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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Least-Squares Solutions 41
Local surface fitting to 3D points
We have already seen how LS fitting is useful for fitting a poly-
nomial to a set of points coming from a curve. Can we do some-
thing similar if the points come from a surface? More importantly,
is it useful to locally fit a polynomial surface to a set of points
in 3D? This scenario (see Figure 3.3) comes up often in computer
graphics and digital shape acquisition, for example, when we get
a rough sampling of a shape using a 3D laser or range scanner.
Such a 3D point set P := {p
i
} can be treated as a sampling of the
underlying shape or surface S, similar to how a point set can be
generated from ...
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