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h1. Geometric Primitives
What good is a geometry library without geometric primitives? By this
I mean the very basic stuff, Points/Vectors, Matrices, etc.
2geom's primitives are descendant from libNR's geometric primitives.
They have been modified quite a bit since that initial import.
h2. Point
!media/point.png!
The mathematical concepts of points and vectors are merged into the
2geom class called *Point*. See Appendix A for a further
discussion of this decision.
Point may be interpreted as a D2<double> with some additional operations.
(TODO: document these ops.)
\section{Transformations}
Affine transformations are either represented with a canonical 6
element matrix, or special forms.
\subsection{Scale}
\includegraphics[height=50mm]{media/scale.png}
A \code{Scale} transformation stores a vector representing a scaling
transformation.
\subsection{Rotate}
\includegraphics[height=50mm]{media/rotate.png}
A \code{Rotate} transformation uses a vector(\code{Point}) to store
a rotation about the origin.
In correspondence with mathematical convention (y increasing upwards),
0 degrees is encoded as a vector pointing along the x axis, and positive
angles indicate anticlockwise rotation. So, for example, a vector along
the y axis would encode a 90 degree anticlockwise rotation of 90 degrees.
In the case that the computer convention of y increasing downwards,
the \verb}Rotate} transformation works essentially the same, except
that positive angles indicate clockwise rotation.
\subsection{Translate}
\includegraphics[height=70mm]{media/translate.png}
A \code{Translate} transformation is a simple vector(\code{Point})
which stores an offset.
\subsection{Matrix}
\includegraphics[height=70mm]{media/matrix.png}
A \code{Matrix} is a general affine transform. Code is provided for
various decompositions, constructions, and manipulations. A
\code{Matrix} is composed of 6 coordinates, essentially storing the
x axis, y axis, and offset of the transformation. A detailed
explanation for matrices is given in Appendix B.
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