Carnegie Mellon University
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Paul Heckbert
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No longer a member of RI.
Research Interests

My interests are centered in computer graphics but include related fields such as image processing, computer vision, and scientific computing. I enjoy working with a variety of issues, including mathematical, computational, user-interface, and artistic concerns. A broad summary of my research goals is: the development of algorithms and software tools to facilitate the creation and manipulation of pictures and other multidimensional data. Some applications which motivate much of my work are: computer animation for movies, computer aided design, and scientific visualization for education, science, and engineering. Some of my recent research is in the area of image synthesis, also known as rendering. Realistic image synthesis, the generation of images of mathematically-described three-dimensional scenes that are indistinguishable from reality, is a very challenging goal. One of the fundamental computational challenges of realistic image synthesis is the simulation of global illumination, the interreflection of light in a 3-D scene. I am currently investigating radiosity methods for doing such simulations, in which a surface is subdivided using a mesh and a large system of equations is solved to compute the brightness of each triangle in the mesh. Our current research involves better methods for meshing that take occlusion into account, wavelet techniques for solving the equations efficiently, and fast methods for generating shadows. Future work will generalize these methods to work well on curved and shiny surfaces.

Another area of my research is surface modeling: their interactive design, their representation, and their efficient display. Prof. Andy Witkin and I developed a particle-based technique that allows very general, interactive design of implicit surfaces. Our repelling particle technique has also been generalized to create a flexible 2-D mesh generator useful for surface meshing in computer graphics and other applications in scientific computing.

To speed up the display of complex geometric models, I am currently developing new multiresolution modeling techniques that represent objects at multiple levels of detail. When an object is viewed from up close, a detailed model is drawn; but when viewed from the distance, a coarse approximation is drawn. How do we make multiresolution models quick, accurate, and seamless? Multiresolution techniques have applications in flight simulators, video games, computer aided design, geographic information systems, and cartography. A graduate student and I have recently developed some fast algorithms for simplifying terrain data and more general 3-D objects that generate quite accurate approximations.

This is a summary of my current research, but my interests are not limited to these topics.

Research Interest Keywords
computer graphicsgeometric modeling