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removed syntax and grammar errors

This commit is contained in:
Peter Hachenberger 2009-05-15 18:20:53 +00:00
parent 04b5499caf
commit 863cb32a0b
3 changed files with 8 additions and 15 deletions
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2
Minkowski_sum_3/doc_tex/Minkowski_sum_3/PkgDescription.tex
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@ -5,7 +5,7 @@ This package provides a function, which computes the Minkowski sum of
two point sets in $\mathbb{R}^3$. These point sets may consist of two point sets in $\mathbb{R}^3$. These point sets may consist of
isolated vertices, isolated edges, surfaces with convex facets without isolated vertices, isolated edges, surfaces with convex facets without
holes, and open and closed solids. Thus, it is possible to compute holes, and open and closed solids. Thus, it is possible to compute
configuration space of translational robots (even in tight passage the configuration space of translational robots (even in tight passage
scenarios) as well as several graphics operations, like for instance scenarios) as well as several graphics operations, like for instance
the glide operation, which computes the point set swept by a the glide operation, which computes the point set swept by a
polyhedron that moves along a polygonal line. polyhedron that moves along a polygonal line.

19
Minkowski_sum_3/doc_tex/Minkowski_sum_3/main.tex
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@ -79,18 +79,12 @@ $-P$ on $Q$, such that $-r$ is on the boundary of $Q$. Finally, move
$-P$ along the complete boundary of $Q$. The union of $Q$ and the $-P$ along the complete boundary of $Q$. The union of $Q$ and the
points swept by $-P$ is the Minkowski sum of $P$ and $Q$. points swept by $-P$ is the Minkowski sum of $P$ and $Q$.
Implementing the Minkowski sum, the reference point needs not be Implementing the Minkowski sum, the reference point does not need to
chosen. It is implicitly given as the origin of the coordinate be chosen. It is implicitly given as the origin of the coordinate
system. Choosing a different reference point is equivalent to system. Choosing a different reference point is equivalent to
translating the coordinate system. Such a translation does not change translating the coordinate system. Such a translation does not change
the shape of the Minkowski sum; it only translates Minkowski sum by the shape of the Minkowski sum; it only translates the Minkowski sum
the same vector. by the same vector.
Note, that the described method is helpful for illustrating the
operation and for constructing a drawing of a Minkowski sum, but its
not always accurate. It only works if the reference point is part of
$P$, while the origin of the coordinate system needs not to be within
$P$.
This package provides a function \ccc{minkowski_sum_3} that computes This package provides a function \ccc{minkowski_sum_3} that computes
the Minkowski sum of two Nef polyhedra. We do not support arbitrary the Minkowski sum of two Nef polyhedra. We do not support arbitrary
@ -193,8 +187,7 @@ polyhedron and therefore selected, but in case of the open unit cube
$[0,1)^3$ they are unselected. Each item has its own selection mark, $[0,1)^3$ they are unselected. Each item has its own selection mark,
which allows the correct representation of Nef polyhedra, which are which allows the correct representation of Nef polyhedra, which are
closed under Boolean and topological operations. Details can be found closed under Boolean and topological operations. Details can be found
in the chapter on 3D Boolean operations on Nef polyhedra for more in the chapter on 3D Boolean operations on Nef polyhedra~\ref{chapterNef3}.
details~\ref{chapterNef3}.
The use of \ccc{Nef_polyhedron_3} allows many scenarios beyond the The use of \ccc{Nef_polyhedron_3} allows many scenarios beyond the
Minkowski sum of two solids. First, they can model the input and the Minkowski sum of two solids. First, they can model the input and the
@ -242,7 +235,7 @@ selection mark without spoiling the correctness of the Minkowski sum.
The function \ccc{minkowski_sum_3} should be used with the The function \ccc{minkowski_sum_3} should be used with the
\ccc{Extact_predicates_exact_constructions_kernel}, which often is \ccc{Extact_predicates_exact_constructions_kernel}, which often is
the most efficient choice and allows the floating-point input. Consult the most efficient choice and allows floating-point input. Consult
Section~\label{sectionNef_3IO} for more details. Section~\label{sectionNef_3IO} for more details.
The following example code illustrates the usage of the function The following example code illustrates the usage of the function

2
Minkowski_sum_3/doc_tex/Minkowski_sum_3_ref/minkowski_sum_3.tex
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@ -23,7 +23,7 @@ $m$ are the complexities of the two input polyhedra (the complexity of
a \ccc{Nef_polyhedron_3} is the sum of its \ccc{Vertices}, a \ccc{Nef_polyhedron_3} is the sum of its \ccc{Vertices},
\ccc{Halfedges} and \ccc{SHalfedges}). \ccc{Halfedges} and \ccc{SHalfedges}).
\ccGlobalFunction{Nef_polyhedron_3 minowski_sum_3(Nef_polyhedron_3 N0, Nef_polyhedron_3 N1);} \ccGlobalFunction{Nef_polyhedron_3 minkowski_sum_3(Nef_polyhedron_3 N0, Nef_polyhedron_3 N1);}
\ccPrecond \ccPrecond