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

Computationally efficient ray tracing of parametric surfaces

Includes bibliographical references (page 9).Abstract also in Japanese.Algorithms for ray tracing parametric surfaces are in general too computationally expensive to be widely applicable. The algorithm presented here combines well-known graphics procedures with a modified Newton iteration to provide a computationally efficient means of including parametric surfaces in a ray traced image. By allowing only planar surfaces to be reflective and/or refractive the resulting high degree of ray coherence is utilized to make the algorithm incremental and results in an order of magnitude improvement in computation speed over existing algorithms

A tool for generating three dimensional animation on computers

Ankara : The Department of Graphic Design and the Institute of Fine Arts of Bilkent Univ. , 1991.Thesis (Master's) -- Bilkent University, 1991.Includes bibliographical references leaves 31-32.In this work, a three dimensional computer animation system has been designed to be employed in schools, for the training of art students on basic three dimensional animation techniques. Puppet Theater, as we have called the system, utilizes the flexibility and effectiveness of the low-end hardware, namely IBM PC™ computers supported with Targa 16™ graphics board and gives special emphasis to user friendliness. It Is basically a software to design three dimensional objects and choreograph the object data in the computer's memory, before rendering the resulting scenery with shading methods. The system is the result of reflecting the recent advances in the field of computer graphics and pushing the potentials of the existing platform. Software is Implemented in C language, thus the code is transportable. A custom designed object oriented windowing system called WODNTW is used as the user Interface. This open windowing system supports pull-down menus, interactive buttons, scalable windows and other popular user interface elements.Türün, Cemil ŞinasiM.S

The Computer Graphics Scene in the United States

We briefly survey the major thrusts of computer graphics activities, examining trends and topics rather than offering a comprehensive survey of all that is happening. The directions of professional activities, hardware, software, and algorithms are outlined. Within hardware we examine workstations, personal graphics systems, high performance systems, and low level VLSI chips; within software, standards and interactive system design; within algorithms, visible surface rendering and shading, three-dimensional modeling techniques, and animation. Note: This paper was presented at Eurographics\u2784 in Copenhagen, Denmark

Hidden curve removal for free form surfaces

Journal ArticleThis paper describes a hidden curve algorithm specifically designed for sculptured surfaces. A technique is described to extract the visible curves for a given scene without the need to approximate the surface by polygons. This algorithm produces higher quality results than polygon based algorithms, as most of the output set has an exact representation. Surface coherence is used to speed up the process. Although designed for sculptured surfaces, this algorithm is also suitable for polygonal data

Discrete B-splines and subdivision techniques in compter-aided geometric design and computer graphics

Journal ArticleThe relevant theory of discrete 5-sphnes with associated new algorithms is extended to provide a framework for understanding and implementing general subdivision schemes for nonuniform B-splines. The new derived polygon corresponding to an arbitrary refinement of the knot vector for an existing .B-spline curve, including multiplicities, is shown to be formed by successive evaluations of the discrete B-spline defined by the original vertices, the original knot vector, and the new refined knot vector. Existing subdivision algorithms can be seen as proper special cases. General subdivision has widespread applications in computer-aided geometric design, computer graphics, and numerical analysis. The new algorithms resulting from the new theory lead to a unification of the display model, the analysis model, and other needed models into a single geometric model from which other necessary models are easily derived. New sample algorithms for interference calculation, contouring, surface rendering, and other important calculations are presented

Interactive visualization tools for topological exploration

Thesis (Ph.D.) - Indiana University, Computer Science, 1992This thesis concerns using computer graphics methods to visualize mathematical objects. Abstract mathematical concepts are extremely difficult to visualize, particularly when higher dimensions are involved; I therefore concentrate on subject areas such as the topology and geometry of four dimensions which provide a very challenging domain for visualization techniques. In the first stage of this research, I applied existing three-dimensional computer graphics techniques to visualize projected four-dimensional mathematical objects in an interactive manner. I carried out experiments with direct object manipulation and constraint-based interaction and implemented tools for visualizing mathematical transformations. As an application, I applied these techniques to visualizing the conjecture known as Fermat's Last Theorem. Four-dimensional objects would best be perceived through four-dimensional eyes. Even though we do not have four-dimensional eyes, we can use computer graphics techniques to simulate the effect of a virtual four-dimensional camera viewing a scene where four-dimensional objects are being illuminated by four-dimensional light sources. I extended standard three-dimensional lighting and shading methods to work in the fourth dimension. This involved replacing the standard "z-buffer" algorithm by a "w-buffer" algorithm for handling occlusion, and replacing the standard "scan-line" conversion method by a new "scan-plane" conversion method. Furthermore, I implemented a new "thickening" technique that made it possible to illuminate surfaces correctly in four dimensions. Our new techniques generate smoothly shaded, highlighted view-volume images of mathematical objects as they would appear from a four-dimensional viewpoint. These images reveal fascinating structures of mathematical objects that could not be seen with standard 3D computer graphics techniques. As applications, we generated still images and animation sequences for mathematical objects such as the Steiner surface, the four-dimensional torus, and a knotted 2-sphere. The images of surfaces embedded in 4D that have been generated using our methods are unique in the history of mathematical visualization. Finally, I adapted these techniques to visualize volumetric data (3D scalar fields) generated by other scientific applications. Compared to other volume visualization techniques, this method provides a new approach that researchers can use to look at and manipulate certain classes of volume data