Tony Barrera

Faster shading by equal angle interpolation of vectors

We show how spherical linear interpolation can be used to produce shading with a quality at least similar to Phong shading at a computational effort in the inner loop that is close to that of the Gouraud method. We show how to use the Chebyshevs recurrence relation in order to compute the shading very efficiently. Furthermore, it can also be used to interpolate vectors in such a way that normalization is not necessary, which will make the interpolation very fast. The somewhat larger setup effort required by this approach can be handled through table look up techniques.

A chronological and mathematical overview of digital circle generation algorithms : Introducing efficient 4- and 8-connected circles

Circles are one of the basic drawing primitives for computers and while the naive way of setting up an equation for drawing circles is simple, implementing it in an efficient way using integer arithmetic has resulted in quite a few different algorithms. We present a short chronological overview of the most important publications of such digital circle generation algorithms. Bresenham is often assumed to have invented the first all integer circle algorithm. However, there were other algorithms published before his first official publication, which did not use floating point operations. Furthermore, we present both a 4- and an 8-connected all integer algorithm. Both of them proceed without any multiplication, using just one addition per iteration to compute the decision variable, which makes them more efficient than previously published algorithms.

Fast specular highlights by modifying the Phong-Blinn model

Shading is a technique that is used in computer graphics to make faceted objects appear smooth and more realistic. In the research presented in this thesis we have investigated how shading can be generated as efficiently as possible without sacrificing quality.In the classical approach to high quality shading proposed by Phong, the illumination equation is computed per pixel using an interpolated normal. The normals at the vertices are bi-linearly interpolated over the polygon to obtain a normal per pixel. Correct shading requires normalization of these normals, which is computationally demanding involving a square root. In our research we have shown how this normalization can be eliminated through the use of spherical interpolation and the Chebyshev recurrence formula, reducing the calculation to a few single arithmetic operations per pixel.Still a substantial setup operation is needed for each scanline. We have studied how also this can be made more efficient, with some limited progress so far. An alternative approach is to do the most of the setup on polygon level and incrementally compute the setup needed per scanline. In particular, we have studied quadratic shading approaches, i.e. fitting second degree surfaces to the polygons. The most successful approach has been through what we have called X-shading, where the setup is calculated by using an efficient approximation for the mid-edge normals. This setup is about four times faster than previously known methods.In the process of studying shading methods we have also made some contributions to improving bump-mapping and simulation of different kinds of light sources.The developed methods will be of interest in future generations of computer graphics software and hardware systems, ranging from high end systems to generate realistic movies and 3D games, to handheld devices such as mobile phones with graphics displays.

An algorithm for parallel calculation of trigonometric functions

We propose a new way of calculating the sine and cosine functions. The method is based on recursive applications of a modified complex power algorithm. On a machine with multiple complex multipliers the method can be used to calculate sines and cosines in logarithmic time. The serial version of the presented method requires only two precomputed constants and no tables. In the parallel versions a trade off can be made between the number of parallel processing elements and the size of tables.