Symmetry

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34 pages, 1130 KiB

Open AccessArticle

Integrated Hybrid Second Order Algorithm for Orthogonal Projection onto a Planar Implicit Curve

by Xiaowu Li, Feng Pan, Taixia Cheng, Zhinan Wu, Juan Liang and Linke Hou

Symmetry 2018, 10(5), 164; https://doi.org/10.3390/sym10050164 - 15 May 2018

Cited by 3 | Viewed by 3365

The computation of the minimum distance between a point and a planar implicit curve is a very important problem in geometric modeling and graphics. An integrated hybrid second order algorithm to facilitate the computation is presented. The proofs indicate that the convergence of [...] Read more.

The computation of the minimum distance between a point and a planar implicit curve is a very important problem in geometric modeling and graphics. An integrated hybrid second order algorithm to facilitate the computation is presented. The proofs indicate that the convergence of the algorithm is independent of the initial value and demonstrate that its convergence order is up to two. Some numerical examples further confirm that the algorithm is more robust and efficient than the existing methods. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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15 pages, 12329 KiB

Open AccessArticle

Automatic Generation of Dynamic Skin Deformation for Animated Characters

by Shaojun Bian, Anzong Zheng, Ehtzaz Chaudhry, Lihua You and Jian J. Zhang

Symmetry 2018, 10(4), 89; https://doi.org/10.3390/sym10040089 - 31 Mar 2018

Cited by 6 | Viewed by 6998

Abstract

Since non-automatic rigging requires heavy human involvements, and various automatic rigging algorithms are less efficient in terms of computational efficiency, especially for current curve-based skin deformation methods, identifying the iso-parametric curves and creating the animation skeleton requires tedious and time-consuming manual work. Although [...] Read more.

Since non-automatic rigging requires heavy human involvements, and various automatic rigging algorithms are less efficient in terms of computational efficiency, especially for current curve-based skin deformation methods, identifying the iso-parametric curves and creating the animation skeleton requires tedious and time-consuming manual work. Although several automatic rigging methods have been developed, but they do not aim at curve-based models. To tackle this issue, this paper proposes a new rigging algorithm for automatic generation of dynamic skin deformation to quickly identify iso-parametric curves and create an animation skeleton in a few milliseconds, which can be seamlessly used in curve-based skin deformation methods to make the rigging process fast enough for highly efficient computer animation applications. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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25 pages, 1287 KiB

Open AccessArticle

Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering

by Andrés Iglesias, Akemi Gálvez, Patricia Suárez, Mikio Shinya, Norimasa Yoshida, César Otero, Cristina Manchado and Valentin Gomez-Jauregui

Symmetry 2018, 10(3), 58; https://doi.org/10.3390/sym10030058 - 3 Mar 2018

Cited by 28 | Viewed by 5302

Abstract

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric [...] Read more.

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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22 pages, 10153 KiB

Open AccessArticle

Interactive Cutting of Thin Deformable Objects

by Bin Weng and Alexei Sourin

Symmetry 2018, 10(1), 17; https://doi.org/10.3390/sym10010017 - 5 Jan 2018

Viewed by 4152

Abstract

Simulation of cutting is essential for many applications such as virtual surgical training. Most existing methods use the same triangle mesh for both visualization and collision handling, although the requirements for them in the interactive simulation are different. We introduce visual-collision binding between [...] Read more.

Simulation of cutting is essential for many applications such as virtual surgical training. Most existing methods use the same triangle mesh for both visualization and collision handling, although the requirements for them in the interactive simulation are different. We introduce visual-collision binding between high-resolution visual meshes and low-resolution collision meshes, and thus extend the spatially reduced framework to support cutting. There are two phases in our framework: pre-processing and simulation. In the pre-processing phase, the fvisual-collision binding is built based on the computation of geodesic paths. In the simulation phase, the cutting paths are detected on the collision triangles and then mapped to local 2D coordinates systems in which the intersections between visual mesh and the cutting paths are calculated. Both collision and visual meshes are then re-meshed locally. The visual-collision binding is updated after cutting, based on which the collision-simulation and visual-simulation embedding are updated locally. Experimental results show that our cutting method is an efficient and flexible tool for interactive cutting simulation. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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17433 KiB

Open AccessArticle

Tangible Visualization Table for Intuitive Data Display

by Jongyong Kim, Cheongun Lee, Seung-Hyun Yoon and Sanghun Park

Symmetry 2017, 9(12), 316; https://doi.org/10.3390/sym9120316 - 13 Dec 2017

Viewed by 4922

Abstract

We propose a new tangible visualization table for intuitive and effective visualization of terrain data transferred from a remote server in real time. The shape display approximating the height field of remote terrain data is generated by linear actuators, and the corresponding texture [...] Read more.

We propose a new tangible visualization table for intuitive and effective visualization of terrain data transferred from a remote server in real time. The shape display approximating the height field of remote terrain data is generated by linear actuators, and the corresponding texture image is projected onto the shape display. To minimize projection distortions, we present a sophisticated technique for projection mapping. Gesture-based user interfaces facilitate intuitive manipulations of visualization results. We demonstrate the effectiveness of our system by displaying and manipulating various terrain data using gesture-based interfaces. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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5986 KiB

Open AccessArticle

A Study for Parametric Morphogeometric Operators to Assist the Detection of Keratoconus

by Laurent Bataille, Francisco Cavas-Martínez, Daniel G. Fernández-Pacheco, Francisco J. F. Cañavate and Jorge L. Alio

Symmetry 2017, 9(12), 302; https://doi.org/10.3390/sym9120302 - 5 Dec 2017

Cited by 3 | Viewed by 4847

Abstract

The aim of this study is to describe a new keratoconus detection method based on the analysis of certain parametric morphogeometric operators extracted from a custom patient-specific three-dimensional (3D) model of the human cornea. A corneal geometric reconstruction is firstly performed using zonal [...] Read more.

The aim of this study is to describe a new keratoconus detection method based on the analysis of certain parametric morphogeometric operators extracted from a custom patient-specific three-dimensional (3D) model of the human cornea. A corneal geometric reconstruction is firstly performed using zonal functions and retrospective Scheimpflug tomography data from 107 eyes of 107 patients. The posterior corneal surface is later analysed using an optimised computational geometry technique and the morphology of healthy and keratoconic corneas is characterized by means of geometric variables. The performance of these variables as predictors of a new geometric marker is assessed through a receiver operating characteristic (ROC) curve analysis and their correlations are analysed through Pearson or Spearman coefficients. The posterior apex deviation variable shows the best keratoconus diagnosis capability. However, the strongest correlations in both healthy and pathological corneas are provided by the metrics directly related to the thickness as the sagittal plane area at the apex and the sagittal plane area at the minimum thickness point. A comparison of the screening of keratoconus provided by the Sirius topographer and the detection of corneal ectasia using the posterior apex deviation parameter is also performed, demonstrating the accuracy of this characterization as an effective marker of the diagnosis and ectatic disease progression. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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819 KiB

Open AccessArticle

Convergence Analysis on a Second Order Algorithm for Orthogonal Projection onto Curves

by Xiaowu Li, Lin Wang, Zhinan Wu, Linke Hou, Juan Liang and Qiaoyang Li

Symmetry 2017, 9(10), 210; https://doi.org/10.3390/sym9100210 - 1 Oct 2017

Cited by 6 | Viewed by 3830

Abstract

Regarding the point projection and inversion problem, a classical algorithm for orthogonal projection onto curves and surfaces has been presented by Hu and Wallner (2005). The objective of this paper is to give a convergence analysis of the projection algorithm. On the point [...] Read more.

Regarding the point projection and inversion problem, a classical algorithm for orthogonal projection onto curves and surfaces has been presented by Hu and Wallner (2005). The objective of this paper is to give a convergence analysis of the projection algorithm. On the point projection problem, we give a formal proof that it is second order convergent and independent of the initial value to project a point onto a planar parameter curve. Meantime, for the point inversion problem, we then give a formal proof that it is third order convergent and independent of the initial value. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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2520 KiB

Open AccessArticle

Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

by Xiaowu Li, Lin Wang, Zhinan Wu, Linke Hou, Juan Liang and Qiaoyang Li

Symmetry 2017, 9(8), 146; https://doi.org/10.3390/sym9080146 - 5 Aug 2017

Cited by 10 | Viewed by 4664

Abstract

To compute the minimum distance between a point and a parametric surface, three well-known first-order algorithms have been proposed by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, the First-Order method). In this paper, we prove the method’s first-order [...] Read more.

To compute the minimum distance between a point and a parametric surface, three well-known first-order algorithms have been proposed by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, the First-Order method). In this paper, we prove the method’s first-order convergence and its independence of the initial value. We also give some numerical examples to illustrate its faster convergence than the existing methods. For some special cases where the First-Order method does not converge, we combine it with Newton’s second-order iterative method to present the hybrid second-order algorithm. Our method essentially exploits hybrid iteration, thus it performs very well with a second-order convergence, it is faster than the existing methods and it is independent of the initial value. Some numerical examples confirm our conclusion. Full article

(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)

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