%0 Journal Article %1 Franchini2009346 %A Franchini, Silvia %A Gentile, Antonio %A Sorbello, Filippo %A Vassallo, Giorgio %A Vitabile, Salvatore %D 2009 %J Integration, the \VLSI\ Journal %K geometricalgebra %N 3 %P 346 - 355 %R http://dx.doi.org/10.1016/j.vlsi.2008.09.010 %T An embedded, FPGA-based computer graphics coprocessor with native geometric algebra support %U http://www.sciencedirect.com/science/article/pii/S0167926008000497 %V 42 %X The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for symbolic calculations. In this paper, the architecture of Clifford coprocessor (CliffoSor) is introduced. CliffoSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on a programmable gate array (FPGA) board is detailed. Initial test results show the potential to achieve a 20× speedup for 3D vector rotations, a 12× speedup for Clifford sums and differences, and more than a 4× speedup for Clifford products, compared to the analogous operations in GAIGEN, a standard geometric algebra library generator for general-purpose processors. An execution analysis of a raytracing application is also presented.

@article{Franchini2009346, abstract = {The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for symbolic calculations. In this paper, the architecture of Clifford coprocessor (CliffoSor) is introduced. CliffoSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on a programmable gate array (FPGA) board is detailed. Initial test results show the potential to achieve a 20× speedup for 3D vector rotations, a 12× speedup for Clifford sums and differences, and more than a 4× speedup for Clifford products, compared to the analogous operations in GAIGEN, a standard geometric algebra library generator for general-purpose processors. An execution analysis of a raytracing application is also presented. }, added-at = {2015-12-16T01:32:53.000+0100}, author = {Franchini, Silvia and Gentile, Antonio and Sorbello, Filippo and Vassallo, Giorgio and Vitabile, Salvatore}, biburl = {https://www.bibsonomy.org/bibtex/2015fd8a8544af842d6b1d9922ad3cbaf/wolftype}, doi = {http://dx.doi.org/10.1016/j.vlsi.2008.09.010}, interhash = {a10da2f0a2dcd44097aa2c48fa87dada}, intrahash = {015fd8a8544af842d6b1d9922ad3cbaf}, issn = {0167-9260}, journal = {Integration, the \{VLSI\} Journal }, keywords = {geometricalgebra}, note = {Special Section on \{DCIS2006\} }, number = 3, pages = {346 - 355}, timestamp = {2015-12-16T01:32:53.000+0100}, title = {An embedded, FPGA-based computer graphics coprocessor with native geometric algebra support }, url = {http://www.sciencedirect.com/science/article/pii/S0167926008000497}, volume = 42, year = 2009 }