{"title":"St. Venant-Kirchhoff变形模型的实时子空间集成","authors":"J. Barbič, Doug L. James","doi":"10.1145/1186822.1073300","DOIUrl":null,"url":null,"abstract":"In this paper, we present an approach for fast subspace integration of reduced-coordinate nonlinear deformable models that is suitable for interactive applications in computer graphics and haptics. Our approach exploits dimensional model reduction to build reduced-coordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation models with linear materials (as commonly used in graphics) result in internal force models that are simply cubic polynomials in reduced coordinates. Coefficients of these polynomials can be precomputed, for efficient runtime evaluation. This allows simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interactive sketching technique. Mass-scaled principal component analysis (mass-PCA) is suggested for dimensionality reduction. Finally, several examples are given from computer animation to illustrate high performance, including force-feedback haptic rendering of a complicated object undergoing large deformations.","PeriodicalId":211118,"journal":{"name":"ACM SIGGRAPH 2005 Papers","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2005-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"475","resultStr":"{\"title\":\"Real-Time subspace integration for St. Venant-Kirchhoff deformable models\",\"authors\":\"J. Barbič, Doug L. James\",\"doi\":\"10.1145/1186822.1073300\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present an approach for fast subspace integration of reduced-coordinate nonlinear deformable models that is suitable for interactive applications in computer graphics and haptics. Our approach exploits dimensional model reduction to build reduced-coordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation models with linear materials (as commonly used in graphics) result in internal force models that are simply cubic polynomials in reduced coordinates. Coefficients of these polynomials can be precomputed, for efficient runtime evaluation. This allows simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interactive sketching technique. Mass-scaled principal component analysis (mass-PCA) is suggested for dimensionality reduction. Finally, several examples are given from computer animation to illustrate high performance, including force-feedback haptic rendering of a complicated object undergoing large deformations.\",\"PeriodicalId\":211118,\"journal\":{\"name\":\"ACM SIGGRAPH 2005 Papers\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"475\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM SIGGRAPH 2005 Papers\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1186822.1073300\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM SIGGRAPH 2005 Papers","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1186822.1073300","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 475
摘要
在本文中,我们提出了一种适合于计算机图形学和触觉交互应用的简化坐标非线性变形模型的快速子空间积分方法。我们的方法利用维度模型约简来为具有复杂几何形状的对象建立减少坐标的可变形模型。我们利用这样一个事实,即使用线性材料的大变形模型(如图形中常用的)的模型简化导致内力模型是简化坐标中的简单三次多项式。这些多项式的系数可以预先计算,为有效的运行时评估。这允许使用快速隐式Newmark子空间积分器模拟非线性动力学,子空间积分成本与几何复杂性无关。我们提出了两种有用的方法来生成低维子空间基:模态导数和交互素描技术。建议采用大规模主成分分析(mass- scale principal component analysis, mass-PCA)进行降维。最后,从计算机动画中给出了几个例子来说明高性能,包括经过大变形的复杂物体的力反馈触觉渲染。
Real-Time subspace integration for St. Venant-Kirchhoff deformable models
In this paper, we present an approach for fast subspace integration of reduced-coordinate nonlinear deformable models that is suitable for interactive applications in computer graphics and haptics. Our approach exploits dimensional model reduction to build reduced-coordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation models with linear materials (as commonly used in graphics) result in internal force models that are simply cubic polynomials in reduced coordinates. Coefficients of these polynomials can be precomputed, for efficient runtime evaluation. This allows simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interactive sketching technique. Mass-scaled principal component analysis (mass-PCA) is suggested for dimensionality reduction. Finally, several examples are given from computer animation to illustrate high performance, including force-feedback haptic rendering of a complicated object undergoing large deformations.