clipper
clipper Documentation

This is an implementation of three root finding algorithms for polynomials using geometric clipping in the Bezier representation. It was written for a lab exercise course in numerical mathematics in winter semester 2011/12 at the FernUniversity of Hagen, Germany.

The code implements the three algorithms BezierClip, QuadClip [1] and CubeClip [2] (both in one class KCLip) described in the referenced papers. The program follows the unusual method to printing out debug information as a LaTeX document, which itself must be compiled by pdflatex for comfortable viewing. This technique allows the algorithm code to be interleaved with ltx(...) debug lines which are can contain plots and equations.

There are six main parts in this source:

• floating-point Numeric classes
• polynomial classes for monomial and Bezier representation
• implementation of the degree reduction matrices
• the BezierClip and KClip algorithms
• a test suite to check above algorithms
• a collection of demos and speedtests

Each part is separately documented below (or in Related Pages).

References:

[1] Barton, M. and Juettler, B. "Computing roots of polynomials by quadratic clipping", Computer Aided Geometric Design 24, (2007) p. 125-141.

[2] Liu, L., Zhang, L., Lin, B., Wang, G. "Fast approach for computing roots of polynomials using cubic clipping", Computer Aided Geometric Design 26, (2009), p. 524-599.

----------------------------------------------------------------------------

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.

----------------------------------------------------------------------------