May 2015
Intermediate to advanced
246 pages
6h 33m
English
book
A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing
by Daniel Cohen-Or, Chen Greif, Tao Ju, Niloy J. Mitra, Ariel Shamir, Olga Sorkine-Hornung, Hao Zhang
Content preview from A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing
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Chapter 7
Laplace and Poisson
Daniel Cohen-Or and Gil Hoffer
Figure 7.1: Pierre-Simon, Marquis de Laplace (left) and Simon-Denis
Poisson (right).
One of the enjoyable experiences of scientists today is solving new
problems with mathematical tools that were developed hundreds
of years ago. These tools are typically generic and were originally
developed to solve problems in physics. In this chapter we make
use of the well-known equations of Laplace (Pierre-Simon, Marquis
de Laplace 1749–1827) and Poisson (Simon-Denis Poisson 1781–
1840). (See Figure 7.1.) The two equations, respectively, have an
extremely simple form:
∆f = 0 for some function f (7.1)
and
∆f
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