Adaptive and robust curve smoothing on surface meshes

Lawonn, Kai; Gasteiger, Rocco; Rössl, Christian; Preim, Bernhard

doi:10.1016/j.cag.2014.01.004

Cited by 16 publications

(7 citation statements)

References 22 publications

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“…There have been many other studies on geodesic computation on a polygonal mesh [18][19][20][21]. Cheng et al [18] constructed a smooth surface that approximates a polygonal mesh and computed a geodesic curve on the surface by solving a first-order ordinary differential equation of tangent vector.…”

Section: Related Workmentioning

confidence: 99%

“…The discrete geodesic is then obtained by projecting the geodesic curve on the smooth surface onto the polygonal mesh. Lawonn et al [19] proposed a method for smoothing polylines on a triangular mesh based on local reduction in geodesic curvature and made it possible for users to adjust their proximity to be the straightest geodesic. Qin et al [20] proposed scenarios for effective window propagation and pruning, and developed triangle-oriented region growing techniques to reduce computational costs and memory usage significantly.…”

Section: Related Workmentioning

confidence: 99%

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Geodesic Hermite Spline Curve on Triangular Meshes

Park

Yoon

2021

Symmetry

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Curves on a polygonal mesh are quite useful for geometric modeling and processing such as mesh-cutting and segmentation. In this paper, an effective method for constructing C1 piecewise cubic curves on a triangular mesh M while interpolating the given mesh points is presented. The conventional Hermite interpolation method is extended such that the generated curve lies on M. For this, a geodesic vector is defined as a straightest geodesic with symmetric property on edge intersections and mesh vertices, and the related geodesic operations between points and vectors on M are defined. By combining cubic Hermite interpolation and newly devised geodesic operations, a geodesic Hermite spline curve is constructed on a triangular mesh. The method follows the basic steps of the conventional Hermite interpolation process, except that the operations between the points and vectors are replaced with the geodesic. The effectiveness of the method is demonstrated by designing several sophisticated curves on triangular meshes and applying them to various applications, such as mesh-cutting, segmentation, and simulation.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Geodesic Hermite Spline Curve on Triangular Meshes

Park

Yoon

2021

Symmetry

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show abstract

“…Several characteristic point detection algorithms have been proposed and widely used in computer vision [24][25][26][27][28], pattern recognition, intelligent identification [29], and retrieval [30]. Awrangjeb et al [31] identified five main detection steps from these algorithms, namely, edge extraction and selection [32][33][34], smoothing [35][36][37][38][39], estimation, characteristic point detection, and coarse-to-fine characteristic point tracking. However, these algorithms cannot directly detect the feature points of trajectories because the calculated results must meet the requirements of the similarity measurement model that is proposed in this paper.…”

Section: State Of the Artmentioning

confidence: 99%

A Measure of Similarity Between Trajectories of Vessels

Qi¹,

Zheng²

2016

JESTR

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The measurement of similarity between trajectories of vessels is one of the kernel problems that must be addressed to promote the development of maritime intelligent traffic system (ITS). In this study, a new model of trajectory similarity measurement was established to improve the data processing efficiency in dynamic application and to reflect actual sailing behaviors of vessels. In this model, a feature point detection algorithm was proposed to extract feature points, reduce data storage space and save computational resources. A new synthesized distance algorithm was also created to measure the similarity between trajectories by using the extracted feature points. An experiment was conducted to measure the similarity between the real trajectories of vessels. The growth of these trajectories required measurements to be conducted under different voyages. The results show that the similarity measurement between the vessel trajectories is efficient and correct. Comparison of the synthesized distance with the sailing behaviors of vessels proves that results are consistent with actual situations. The experiment results demonstrate the promising application of the proposed model in studying vessel traffic and in supplying reliable data for the development of maritime ITS.

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“…With respect to smoothing curves or surfaces for given control points, it has been a popular topic in the field of computer graphics. For example, Lawonnn et al (2014) developed a smoothing method based on a reduction of geodesic curvature with an application example to surgical planning; Taubin (1995) introduced a method based on Gaussian smoothing that does not cause a shrinkage. The common situation in these researches is that the observed or simulated data are abundant but they include noises or errors.…”

Section: Storage Format and Intended Usementioning

confidence: 99%

Storage-efficient reconstruction framework for planar contours

Goto

Shimakawa

2016

Geo-spatial Information Science

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A storage-efficient reconstruction framework for cartographic planar contours is developed. With a smaller number of control points, we aim to calculate the area and perimeter as well as to reconstruct a smooth curve. The input data forms an oriented contour, each control point of which consists of three values: the Cartesian coordinates (x, y) and tangent angle θ. Two types of interpolation methods are developed, one of which is based on an arc spline while the other one is on a cubic Hermite spline. The arc spline-based method reconstructs a G 1 continuous curve, with which the exact area and perimeter can be calculated. The benefit of using the Hermite spline-based method is that it can achieve G 2 continuity on most control points and can obtain the exact area, whereas the resulting perimeter is approximate. In a numerical experiment for analytically defined curves, more accurate computation of the area and perimeter was achieved with a smaller number of control points. In another experiment using a digital elevation model data, the reconstructed contours were smoother than those by a conventional method.

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Adaptive and robust curve smoothing on surface meshes

Cited by 16 publications

References 22 publications

Geodesic Hermite Spline Curve on Triangular Meshes

Geodesic Hermite Spline Curve on Triangular Meshes

A Measure of Similarity Between Trajectories of Vessels

Storage-efficient reconstruction framework for planar contours

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