Lecture Notes in Computer Science
1 primary work
Book 703
Computational geometry is the part of theoretical computer
science that concerns itself with geometrical objects; it
aims to define efficient algorithms for problems involving
points, lines, polygons, and so on. The field has gained
popularity very rapidly during the last decade. This is
partly due to the many application areas of computational
geometry and partly due to the beauty of the field itself.
This monograph focuses on three problems that arise in
three-dimensional computational geometry. The first problem
is the ray shooting problem: preprocess a set of polyhedra
into a data structure such that the first polyhedron that is
hit by a query ray can be determined quickly. The second
problem is that of computing depth orders: we want to sort a
set of polyhedra such thatif one polyhedron is (partially)
obscured by another polyhedron then it comes first in the
order. The third problem is the hidden surface removal
problem: given a set of polyhedra and a view point, compute
which parts of the polyhedra are visible from the view
point. These three problems involve issues that are
fundamental to three-dimensional computational geometry.
The book also contains a large introductory part discussing
the techniques used to tackle the problems. This part should
interest not only those who need the background for the rest
of the book but also anyone who wants to know more about
some recent techniques in computational geometry.
science that concerns itself with geometrical objects; it
aims to define efficient algorithms for problems involving
points, lines, polygons, and so on. The field has gained
popularity very rapidly during the last decade. This is
partly due to the many application areas of computational
geometry and partly due to the beauty of the field itself.
This monograph focuses on three problems that arise in
three-dimensional computational geometry. The first problem
is the ray shooting problem: preprocess a set of polyhedra
into a data structure such that the first polyhedron that is
hit by a query ray can be determined quickly. The second
problem is that of computing depth orders: we want to sort a
set of polyhedra such thatif one polyhedron is (partially)
obscured by another polyhedron then it comes first in the
order. The third problem is the hidden surface removal
problem: given a set of polyhedra and a view point, compute
which parts of the polyhedra are visible from the view
point. These three problems involve issues that are
fundamental to three-dimensional computational geometry.
The book also contains a large introductory part discussing
the techniques used to tackle the problems. This part should
interest not only those who need the background for the rest
of the book but also anyone who wants to know more about
some recent techniques in computational geometry.