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Numerical Integration
Parametric Curve
Related Publications
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Computing the arc length of parametric curves
Computing the arc length of parametric curves,10.1109/38.55155,IEEE Computer Graphics and Applications,Brian Guenter,Richard Parent
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Computing the arc length of parametric curves
(
Citations: 35
)
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Brian Guenter
,
Richard Parent
Specifying constraints on motion is simpler if the curve is parameterized by arc length, but many parametric curves of practical interest cannot be parameterized by arc length. An approximate numerical reparameterization technique that improves on a previous algorithm by using a different
numerical integration
procedure that recursively subdivides the curve and creates a table of the subdivision points is presented. The use of the table greatly reduces the computation required for subsequent arc length calculations. After table construction, the algorithm takes nearly constant time for each arc length calculation. A linear increase in the number of control points can result in a more than linear increase in computation. Examples of this type of behavior are shown
Journal:
IEEE Computer Graphics and Applications  CGA
, vol. 10, no. 3, pp. 7278, 1990
DOI:
10.1109/38.55155
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Citation Context
(13)
...as Gaussian Quadrature or Simpson’s rule (
Guenter and Parent 1990;
Wang, Kearney, and Atkinson 2003)...
Inci Guneralp
,
et al.
Continuous Characterization of the Planform Geometry and Curvature of ...
...Computing the arc length of a parametric curve is a standard task in applied geometry, and many papers have been written about it or related issues, including [
12
], [17], [16], [11], [13], [19], [18], [2], [5], [3], [8], [9] and [10]...
Michael S. Floater
,
et al.
Extrapolation methods for approximating arc length and surface area
...In [
11
], Guenter and Parent use numerical integration on the derivative of the curve...
...Guenter and Parent [
11
] apply such a method adaptively...
Michael S. Floater
,
et al.
Pointbased methods for estimating the length of a parametric curve
...Speed control is achieved by considering the distance along a curve of interpolation or, in other words, by establishing a reparameterization of the curve by arc length [
17
]...
Jordi Gonzàlez
,
et al.
A Comparison Framework for Walking Performances using aSpaces
...Speed control is achieved by considering the distance along a curve of interpolation or, in other words, by establishing a reparameterization of the curve by arc length [
7
]...
Jordi Gonzàlez
,
et al.
Analysis of Human Walking Based on aSpaces
References
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(
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Numerical analysis
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Citations
(35)
Continuous Characterization of the Planform Geometry and Curvature of Meandering Rivers
(
Citations: 3
)
Inci Guneralp
,
Bruce L. Rhoads
Published in 2008.
Extrapolation methods for approximating arc length and surface area
Michael S. Floater
,
Atgeirr F. Rasmussen
,
Ulrich Reif
Journal:
Numerical Algorithms
, vol. 44, no. 3, pp. 235248, 2007
Continuous Characterization of the Planform Geometry and Curvature of Meandering Rivers: Planform Geometry and Curvature of Meandering Rivers
İnci Güneralp
,
Bruce L. Rhoads
Journal:
Geographical Analysis  GEOGR ANAL
, vol. 40, no. 1, pp. 125, 2007
Pointbased methods for estimating the length of a parametric curve
(
Citations: 4
)
Michael S. Floater
,
Atgeirr F. Rasmussen
Journal:
Journal of Computational and Applied Mathematics  J COMPUT APPL MATH
, vol. 196, no. 2, pp. 512522, 2006
Pointbased methods for estimating the length of a parametric curve
(
Citations: 3
)
Michael S. Floater
,
Atgeirr F. Rasmussen
Published in 2005.