A parametric-space-based scan-line algorithm for rendering of bicubic surfaces

A novel scan-line algorithm for displaying bicubic surfaces is presented. Patches are decomposed on regions of constant sign of the z component of the normal before the scan process. Most of the computations are done in parametric space. The algorithm computes the intersection of the surfaces with only a restricted subset of scan planes and obtains the intersection with other scan planes by linear interpolation between exact intersections. A bound of the algorithm's error is given. The method is compared with Whitted's algorithm.Postprint (published version

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

Subdivision Surface based One-Piece Representation

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject\u27s topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications

Efficient Culling Techniques for Interactive Deformable NURBS Surfaces on GPU

[Abstrtact] InfoValue: NURBS (Non-uniform rational B-splines) surfaces are the standard freeform representation in Computer-Aided Design (CAD) applications. Rendering NURBS surfaces accurately while they are interactively manipulated and deformed is a challenging task. In order to achieve it, the elimination from pipeline in early stages of back-facing surfaces or surface pieces is a key advantage. Furthermore, an effective interactive manipulation implies that all the culling computations should be performed for each frame, facing the possibility of fast changes in occlusion information. In this paper, different interactive culling strategies for NURBS surfaces are presented and analyzed. These culling techniques are based on the exploitation of the geometric properties presented in a NURBS surface, that allow easily to find bounds for it in screen space for each frame. Furthermore, the culling overhead for our proposals is small compared to the computational saving, outperforming a proposal without culling. An implementation of these strategies using current GPUs is presented, achieving real-time and interactive rendering rates of complex parametric models.Xunta de Galicia y fondos FEDER; GRC2013/055Ministerio de Economía y Competitividad y fondos FEDER; TIN2013-42148-

High-performance geometric vascular modelling

Image-based high-performance geometric vascular modelling and reconstruction is an essential component of computer-assisted surgery on the diagnosis, analysis and treatment of cardiovascular diseases. However, it is an extremely challenging task to efficiently reconstruct the accurate geometric structures of blood vessels out of medical images. For one thing, the shape of an individual section of a blood vessel is highly irregular because of the squeeze of other tissues and the deformation caused by vascular diseases. For another, a vascular system is a very complicated network of blood vessels with different types of branching structures. Although some existing vascular modelling techniques can reconstruct the geometric structure of a vascular system, they are either time-consuming or lacking sufficient accuracy. What is more, these techniques rarely consider the interior tissue of the vascular wall, which consists of complicated layered structures. As a result, it is necessary to develop a better vascular geometric modelling technique, which is not only of high performance and high accuracy in the reconstruction of vascular surfaces, but can also be used to model the interior tissue structures of the vascular walls.This research aims to develop a state-of-the-art patient-specific medical image-based geometric vascular modelling technique to solve the above problems. The main contributions of this research are:- Developed and proposed the Skeleton Marching technique to reconstruct the geometric structures of blood vessels with high performance and high accuracy. With the proposed technique, the highly complicated vascular reconstruction task is reduced to a set of simple localised geometric reconstruction tasks, which can be carried out in a parallel manner. These locally reconstructed vascular geometric segments are then combined together using shape-preserving blending operations to faithfully represent the geometric shape of the whole vascular system.- Developed and proposed the Thin Implicit Patch method to realistically model the interior geometric structures of the vascular tissues. This method allows the multi-layer interior tissue structures to be embedded inside the vascular wall to illustrate the geometric details of the blood vessel in real world

Automatic tool path generation for numerically controlled machining of sculptured surfaces

This dissertation presents four new tool path generation approaches for numerically controlled machining of sculptured surfaces: TRI\sb-XYINDEX, FINISH, FIVEX\sb-INDEX, FIX\sb-AXIS\sb-INDEX. All of the above systems index the tool across the object surface in the Cartesian space so that evenly distributed tool paths are accomplished. TRI\sb-XYINDEX is a three-axis tool path generation system which uses a surface triangle set (STS) representation of the surface for tool position calculations. Surface edges are detected with local searching algorithms. Quick tool positioning is achieved by selecting candidate elements of polygons. Test results show that TRI\sb-XYINDEX is more efficient when machining surfaces which are relatively flat while the discrete point approach is faster for highly curved surfaces. FINISH was developed for generating three-axis ball-end tool paths for local surface finishing. It was based on the SPS. Given a surface with excess material represented by a set of discrete points, FINISH automatically identifies the undercut areas. Results show that FINISH provides significant improvements in machining efficiency. FIVEX\sb-INDEX is developed for generating five-axis flat-end tool paths. It uses an STS approximation. Contact points on the surface are derived from edge lists obtained from the intersections of vertical cutting planes with the polygon set. The distances between adjacent end points set an initial step-forward increment between surface contact points. To verify tool movements, some intermediate tool positions are interpolated. The key features of FIVEX\sb-INDEX are: (1) a polygon set representing an object which may be composed of multiple surfaces; (2) Surface contact point generation by cutting plane intersection; (3) simple tool incrementing and positioning algorithms; (4) minimal user interaction; (5) user controlled accuracy of resulting tool paths. FIX\sb-AXIS\sb-INDEX is a subsystem of FIVEX\sb-INDEX, generating tool paths for a tool with fixed orientations. Surface contact points are generated similar to FIVEX\sb-INDEX while tool positions are corrected with the highest point technique along the tool axis direction. Linear fitting is applied to output tool positions. FIX\sb-AXIS\sb-INDEX is preferred for machining surfaces curved in one direction, such as ruled surfaces. Test results show that FIX\sb-AXIS\sb-INDEX can serve as a three-axis tool path generation system but a five-axis machine is required to do it. (Abstract shortened by UMI.)

Computer-Aided Geometry Modeling

Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design

Parallel hierarchical global illumination

Solving the global illumination problem is equivalent to determining the intensity of every wavelength of light in all directions at every point in a given scene. The complexity of the problem has led researchers to use approximation methods for solving the problem on serial computers. Rather than using an approximation method, such as backward ray tracing or radiosity, we have chosen to solve the Rendering Equation by direct simulation of light transport from the light sources. This paper presents an algorithm that solves the Rendering Equation to any desired accuracy, and can be run in parallel on distributed memory or shared memory computer systems with excellent scaling properties. It appears superior in both speed and physical correctness to recent published methods involving bidirectional ray tracing or hybrid treatments of diffuse and specular surfaces. Like progressive radiosity methods, it dynamically refines the geometry decomposition where required, but does so without the excessive storage requirements for ray histories. The algorithm, called Photon, produces a scene which converges to the global illumination solution. This amounts to a huge task for a 1997-vintage serial computer, but using the power of a parallel supercomputer significantly reduces the time required to generate a solution. Currently, Photon can be run on most parallel environments from a shared memory multiprocessor to a parallel supercomputer, as well as on clusters of heterogeneous workstations

A parallel progressive radiosity algorithm based on patch data circulation

Cataloged from PDF version of article.Current research on radiosity has concentrated on increasing the accuracy and the speed of the solution. Although algorithmic and meshing techniques decrease the execution time, still excessive computational power is required for complex scenes. Hence, parallelism can be exploited for speeding up the method further. This paper aims at providing a thorough examination of parallelism in the basic progressive refinement radiosity, and investigates its parallelization on distributed-memory parallel architectures. A synchronous scheme, based on static task assignment, is proposed to achieve better coherence for shooting patch selections. An efficient global circulation scheme is proposed for the parallel light distribution computations, which reduces the total volume of concurrent communication by an asymptotical factor. The proposed parallel algorithm is implemented on an Intel's iPSC/2 hypercube multicomputer. Load balance qualities of the proposed static assignment schemes are evaluated experimentally. The effect of coherence in the parallel light distribution computations on the shooting patch selection sequence is also investigated. Theoretical and experimental evaluation is also presented to verify that the proposed parallelization scheme yields equally good performance on multicomputers implementing the simplest (e.g. ring) as well as the richest (e.g. hypercube) interconnection topologies. This paper also proposes and presents a parallel load re-balancing scheme which enhances our basic parallel radiosity algorithm to be usable in the parallelization of radiosity methods adopting adaptive subdivision and meshing techniques. (C) 1996 Elsevier Science Lt