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Planar G2 Hermite interpolation with some fair, C-shaped curves
2002
Journal of Computational and Applied Mathematics
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The planar G 2 Hermite interpolation problem is to ÿnd a planar curve matching planar G 2 Hermite data. In this paper, a C-shaped interpolating curve made of one or two spirals is sought. ...
The new curve is compared to the cubic BÃ ezier curve and to a curve made from a G 2 join of a pair of quadratics. ...
Acknowledgements The authors acknowledge the ÿnancial support of the Natural Sciences and Engineering Research Council of Canada for this research. ...
doi:10.1016/s0377-0427(01)00385-5
fatcat:tkgkcrvrbrdh3pis5t7upobtde
Geometric Hermite interpolation by logarithmic arc splines
2014
Computer Aided Geometric Design
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This paper considers the problem of G 1 curve interpolation using a special type of discrete logarithmic spirals. A "logarithmic arc spline" is defined as a set of smoothly connected circular arcs. ...
Given two points together with two unit tangents at the points, interpolation of logarithmic arc splines with a user specified winding angle is formulated into finding the positive solutions to a vector ...
One reviewer's suggestion of the use of Descartes rule of signs simplified the proof of Theorem 3.1 considerably. This work is supported by NNSF of China grants (11290142, 61272300, 60970077). ...
doi:10.1016/j.cagd.2014.09.001
fatcat:qttmsrpspvcyxnnpr2tuiy2m74
Page 1517 of Mathematical Reviews Vol. , Issue 95c
[page]
1995
Mathematical Reviews
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D. (3-MB-A; Winnipeg, MB) Hermite interpolation with a pair of spirals. (English summary) Comput. Aided Geom. Design 10 (1993), no. 6, 491-507. ...
When can we find a smooth curve consisting of a pair of spirals joining these points with the associated tangents and curvatures? ...
Geometric Hermite interpolation by a family of intrinsically defined planar curves
2016
Computer-Aided Design
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This paper proposes techniques of interpolation of intrinsically defined planar curves to Hermite data. ...
By choosing low order polynomials for representing the curvature radius functions, the interpolating curves can be spirals that have monotone curvatures or fair curves with small numbers of curvature extremes ...
This work is supported by the National Natural Science Foundation of China grants (11290142, 61272300). ...
doi:10.1016/j.cad.2016.04.001
fatcat:s6o4z2diwzhsrnwsulftc6q33y
Planar interpolation with a pair of rational spirals
2007
Journal of Computational and Applied Mathematics
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Two situations where the planar, two-point G 2 Hermite interpolation problem can be solved with a pair of rational spiral segments are outlined here. ...
Spirals are curves of one-signed, monotone increasing or decreasing curvature. Spiral segments have the advantage that the minimum and maximum curvatures are at their endpoints. ...
The second author appreciates the hospitality of the University of Dundee, Dundee, Scotland, and acknowledges the financial support of the Natural Sciences and Engineering Research Council of Canada. ...
doi:10.1016/j.cam.2006.02.003
fatcat:wirvbtsbmndyhbvoau53woui7i
A two-point G1 Hermite interpolating family of spirals
2009
Journal of Computational and Applied Mathematics
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It is shown that there is a unique G 1 Hermite interpolating spiral that passes through a given point in an allowable region. ...
A one-parameter family of spirals that can match planar, two-point G 1 Hermite data is presented. ...
The authors appreciate the financial support of the National Science and Engineering Research Council of Canada for this research. ...
doi:10.1016/j.cam.2007.12.027
fatcat:vfw6r7mgefayfjpo7h2yzwnaee
Spiral arc spline approximation to a planar spiral
1999
Journal of Computational and Applied Mathematics
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The resulting collection of biarcs forms a G 1 arc spline that interpolates the entire set of G 1 Hermite data. ...
An arc spline approximation to a smooth planar curve can be found by reading G 1 Hermite data from the curve and ÿtting a biarc between each pair of data points. ...
Acknowledgements The authors acknowledge the ÿnancial support of the Natural Sciences and Engineering Research Council of Canada for this research. ...
doi:10.1016/s0377-0427(99)00072-2
fatcat:j5vcovxe3nfjpg4ahiyrm5rq4m
3D Euler spirals for 3D curve completion
2012
Computational geometry
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Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. ...
It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve -properties that have been shown to be important for the appeal of curves. ...
A. Gilboa and the Zinman Institute of Archaeology at the University of Haifa for providing the archaeological models. ...
doi:10.1016/j.comgeo.2011.10.001
fatcat:r6lkxhbmbna4bhtk65ejuwwbw4
3D Euler spirals for 3D curve completion
2010
Proceedings of the 2010 annual symposium on Computational geometry - SoCG '10
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Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. ...
It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve -properties that have been shown to be important for the appeal of curves. ...
A. Gilboa and the Zinman Institute of Archaeology at the University of Haifa for providing the archaeological models. ...
doi:10.1145/1810959.1811025
dblp:conf/compgeom/HararyT10a
fatcat:mcdobufxmbdfrar3fa7eggi2ge
G1 interpolation with a single Cornu spiral segment
2009
Journal of Computational and Applied Mathematics
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Cornu spiral segments are used in applications such as the geometric design of highways and railways, robot path planning, and shape completion. ...
An improved method for doing so using a Cornu spiral segment is discussed. ...
Acknowledgements The authors acknowledge with thanks the suggestions of the anonymous reviewer which helped to improve the paper. ...
doi:10.1016/j.cam.2007.12.022
fatcat:eldytdz3sras5oiz6hl73rtwym
A further generalisation of the planar cubic Bézier spiral
2012
Journal of Computational and Applied Mathematics
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Spiral segments are useful in the design of fair curves. ...
They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. ...
Acknowledgment This work was supported by The Natural Sciences and Engineering Research Council of Canada. ...
doi:10.1016/j.cam.2012.01.024
fatcat:opz6onzz7ncq7azjcxqsnsfdja
Coaxing a planar curve to comply
2002
Journal of Computational and Applied Mathematics
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We concentrate on the ÿrst of these, interpolation methods. ...
A long-standing problem in computer graphics is to ÿnd a planar curve that is shaped the way you want it to be shaped. A selection of various methods for achieving this goal is presented. ...
Pair of spirals A single spiral can match a rather restricted set of two-point G 2 data; a pair of spirals can match a wider range of G 2 data. ...
doi:10.1016/s0377-0427(01)00478-2
fatcat:jr43wuflt5ftborljhiyfdeoum
Planar two-point G1 Hermite interpolating log-aesthetic spirals
2012
Journal of Computational and Applied Mathematics
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This paper proves that for any member of the family, a unique segment of that spiral can be found that matches given two-point G 1 Hermite data. ...
A family of planar log-aesthetic spirals that include a point of zero curvature is used in this paper. The two-point G 1 Hermite data that is considered has some restrictions on the angles. ...
Acknowledgements The authors wish to express appreciation for the financial support of the Natural Sciences and Engineering Research Council of Canada. ...
doi:10.1016/j.cam.2012.04.021
fatcat:ln3zknjihbhrvo6jneecp7zose
Visualizing 3D Euler spirals
2010
Proceedings of the 2010 annual symposium on Computational geometry - SoCG '10
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This video describes a new type of 3D curves, which generalizes the family of 2D Euler spirals. ...
The utility of these spirals for curve completion applications is demonstrated. This video accompanies the paper presented in [4] . ...
Roundness: If C interpolates two point-tangent pairs lying on a circle, then C is a circle.
3D CURVE COMPLETION 3D curve features convey important information about the shape. ...
doi:10.1145/1810959.1810977
dblp:conf/compgeom/HararyT10
fatcat:4ez5ye5ykbcp3l4f2sc6tss2kq
Page 8453 of Mathematical Reviews Vol. , Issue 2002K
[page]
2002
Mathematical Reviews
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Hermite interpolation problem is to find a planar curve matching planar G? Hermite data. In this paper, a C-shaped interpolating curve made of one or two spirals is sought. ...
join of a pair of quadratics. ...
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