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Peter Hachenberger
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@ -2741,7 +2741,6 @@ Minkowski_sum_3/doc_tex/Minkowski_sum_3/fig/decomposition_method.pdf -text
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Minkowski_sum_3/doc_tex/Minkowski_sum_3/fig/glide.eps -text
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Minkowski_sum_3/doc_tex/Minkowski_sum_3/fig/spoon_star.ps -text
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Minkowski_sum_3/doc_tex/Minkowski_sum_3/fig/tight_passage.ps -text
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Minkowski_sum_3/doc_tex/Minkowski_sum_3/main.aux -text
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Minkowski_sum_3/doc_tex/Minkowski_sum_3_ref/main.aux -text
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Minkowski_sum_3/examples/Minkowski_sum_3/cube.nef3 -text
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Minkowski_sum_3/examples/Minkowski_sum_3/cube_offset.cin -text
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@ -1,45 +0,0 @@
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\relax
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\@writefile{toc}{\contentsline {chapter}{\numberline {1}Minkowski Sum of Polyhedra }{1}{chapter.1}}
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\@writefile{lof}{\addvspace {10\p@ }}
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\@writefile{lot}{\addvspace {10\p@ }}
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\newlabel{chapterMinkowskiSum3}{{1}{1}{Minkowski Sum of Polyhedra \label {chapterMinkowskiSum3}\relax }{chapter.1}{}}
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\@writefile{lof}{\contentsline {xchapter}{Minkowski Sum of Polyhedra }{1}{chapter.1}}
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\@writefile{lot}{\contentsline {xchapter}{Minkowski Sum of Polyhedra }{1}{chapter.1}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.1}Introduction}{1}{section.1.1}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.2}Decomposition Method}{1}{section.1.2}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.3}Features and Restrictions}{1}{section.1.3}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces The Minkowski sum of a spoon and a star.}}{1}{figure.1.1}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.3}{\ignorespaces The Minkowski sum of a spoon and a star.}}{2}{figure.1.3}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.4}Usage}{2}{section.1.4}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1.4}{\ignorespaces The Minkowski sum of a spoon and a star.}}{4}{figure.1.4}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.5}Glide}{4}{section.1.5}}
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}
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@ -19,7 +19,7 @@
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% +------------------------------------------------------------------------+
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\section{Introduction}
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\begin{figure}
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\begin{figure}[h]
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\begin{ccTexOnly}
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\begin{center}
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\includegraphics[width=0.8\textwidth]{Minkowski_sum_3/fig/spoon_star}
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@ -33,7 +33,7 @@
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\caption{The Minkowski sum of a spoon and a star.}
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\end{figure}
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The Minkowski sum of two point sets $P$ and $Q$ in $R^d$, denoted by
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The Minkowski sum of two point sets $P$ and $Q$ in $\mathbb{R}^d$, denoted by
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$P \oplus Q$, is defined as the set $\{p+q:p \in P, q \in Q
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\}$. Minkowski sums are used in a wide range of applications such as
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robot motion planning and computer-aided design. This
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@ -57,10 +57,12 @@ the convex pieces and merges the pairwise sums.
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\end{ccTexOnly}
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\begin{ccHtmlOnly}
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<p><center>
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<img src="./fig/decomposition_method.gif" border=0 alt="Minkowski sum example">
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<img src="./fig/decomposition_method.gif" border=0 alt="decomposition method">
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</center>
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\end{ccHtmlOnly}
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\caption{The Minkowski sum of a spoon and a star.}
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\caption{The decomposition method decomposes both input polyhedra
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into convex parts, computes all pairwise Minkowski sums
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of the convex parts, and merges the pairwise sums.}
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\end{figure}
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The Minkowski sum is an iherent complex method. Using the
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@ -82,15 +84,18 @@ possible with the current implementation.
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\begin{figure}
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\begin{ccTexOnly}
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\begin{center}
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\includegraphics[width=0.8\textwidth]{Minkowski_sum_3/fig/tight_passage}
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\includegraphics[width=0.5\textwidth]{Minkowski_sum_3/fig/tight_passage}
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\end{center}
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\end{ccTexOnly}
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\begin{ccHtmlOnly}
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<p><center>
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<img src="./fig/tigh_passage.gif" border=0 alt="Minkowski sum example">
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<img src="./fig/tigh_passage.gif" border=0 alt="tight passage">
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</center>
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\end{ccHtmlOnly}
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\caption{The Minkowski sum of a spoon and a star.}
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\caption{The Minkowski sum of a maze and a cube that exactly fits through
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the corridor of the maze. Modeling the cube as an open set, the
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Minkowski sum includes facets that represent the remaining path
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for the cubical robot.}
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\end{figure}
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We strife for extending the package to work for arbitrary
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@ -126,7 +131,7 @@ destroyed by the function. So, if they are further on needed, they
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need to be copied, first. The copying is not done by the function
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itself to keep the memory usage as small as possible.
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\ccIncludeExampleCode{Minkowski_sum_3/minkowski_sum.cpp}
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\ccIncludeExampleCode{Minkowski_sum_3/cube_offset.cpp}
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% +------------------------------------------------------------------------+
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\section{Glide}
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@ -134,15 +139,15 @@ itself to keep the memory usage as small as possible.
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\begin{figure}
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\begin{ccTexOnly}
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\begin{center}
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\includegraphics[width=0.8\textwidth]{Minkowski_sum_3/fig/glide}
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\includegraphics[width=0.5\textwidth]{Minkowski_sum_3/fig/glide}
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\end{center}
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\end{ccTexOnly}
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\begin{ccHtmlOnly}
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<p><center>
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<img src="./fig/glide.gif" border=0 alt="Minkowski sum example">
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<img src="./fig/glide.gif" border=0 alt="glide operation">
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</center>
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\end{ccHtmlOnly}
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\caption{The Minkowski sum of a spoon and a star.}
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\caption{The region swept by a star that moves along a polygonal path.}
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\end{figure}
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With the function \ccc{minkowski_sum_3} it is also possible to realize
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@ -1,13 +1,13 @@
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\relax
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\@writefile{@@@}{\chapterbegin }
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\@writefile{toc}{\contentsline {section}{\numberline {1.6}Classified Reference Pages}{7}{section.1.6}}
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\@writefile{toc}{\contentsline {section}{\numberline {1.7}Alphabetical List of Reference Pages}{7}{section.1.7}}
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