Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs

Drysdale, Robert L. Scot; Rote, Günter; Sturm, Astrid

doi:10.1016/j.comgeo.2007.10.009

Cited by 37 publications

(22 citation statements)

References 13 publications

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“…It is unclear whether such solutions are useful for schematization: in this context it is generally not desirable to assume that the original shape is relatively smooth. A non-smooth approach is given by Drysdale et al [7]. This method imposes restrictions on "gates" which hinder a high complexity reduction.…”

Section: Introductionmentioning

confidence: 99%

Exploring Curved Schematization of Territorial Outlines

Goethem

Meulemans

Speckmann

et al. 2015

IEEE Trans. Visual. Comput. Graphics

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Abstract-Hand-drawn schematized maps traditionally make extensive use of curves. However, there are few automated approaches for curved schematization; most previous work focusses on straight lines. We present a new algorithm for areapreserving curved schematization of geographic outlines. Our algorithm converts a simple polygon into a schematic crossing-free representation using circular arcs. We use two basic operations to iteratively replace consecutive arcs until the desired complexity is reached. Our results are not restricted to arcs ending at input vertices. The method can be steered towards different degrees of "curviness": we can encourage or discourage the use of arcs with a large central angle via a single parameter. Our method creates visually pleasing results even for very low output complexities. To evaluate the effectiveness of our design choices we perform a geometric evaluation of the resulting schematizations. Besides the geometric qualities of our algorithm, we also investigate the potential of curved schematization as a concept. We conducted an online user study investigating the effectiveness of curved schematizations compared to straight-line schematizations. While the visual complexity of curved shapes was judged higher than that of straight-line shapes, users generally preferred curved schematizations. We observed that curves significantly improved the ability of users to match schematized shapes of moderate complexity to their unschematized equivalents.

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Section: Introductionmentioning

confidence: 99%

Exploring Curved Schematization of Territorial Outlines

Goethem

Meulemans

Speckmann

et al. 2015

IEEE Trans. Visual. Comput. Graphics

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show abstract

“…[Yang and Du 1996;Pei and Horng 1996;Horng 2003;Safonova and Rossignac 2003;Drysdale et al 2008]. More recently, piecewise clothoids, made of arcs with linear (instead of constant) curvature, have gained an increasing interest in the graphics community [McCrae and Singh 2008;Baran et al 2010] because of their fairness property, allowing for sketching visually pleasing curves.…”

Section: Related Workmentioning

confidence: 99%

Stable inverse dynamic curves

Derouet-JourdanAlexandre

Bertails-DescoubesFlorence

ThollotJoëlle

2010

ACM Trans. Graph.

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Abstract2d animation is a traditional but fascinating domain that has recently regained popularity both in animated movies and video games. This paper introduces a method for automatically converting a smooth sketched curve into a 2d dynamic curve at stable equilibrium under gravity. The curve can then be physically animated to produce secondary motions in 2d animations or simple video games. Our approach proceeds in two steps. We first present a new technique to fit a smooth piecewise circular arcs curve to a sketched curve. Then we show how to compute the physical parameters of a dynamic rod model (super-circle) so that its stable rest shape under gravity exactly matches the fitted circular arcs curve. We demonstrate the interactivity and controllability of our approach on various examples where a user can intuitively setup efficient and precise 2d animations by specifying the input geometry.

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“…Hoschek [15] finds a G 1 planar approximation; Rossignac [16] approximates a space curve by G 0 continuous circular arcs. Drysdale et al [17] compute a minimum segment count G 0 planar approximation with junction point chosen from the input vertices. Several authors [18,19,20] describe the approximation of planar curves using G 1 continuous biarcs (pairs of circular arcs joined G 1 continuously).…”

Section: Related Workmentioning

confidence: 99%

Generating parametric models of tubes from laser scans

Bauer

Polthier

2009

Computer-Aided Design

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We present an automatic method for computing an accurate parametric model of a piecewise defined pipe surface, consisting of cylinder and torus segments, from an unorganized point set. Our main contributions are reconstruction of the spine curve of a pipe surface from surface samples, and approximation of the spine curve by G 1 continuous circular arcs and line segments. Our algorithm accurately outputs the parametric data required for bending machines to create the reconstructed tube.

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Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs

Cited by 37 publications

References 13 publications

Exploring Curved Schematization of Territorial Outlines

Exploring Curved Schematization of Territorial Outlines

Stable inverse dynamic curves

Generating parametric models of tubes from laser scans

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