
April 25, 2015.
Removed documents that are not accessed frequently or need significant rewriting.
CommandLineParsing.pdf ("Command Line Parsing")
CollinearityTest.pdf ("A Collinearity Test Independent of Point Order")
PdeNumericalMethods.pdf ("Numerical Methods for Partial Differential Equations")
OdeNumericalMethods.pdf ("Numerical Methods for Ordinary Differential Equations")
DistancePointToQuadratic.pdf ("Distance from Point to a General Quadratic Curve or a General Quadric Surface")

April 24, 2015. Expanded the document to include more NURBS representations.
In particular, there is a degree3 representation for a full circle that uses an
internal repeated knot to splice together two halfcircles. There is a tensor
product NURBS surface, degree3 in each parameter, that uses the same idea of
an internal repeated knot to splice together two hemispheres.

April 23, 2015.
Major rewrite of the document on converting
between coordinate systems. The original version of this document was
entitled Conversion of LeftHanded Coordinates to RightHanded
Coordinates and was written to handle
the conversion of LightWave coordinate systems (lefthanded) to Wild Magic
coordinate systems (righthanded). The process was specific to LightWave's
choice of representing rotations using Euler angles, and the discussion
included how to deal with cameras, lights, and transformation hierarchies.
The new version is the general process of converting between any two
coordinate systems. An implementation is provided that automates
the process. The old file, LeftHandedToRightHanded.pdf, was deleted.

April 20, 2015.
Added significant improvements to the document for the testintersection
and findintersection queries for ellipses and to the document for computing
the area of intersection of ellipses. The source code implementation for
the testintersection and findintersection queries were updated to use the
details described in the document. Implemented the query for area of
intersection of ellipses.

April 4, 2015. Rewrote the document for computing the roots of lowdegree
polynomials. The new document goes into great detail about the classification
of roots (real or nonreal, multiplicities) and how to use exact rational
arithmetic to correctly classify the roots in a program. This leads to more
robust root finding using the closedform expressions for polynomials of degrees
2, 3, and 4. The motivation for the revisions was based on trying to compute
intersections of ellipses, and the nonrobust root finder for quartic polynomials
created many problems numerically.

April 2, 2015. Fixed the algorithm description for conversion from a
BSRational object to a floatingpoint type. When the roundup
step causes a carryout, so to speak, from the trailing significand, a block of
code was executed to set w to 1 and adjust pq. This was incorrect and,
in fact, not necessary because w is not used as the trailing significand in the
conversion.

March 29, 2015. Added some definitions for variables used in the
equations in the section {\em Separation Tests Involving Other Directions}.
Converted the verbatim pseudocode to use lstlisting format.

March 10, 2015. Fixed typographical errors and added some clarification.

January 26, 2015.
Fixed an error in the description for region 2 and added some clarification
about the sign tests for the partial derivatives of R(s,t).

January 5, 2015. Added comments about fitting lines y = a*x + b and
planes z = a*x + b*y + c, mentioning that the numerical problem for solving the
linear equations in the coefficients is ill conditioned unless you compute the averages
of the data points first and subtract those averages from the data points before
solving the linear system.

January 4, 2015. A new document describing the testintersection query for
boxes and cones.

December 28, 2014.
Modified the document on linecone intersection to give greater detail. The source code
was updated accordingly.

December 12, 2014. The document was rewritten to add more details about
the algorithm. The source code was modified accordingly.

December 7, 2014.
A new document describing a variation of an iterative eigensolver for
symmetric $3 \times 3$ matrices. A source code implementation and a sample application
are provided. The related document Eigensystems for 3x3 Symmetric Matrices (Revisited)
(EigenSymmetric3x3.pdf) has been deleted and that link redirected to the new file. The
document Eigensystem Solvers for Symmetric Matrices has also been deleted. The
GTEngine code now uses only the iterative solvers for symmetric matrices; we also have an
iterative implementation for the singular value decomposition (SVD).

November 27, 2014. The pseudocode for computing the fitted cylinder
subtracted the input point average for numerically stable computations. The
returned center needed the average added to it.

November 25, 2014. Overhauled the arbitrary precision library to
improve the performance and to improve readability. The unsigned integer
arithmetic was factored out of BSNumber into two classes, one
for arbitrary precision with storage of type std::vector and one
for userselected fixed precision with storage of type std::array.
Both classes share code for the arithmetic logic unit. Many computations
are now performed inplace to avoid expensive allocation, deallocation,
and memory copies. A new PDF is posted that greatly expands on the library
compared to the discussion in the GPGPU Programming for Games and Science
book. The document serves as a discussion about the design of the library and
a reference for how to use it. Examples are provided for using BSPrecision
to determine the template parameter of UIntegerFP<N> that represents
the maximum number of bits required to compute the exact results for a sequence
of expressions.

November 6, 2014. Implemented a robust algorithm for computing
the distance between line segments in any dimension. Revised the PDF
for computing distance between segments in 3D to describe the new
algorithm. A GPU implementation is available in the sample application.

October 20, 2014. The volume equation for a dodecahedron was in error.

August 15, 2014.
Fixed a typographical error in Equation (14). Replaced the \LaTeXe verbatim
commands with lstlisting commands for more readable pseudocode.
