compositing\cite{porter1984compositing} into a single image. This allows complex images to be formed from many simple pieces, as well
as allowing for layered translucent objects, which would otherwise require the solution of some very complex constructive geometry problems.
-\subsection{Compositing Digital Images\cite{porter1984compositing}}
-
-
-
-Perter and Duff's classic paper "Compositing Digital Images" lays the
-foundation for digital compositing today. By providing an "alpha channel,"
-images of arbitrary shapes — and images with soft edges or sub-pixel coverage
-information — can be overlayed digitally, allowing separate objects to be
-rasterized separately without a loss in quality.
-
-Pixels in digital images are usually represented as 3-tuples containing
-(red component, green component, blue component). Nominally these values are in
-the [0-1] range. In the Porter-Duff paper, pixels are stored as $(R,G,B,\alpha)$
-4-tuples, where alpha is the fractional coverage of each pixel. If the image
-only covers half of a given pixel, for example, its alpha value would be 0.5.
-
-To improve compositing performance, albeit at a possible loss of precision in
-some implementations, the red, green and blue channels are premultiplied by the
-alpha channel. This also simplifies the resulting arithmetic by having the
-colour channels and alpha channels use the same compositing equations.
-
-Several binary compositing operations are defined:
-\begin{itemize}
-\item over
-\item in
-\item out
-\item atop
-\item xor
-\item plus
-\end{itemize}
-
-The paper further provides some additional operations for implementing fades and
-dissolves, as well as for changing the opacity of individual elements in a
-scene.
-
-The method outlined in this paper is still the standard system for compositing
-and is implemented almost exactly by modern graphics APIs such as \texttt{OpenGL}. It is
-all but guaranteed that this is the method we will be using for compositing
-document elements in our project.
-
-\subsection{Bresenham's Algorithm: Algorithm for computer control of a digital plotter\cite{bresenham1965algorithm}}
-Bresenham's line drawing algorithm is a fast, high quality line rasterization
-algorithm which is still the basis for most (aliased) line drawing today. The
-paper, while originally written to describe how to control a particular plotter,
-is uniquely suited to rasterizing lines for display on a pixel grid.
-
-Lines drawn with Bresenham's algorithm must begin and end at integer pixel
-coordinates, though one can round or truncate the fractional part. In order to
-avoid multiplication or division in the algorithm's inner loop,
-
-The algorithm works by scanning along the long axis of the line, moving along
-the short axis when the error along that axis exceeds 0.5px. Because error
-accumulates linearly, this can be achieved by simply adding the per-pixel
-error (equal to (short axis/long axis)) until it exceeds 0.5, then incrementing
-the position along the short axis and subtracting 1 from the error accumulator.
-
-As this requires nothing but addition, it is very fast, particularly on the
-older CPUs used in Bresenham's time. Modern graphics systems will often use Wu's
-line-drawing algorithm instead, as it produces antialiased lines, taking
-sub-pixel coverage into account. Bresenham himself extended this algorithm to
-produce Bresenham's circle algorithm. The principles behind the algorithm have
-also been used to rasterize other shapes, including B\'{e}zier curves.
+While traditionally, rasterization was done entirely in software, modern computers and mobile devices have hardware support for rasterizing
+some basic primitives --- typically lines and triangles ---, designed for use rendering 3D scenes. This hardware is usually programmed with an
+API like \texttt{OpenGL}\cite{openglspec}.
+
+More complex shapes like B\'ezier curves can be rendered by combining the use of bitmapped textures (possibly using signed-distance
+fields\cite{leymarie1992fast}\cite{frisken2000adaptively}\cite{green2007improved}) with polygons approximating the curve's shape\cite{loop2005resolution}\cite{loop2007rendering}.
+
+Indeed, there are several implementations of these vector graphics
\emph{GPU Rendering}\cite{loop2005resolution}, OpenVG implementation on GLES: \cite{oh2007implementation},
\cite{robart2009openvg}
git.ucc.asn.au / ipdf / documents.git / blobdiff
UCC git Repository :: git.ucc.asn.au