A method for simulating the movement or deformation of objects in real time

Abstract

A method for simulating motion or deformation of an object in real time, comprising: calculating the gradient of the constraint energy according to the constraint energy, and the internal force generated by the energy is Fc=-GradC i ×k i C i ,‑C i ×k i is the magnitude of the internal force, GradC i is the direction of the internal force; combine the gradients of all constraint energies into a Jacobian matrix; make Fc=GradC i ×λ i , C i = α i ×λ i , the strain energy ε at a point at the object t x E = ε t ×D×ε, after being discretized into a volume tetrahedron, the constraints generated by a volume tetrahedron can decompose D into L ‑1 NL, to determine the sum of all external forces of the system F out ; Discretized object motion differential equation solution formula (JM ‑1 J t +Δt ‑2 *α)λ=-Δt ‑1 Jv‑JM ‑1 f out -C(X n )Δt ‑2 , solve the internal force λ; update the position and velocity of the particle or rigid body of the system; the above method realizes the unification of geometric constraint energy and finite element strain energy, and the regularization method introduced at the same time makes the rigidity coefficient of the object infinite, compatible with rigid body simulation and software simulation , so that the simulation can achieve great visual effects and stability under the unified framework.

Description

technical field [0001] The invention relates to a simulation method, in particular to a method for simulating the motion or deformation of an object in real time. Background technique [0002] In the field of computer graphics, real-time physical simulation, including soft body, rigid body and fluid is a very important direction. Due to the extremely high requirements for computing speed and stability, a large number of real-time models have been proposed: [0003] The mainstream methods are: [0004] Finite Element Analysis Methods for Various Nonlinear Strain Energy O.C.Zienkiewicz and R.L.Taylor.<<TheFinite Element Method>> [0005] Linear strain energy finite element method based on stress transformation based on pole decomposition: M.Muller, <<InteractiveVirtual Materials>> [0006] Method based on constraint energy: M.Teschner< > [0007] Constraint-based methods: M. Müller, B. Heidelberger, <<Position Based Dynamics>> ...

AI Technical Summary

Problems solved by technology

Or soft bodies - geometric constraints, collisions, etc. are very bad

Images