Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
ArtDefo: accurate real time deformable objects
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Physics-Based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging
Physics-Based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation
IEEE Transactions on Visualization and Computer Graphics
Approximate simulation of elastic membranes by triangulated spring meshes
Journal of Graphics Tools
GI '04 Proceedings of the 2004 Graphics Interface Conference
Invertible finite elements for robust simulation of large deformation
SCA '04 Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation
Improved 2D mass-spring-damper model with unstructured triangular meshes
The Visual Computer: International Journal of Computer Graphics
Triangular Springs for Modeling Nonlinear Membranes
IEEE Transactions on Visualization and Computer Graphics
Biquadratic and Quadratic Springs for Modeling St Venant Kirchhoff Materials
ISBMS '08 Proceedings of the 4th international symposium on Biomedical Simulation
Deformable tissue parameterized by properties of real biological tissue
IS4TM'03 Proceedings of the 2003 international conference on Surgery simulation and soft tissue modeling
Identification of Spring Parameters for Deformable Object Simulation
IEEE Transactions on Visualization and Computer Graphics
Haptic Interaction with Elastic Volumetric Structures
International Journal of Creative Interfaces and Computer Graphics
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Lumped element models, also known as, mass-spring-damper models, are widely used to simulate deformable objects because of their simplicity and computational efficiency. However, the parameters of lumped element models are typically determined in an ad hoc fashion through trial-and-error, as these models are not directly based on continuum mechanics of deformable objects. In this paper, an alternative method to determine the elasticity parameters of lumped element models of deformable objects is presented. The elasticity parameters are determined using an optimization that minimizes the matrix norm of the error between the stiffness matrices of the linear lumped element model and the linear finite element model of the same object. The method has been developed for two-dimensions and for three-dimensional volumetric objects with tetrahedral and hexahedral (brick) elements. The method has been validated by comparing deformation results of the lumped element models with the deformation results given by finite element models, under various tension, and compression loading conditions.