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Exploring 2D and 3D graphics algorithms and representations for rendering, geometric modeling, and animation

Graphics Group

Computer graphics is notoriously compute-hungry. Yet the ambition of synthesizing all known or imaginable visual effects in real-time remains far from fully realized and will require even more computation. Fortunately, specialized graphics hardware is becoming more powerful. Multi-core computers with many processors are also developing. The amount of computation that can be done in parallel and per memory reference both continue to grow. Efficient graphics algorithms must therefore be computed in parallel, respect the memory hierarchy, and minimize communication between threads and between the CPU and graphics co-processor (GPU). Hardware trends favor algorithms that perform computation only over a small, local working set, stream data from input to output, and amplify data as it moves through memory hierarchy levels successively closer to the computational units. We are exploring new graphics representations and algorithms that take advantage of existing and upcoming hardware features to heighten the quality of real-time computer graphics.



Procedural Geometric Representations

Rendering and processing parametric, procedurally-defined representations directly.


Understanding Polynomials

A catalog of the types of shapes generated by polynomials of various orders in one, two and three dimensions.

Direct GPU Rendering of Piecewise Algebraic Curves and Surfaces

Direct rendering on the GPU of curves and surfaces defined implicitly as solutions to polynomials. 

Approximating Subdivision Surfaces for Hardware Tessellation

Accelerated rendering of high-order surfaces on the GPU using a new programmable tessellator unit proposed for future graphics chips and already shipping on the Xbox 360.  


Efficient Processing of Sampled Geometric Surfaces and Signals

Parameterization techniques to represent surface signals and even geometry via “as small as possible” texture maps.


Random-Access GPU Data Structures

Packing sparse data into compact tables while retaining efficient random access.


3D Surface Acquisition and Reconstruction

Methods and representations to improve the sampling and reconstruction of scanned 3D objects.


Real-Time Texture Synthesis

Fast methods to synthesize arbitrarily large textures from small examples on the GPU.


Real-Time Soft Global Illumination

Real time rendering of soft effects such as shadows from large light sources, subsurface scattering, and participating media.