Blossoms and CAGD Algorithms

Last Updated: October 10, 2012
Blossoming is a technique for analysising polynomial functions. For a degree n, univariate polynomial F, there exists a unique blossom f such that In short, the blossom allows us the analyse polynomial functions by performing repeated affine combinations.

Although the blossom has primarily been used as a theoretical technique, it can also be used to derive efficient algorithms. The goal of this work is to implement an efficient software library to support the blossom abstraction, and to develop algorithms based on these ideas and on this software package.

As a strong, mathematical base layer of software, we have developed a Euclidean geometry abstract data type, which we have implemented in C, C++, and Java. The key observation here is that the matrix abstraction commonly used in graphics programs provides a linear algebra abstraction. Unfortunately, use of this linear algebra abstraction leads to subtle errors when doing the type of geometric programming commonly found in computer graphics. By providing a geometric abstraction, such program errors are eliminated.

People

The following people are currently working on this project:

Software

So far, two libraries have been implemented:

Papers

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