Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio

Real-Time Ultrasound Simulation for Medical Training and Standardized Patient Assessment

With the increasing role played by ultrasound in clinical diagnostics, ultrasound training in medical education has become more and more important. The clinical routine for ultrasound training is on real patients; therefore monitored and guided examinations involving medical students are quite time-constrained. Furthermore, standardized patients (SPs), who are increasingly used in medical school for teaching and assessing medical students, need to be augmented. These SPs are typically healthy individuals who can not accurately portray the variety of abnormalities that are needed for training especially when medical examinations involve instrument interactions. To augment SPs in a realistically effective way and also address the resourced time constraints for sonography training, a computerized ultrasound simulation is essential for medical education. In this dissertation, I investigate a real-time ultrasound simulation methodology based on a virtual 3-dimentional (3-D) mesh organ. This research has developed the simulation technology to augment SPs with synthetic ultrasound images. I present this methodology and its use in simulating echocardiography. This simulated echocardiogram displays the various oriented sonographs in real time according to the placement of a mock transducer without the need of an actual patient

Doctor of Philosophy

dissertationMany algorithms have been developed for synthesizing shaded images of three dimensional objects modeled by computer. In spite of widely differing approaches the current state of the art algorithms are surprisingly similar with respect to the richness of the scenes they can process. One attribute these algorithms have in common is the use of a conventional passive data base to represent the objects being modeled. This paper postulates and explores the use of an alternative modeling technique which uses procedures to represent the objects being modeled. The properties and structure of such "procedure models" are investigated and an algorithm based on them is presented

An exact general remeshing scheme applied to physically conservative voxelization

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as "physically conservative voxelization". At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara (1994), who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3

A Library for Declarative Resolution-Independent 2D Graphics

The design of most 2D graphics frameworks has been guided by what the computer can draw efficiently, instead of by how graphics can best be expressed and composed. As a result, such frameworks restrict expressivity by providing a limited set of shape primitives, a limited set of textures and only affine transformations. For example, non-affine transformations can only be added by invasive modification or complex tricks rather than by simple composition. More general frameworks exist, but they make it harder to describe and analyze shapes. We present a new declarative approach to resolution-independent 2D graphics that generalizes and simplifies the functionality of traditional frameworks, while preserving their efficiency. As a real-world example, we show the implementation of a form of focus+context lenses that gives better image quality and better performance than the state-of-the-art solution at a fraction of the code. Our approach can serve as a versatile foundation for the creation of advanced graphics and higher level frameworks

Shared-Frustum stereo rendering

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (p. 52-54).by Michael Vincent Capps.S.M