Real-time simulation method of elastic materials based on exemplar in Laplace-Beltrami shape space

Abstract

A real-time simulation method of elastic materials based on an exemplar in a Laplace-Beltrami shape space includes the steps that by means of a Laplace-Beltrami operator and a linear finite element discretization method, characteristic functions and characteristic values of a simulation object and the exemplar on a three-dimensional tetrahedral mesh are calculated; the characteristic function of the exemplar and the characteristic function of the simulation object are subjected to registration; the position of the simulation object is projected in the Laplace-Beltrami shape space, and the shape of a target on an exemplar fashion is solved through non-linear shape interpolation; a final deformation result under an Euclidean space is obtained by building a local coordinate system on each vertex at current moment and adding shape details; a deformed object simulation kinetic equation under a non-inertial system is solved by means of a dimensionality reduction subspace built on a modal substrate, and displacement under a dimensionality reduction space at a new moment is obtained; the displacement under the dimensionality reduction space is projected to obtain global displacement by means of a projection matrix calculated in the preprocessing process under global and dimensionality reduction spaces, and a deformation result is drawn.

Description

technical field [0001] The invention belongs to the field of computer graphics and physics-based simulation, and in particular relates to a real-time simulation method for guiding the deformation behavior of a deformable body by using a given sample, so that more comfortable simulation and animation design effects can be obtained. Background technique [0002] Realistic effect and motion design of various solid deformed objects are the focus of attention in recent years. The example-based simulation method proposed in the literature [Martin S, Thomaszewski B, Grinspun E, et al. "Example-based elastic materials," Acm Transactions on Graphics, 30(4), pp.76-79, 2011.], Controlling the deformation mode of the simulated object through a given set of samples has an artistic effect, and provides a new method for the simulation mode of the object. In this method, by defining a deformation energy, the deformation state in the simulation process is guided to the popular surface defin...

AI Technical Summary

Problems solved by technology

[0005] (1) Most of the existing example-based simulation methods use the same topology structure as the simulation object and the example, and lack the diversity of example guidance

[0006] (2) The Laplace-Beltrami shape space proposed by Zhu et al. can make up for the above shortcomings. However, in the process of calculating the target shape, the solution to the secondary energy needs to be solved on the entire grid, resulting in the resolution of the solution process and the grid. Relevant, very time-consuming, and the whole simulation is less efficient

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