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Shape processing defines a set of theoretical and algorithmic tools for creating, measuring and modifying digital representations of shapes.  Such tools are of paramount importance to many disciplines of computer graphics, including modeling, animation, visualization, and image processing.  Many applications of shape processing can be found in the entertainment and medical industries. In an attempt to improve upon many previous shape processing techniques, the present thesis explores the theoretical and algorithmic aspects of a difference measure, which involves fitting a ball (disk in 2D and sphere in 3D) so that it has at least one tangential contact with each shape and the ball interior is disjoint from both shapes. We propose a set of ball-based operators and discuss their properties, implementations, and applications.  We divide the group of ball-based operations into unary and binary as follows: Unary operators include: * Identifying details (sharp, salient features, constrictions) * Smoothing shapes by removing such details, replacing them by fillets and roundings * Segmentation (recognition, abstract modelization via centerline and radius variation) of tubular structures Binary operators include: * Measuring the local discrepancy between two shapes * Computing the average of two shapes * Computing point-to-point correspondence between two shapes * Computing circular trajectories between corresponding points that meet both shapes at right angles * Using these trajectories to support smooth morphing (inbetweening) * Using a curve morph to construct surfaces that interpolate between contours on consecutive slices The technical contributions of this thesis focus on the implementation of these tangent-ball operators and their usefulness in applications of shape processing. We show specific applications in the areas of animation and computer-aided medical diagnosis.  These algorithms are simple to implement, mathematically elegant, and fast to execute.

[Truncated abstract] Currently, one of the active areas of research in computer graphics is related to creating realistic images and animations that mimic the world we see around us. There has been significant work in modeling and simulating natural phenomena such as fire, clouds, water, and vegetation. Some of these works are employed in the entertainment industry, especially as special effects in cinematic films. Of particular interest is the area of vegetation, given the possible structural complexity and variation in different types of plants. This provides a challenge to develop methods and techniques that effectively and realistically model the movement and behavior of plants. In response to this challenge, there has been significant work in the area of modeling plant structure, as well as modeling of the dynamics and wind interaction of tree branches. However, there is a distinct lack of approaches involved with modeling the dynamics and behavior of individual leaves. Most of the previous approaches focus on the modeling of the branches of a tree, and rarely consider the movement of the leaves in detail. This makes it particularly hard to model the interactions of plants with relatively large leaves, where the dynamics of the leaves are important. In other words, there is no method that could effectively simulate the lower canopy of a forest or jungle, where there are many ferns, saplings, and other broad-leafed plants. Therefore, I present in this thesis a leaf animation system that is designed specifically for simulating and animating plants with relatively large leaves with realistic dynamics in real-time. .... These interactions illustrate the flexibility and robustness of the leaf movement model. In particular, I present a novel approach in modeling volumetric wind through the wind cube that approximates wind behavior such as obstruction by leaves, and constructive and destructive interference. This unique approach is based on modeling wind as a spatial collection of wind vectors and the interaction of the vectors is governed by the rules of each cube-shaped cell of the wind cube. In the end, this wind cube allows for convincing behavior of wind and the subsequent interaction with the leaves of a plant. The leaf animation system is also suitable for simulating a number of plants in a landscape. This is possible through another novel method of reducing the rendering time to allow for more plants to be simulated. This method involves using an animated texture in place of plants that are far from the camera, when the difference visually is not blatantly noticeable. This is a form of the commonly used levels of detail to reduce the complexity of the landscape, but my method is novel in that it has not been implemented in a way where the texture itself is animated in place of the plant. I investigate the strengths and limitations of this approach in reducing rendering time for a landscape of plants. Thus, the leaf animation system is suitable for realistic and interactive virtual reality environments. These virtual environments feature heavily in current video games that involve realistic and believable worlds. In addition to the film and video game industry, these virtual environments are also integral in the application of virtual reality as psychological therapies.

Thesis (M.F.A.)--Rochester Institute of Technology, 2008. / Typescript.

Thesis (M.F.A.)--Rochester Institute of Technology, 2008. / Typescript.

Thesis (M.F.A.)--Rochester Institute of Technology, 2008. / Typescript.

Thesis (M.F.A.)--Rochester Institute of Technology, 2009. / Typescript. Includes bibliographical references (leaf 42).

Thesis (M.F.A.)--Rochester Institute of Technology, 2009. / Typescript.

Thesis (M.F.A.)--Rochester Institute of Technology, 2009. / Typescript.

Thesis (M.F.A.)--Rochester Institute of Technology, 2008. / Typescript. Includes bibliographical references (leaf 21).