Geodesic Paths On 3D Surfaces: Survey and Open Problems

This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered

Automatic tailoring and cloth modelling for animation characters.

The construction of realistic characters has become increasingly important to the production of blockbuster films, TV series and computer games. The outfit of character plays an important role in the application of virtual characters. It is one of the key elements reflects the personality of character. Virtual clothing refers to the process that constructs outfits for virtual characters, and currently, it is widely used in mainly two areas, fashion industry and computer animation. In fashion industry, virtual clothing technology is an effective tool which creates, edits and pre-visualises cloth design patterns efficiently. However, using this method requires lots of tailoring expertises. In computer animation, geometric modelling methods are widely used for cloth modelling due to their simplicity and intuitiveness. However, because of the shortage of tailoring knowledge among animation artists, current existing cloth design patterns can not be used directly by animation artists, and the appearance of cloth depends heavily on the skill of artists. Moreover, geometric modelling methods requires lots of manual operations. This tediousness is worsen by modelling same style cloth for different characters with different body shapes and proportions. This thesis addresses this problem and presents a new virtual clothing method which includes automatic character measuring, automatic cloth pattern adjustment, and cloth patterns assembling. There are two main contributions in this research. Firstly, a geodesic curvature flow based geodesic computation scheme is presented for acquiring length measurements from character. Due to the fast growing demand on usage of high resolution character model in animation production, the increasing number of characters need to be handled simultaneously as well as improving the reusability of 3D model in film production, the efficiency of modelling cloth for multiple high resolution character is very important. In order to improve the efficiency of measuring character for cloth fitting, a fast geodesic algorithm that has linear time complexity with a small bounded error is also presented. Secondly, a cloth pattern adjusting genetic algorithm is developed for automatic cloth fitting and retargeting. For the reason that that body shapes and proportions vary largely in character design, fitting and transferring cloth to a different character is a challenging task. This thesis considers the cloth fitting process as an optimization procedure. It optimizes both the shape and size of each cloth pattern automatically, the integrity, design and size of each cloth pattern are evaluated in order to create 3D cloth for any character with different body shapes and proportions while preserve the original cloth design. By automating the cloth modelling process, it empowers the creativity of animation artists and improves their productivity by allowing them to use a large amount of existing cloth design patterns in fashion industry to create various clothes and to transfer same design cloth to characters with different body shapes and proportions with ease

Fast Wavefront Propagation (FWP) for Computing Exact Geodesic Distances on Meshes

Computing geodesic distances on triangle meshes is a fundamental problem in computational geometry and computer graphics. To date, two notable classes of algorithms, the Mitchell-Mount-Papadimitriou (MMP) algorithm and the Chen-Han (CH) algorithm, have been proposed. Although these algorithms can compute exact geodesic distances if numerical computation is exact, they are computationally expensive, which diminishes their usefulness for large-scale models and/or time-critical applications. In this paper, we propose the fast wavefront propagation (FWP) framework for improving the performance of both the MMP and CH algorithms. Unlike the original algorithms that propagate only a single window (a data structure locally encodes geodesic information) at each iteration, our method organizes windows with a bucket data structure so that it can process a large number of windows simultaneously without compromising wavefront quality. Thanks to its macro nature, the FWP method is less sensitive to mesh triangulation than the MMP and CH algorithms. We evaluate our FWP-based MMP and CH algorithms on a wide range of large-scale real-world models. Computational results show that our method can improve the speed by a factor of 3-10