Dynamic Geodesic Convex Hulls in Dynamic Simple Polygons

We consider the geodesic convex hulls of points in a simple polygonal region in the presence of non-crossing line segments (barriers) that subdivide the region into simply connected faces. We present an algorithm together with data structures for maintaining the geodesic convex hull of points in each face in a sublinear update time under the fully-dynamic setting where both input points and barriers change by insertions and deletions. The algorithm processes a mixed update sequence of insertions and deletions of points and barriers. Each update takes O(n^2/3 log^2 n) time with high probability, where n is the total number of the points and barriers at the moment. Our data structures support basic queries on the geodesic convex hull, each of which takes O(polylog n) time. In addition, we present an algorithm together with data structures for geodesic triangle counting queries under the fully-dynamic setting. With high probability, each update takes O(n^2/3 log n) time, and each query takes O(n^2/3 log n) time

Shooting permanent rays among disjoint polygons in the plane

We present a data structure for ray shooting-and-insertion in the free space among disjoint polygonal obstacles with a total of $n$ vertices in the plane, where each ray starts at the boundary of some obstacle. The portion of each query ray between the starting point and the first obstacle hit is inserted permanently as a new obstacle. Our data structure uses O(n log n) space and preprocessing time, and it supports m successive ray shooting-and-insertion queries in O(n log2 n + m log m) total time. We present two applications for our data structure: (1) Our data structure supports efficient implementation of auto-partitions in the plane i.e. binary space partitions where each partition is done along the supporting line of an input segment. If n input line segments are fragmented into m pieces by an auto-partition, then it can now be implemented in O(n log2n+m log m) time. This improves the expected runtime of Patersen and Yao's classical randomized auto-partition algorithm for n disjoint line segments to O(n log2 n). (2) If we are given disjoint polygonal obstacles with a total of n vertices in the plane, a permutation of the reflex vertices, and a half-line at each reflex vertex that partitions the reflex angle into two convex angles, then the folklore convex partitioning algorithm draws a ray emanating from each reflex vertex in the prescribed order in the given direction until it hits another obstacle, a previous ray, or infinity. The previously best implementation (with a semi-dynamic ray shooting data structure) requires O(n3/2-e/2) time using O(n1+e) space. Our data structure improves the runtime to O(n log2 n)

Mutable Objects, Spatial Manipulation and Performance Optimization

Contemporary digital design techniques are powerful, but disjoint. There are myriad emerging ways of manipulating design components, and generating both functional forms and formal functions. With the combination of selective agglomeration, sequencing, and heuristics, it is possible to use these techniques to focus on optimizing performance criteria, and selecting for defined characteristics. With these techniques, complex, performance oriented systems can emerge, with minimal input and high effectiveness and e""ciency. These processes depend on iterative loops for stability and directionality, and are the basis for optimization and refinement. They begin to approach cybernetic principles of self-organization and equilibrium. By rapidly looping this process, design ‘attractors’– shared solution components–become visible and accessible. In the past, we have been dedicated to selecting the contents of the design space. With these tools, we can now ask, what are the inputs to the design process, what is the continuum or spectrum of design inputs, and what are the selection criteria for the success of a design-aspect? These new questions allow for a greater coherence within a particular cognitive model for the designed and desired object. There are ways of using optimization criteria that enable design freedom within these boundaries, while enforcing constraints and maintaining consistency for selected processes and product aspects. The identification and codification of new rules for the process support both flexibility and the potential for cognitive restructuring of the process and sequences of design

Animating physical phenomena with embedded surface meshes

Accurate computational representations of highly deformable surfaces are indispensable in the fields of computer animation, medical simulation, computer vision, digital modeling, and computational physics. The focus of this dissertation is on the animation of physics-based phenomena with highly detailed deformable surfaces represented by triangle meshes. We first present results from an algorithm that generates continuum mechanics animations with intricate surface features. This method combines a finite element method with a tetrahedral mesh generator and a high resolution surface mesh, and it is orders of magnitude more efficient than previous approaches. Next, we present an efficient solution for the challenging problem of computing topological changes in detailed dynamic surface meshes. We then introduce a new physics-inspired surface tracking algorithm that is capable of preserving arbitrarily thin features and reproducing realistic fine-scale topological changes like Rayleigh-Plateau instabilities. This physics-inspired surface tracking technique also opens the door for a unique coupling between surficial finite element methods and volumetric finite difference methods, in order to simulate liquid surface tension phenomena more efficiently than any previous method. Due to its dramatic increase in computational resolution and efficiency, this method yielded the first computer simulations of a fully developed crown splash with droplet pinch off.Ph.D.Committee Chair: Turk, Greg; Committee Member: Essa, Irfan; Committee Member: Liu, Karen; Committee Member: Mucha, Peter J.; Committee Member: Rossignac, Jare

Generating anatomical substructures for physically-based facial animation.

Physically-based facial animation techniques are capable of producing realistic facial deformations, but have failed to find meaningful use outside the academic community because they are notoriously difficult to create, reuse, and art-direct, in comparison to other methods of facial animation. This thesis addresses these shortcomings and presents a series of methods for automatically generating a skull, the superficial musculoaponeurotic system (SMAS – a layer of fascia investing and interlinking the mimic muscle system), and mimic muscles for any given 3D face model. This is done toward (the goal of) a production-viable framework or rig-builder for physically-based facial animation. This workflow consists of three major steps. First, a generic skull is fitted to a given head model using thin-plate splines computed from the correspondence between landmarks placed on both models. Second, the SMAS is constructed as a variational implicit or radial basis function surface in the interface between the head model and the generic skull fitted to it. Lastly, muscle fibres are generated as boundary-value straightest geodesics, connecting muscle attachment regions defined on the surface of the SMAS. Each step of this workflow is developed with speed, realism and reusability in mind

Liquid simulation with mesh-based surface tracking

Animating detailed liquid surfaces has always been a challenge for computer graphics researchers and visual effects artists. Over the past few years, researchers in this field have focused on mesh-based surface tracking to synthesize extremely detailed liquid surfaces as efficiently as possible. This course provides a solid understanding of the steps required to create a fluid simulator with a mesh-based liquid surface. The course begins with an overview of several existing liquid-surface-tracking techniques and the pros and cons of each method. Then it explains how to embed a triangle mesh into a finite-difference-based fluid simulator and describes several methods for allowing the liquid surface to merge together or break apart. The final section showcases the benefits and further applications of a mesh-based liquid surface, highlighting state-of-the-art methods for tracking colors and textures, maintaining liquid volume, preserving small surface features, and simulating realistic surface-tension waves