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(1)
Curves and Surfaces
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Differential Geometry of Curves and Surfaces
Differential Geometry of Curves and Surfaces,M. Do Carmo
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Differential Geometry of Curves and Surfaces
(
Citations: 467
)
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M. Do Carmo
Published in 1976.
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Citation Context
(89)
...FrenetSerret Equations: Given a curvature (s) > 0 and a torsion (s), according to the fundamental theorem of the local theory of curves [
9
], there exists a unique (up to rigid motion) spatial curve, parameterized by the arclength s, dened by its FrenetSerret equations, as follows:...
...ds2 (s) 0. According to the fundamental theorem of local theory of curves, for every dierential function with (s) > 0 and (s), there exists a regular parameterized curve, where (s) is the curvature, (s) is the torsion, and s is the arclength parameterization [
9
]...
...Note that this could be done since all the properties of the FrenetSerret Equations hold for every parameterization, not necessarily the arclength parameterization [
9
] ...
Gur Harary
,
et al.
3D Euler spirals for 3D curve completion
...Given these derivatives, the curvature and the torsion are computed according to their denition [
5
] (where (x;y;z)):...
...du is calculated according to the FrenetSerret equations [
5
]...
David BenHaim
,
et al.
Piecewise 3D Euler spirals
...[2, 13] Using the GaussBonnet theorem for surfaces with boundaries, see, e.g., [
41
], the bending energy contribution that involves the integral over the Gaussian curvature can be reformulated as an integral over the domain boundaries...
Erwin Gutlederer
,
et al.
Polymorphism of vesicles with multidomain patterns
...It is well known that, beside the trivial case of planes, helicoid is the unique (noncylindrical) ruled minimal surface (see [2], [
1
])...
Nguyen Minh Hoang
.
Ruled minimal surfaces in $\Bbb R^3$ with density $e^z$
...(For all the relevant concepts on the differential geometry of surfaces, we refer the reader to [
7
].)...
A. Kumar
,
et al.
Active Contours for visual tracking: a geometric gradient based approa...
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Citations
(467)
Simple and effective variational optimization of surface and volume triangulations
(
Citations: 2
)
Xiangmin JiaoDuo
,
Duo Wang
,
Hongyuan Zha
Journal:
Engineering With Computers  EWC
, vol. 27, no. 1, pp. 8194, 2011
A Quadrature Formula for Diffusion Polynomials Corresponding to a Generalized Heat Kernel
(
Citations: 3
)
F. Filbir
,
H. N. Mhaskar
Journal:
Journal of Fourier Analysis and Applications  J FOURIER ANAL APPL
, vol. 16, no. 5, pp. 629657, 2010
3D Euler spirals for 3D curve completion
(
Citations: 2
)
Gur Harary
,
Ayellet Tal
Conference:
Symposium on Computational Geometry  SOCG
, pp. 393402, 2010
Constrained quantum systems as an adiabatic problem
(
Citations: 1
)
Jakob Wachsmuth
,
Stefan Teufel
Journal:
Physical Review A  PHYS REV A
, vol. 82, no. 2, 2010
Vesicles and Amoebae: On Globally Constrained Shape Deformation
(
Citations: 1
)
Ishay Goldin
,
JeanMarc Delosme
,
Alfred M. Bruckstein
Journal:
Journal of Mathematical Imaging and Vision  JMIV
, vol. 37, no. 2, pp. 112131, 2010