondly, we minimize the distance of the nearest point in two directions, and finally we construct the normal projection operator to complete the mesh registration. In the shape interpolation stage, the grid differential coordinates obtained in the registration stage are directly interpolated, and the differential information lost in the process of the difference is added to reconstruct the "key frame" grid. Compared with the traditional method, the algorithm can be implemented between the homomorphic meshes with arbitrary genus in registration stage, and the number of input meshes is not required, so the target grid can be reconstructed directly by using the link relation of the initial grid. There is no need for common parameter domain, and no mesh segmentation and fusion technology, which avoids many problems. Expanded the practicability, simplified the algorithm flow, improved the operation speed. In the part of shape interpolation, this paper makes good use of the differential coordinates that have been calculated in the registration process, effectively prevents the volume shrinkage of shape interpolation, and achieves a better visual effect. In addition, the proposed morphing technique also has the characteristics of less user interaction. After the user has given the initial matching point pair, the algorithm can automatically generate effective morphing sequences.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TP391.41

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