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Average Vector Field Integration for St. Venant-Kirchhoff Deformable Models.

Junior Rojas, Tiantian Liu, Ladislav Kavan

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    Summary
    This summary is machine-generated.

    We introduce Average Vector Field (AVF) integration for simulating deformable solids in animation. This method ensures exact energy conservation, preventing exploding animations and numerical damping for lively, stable motion.

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    Area of Science:

    • Computer Graphics
    • Physics-Based Animation
    • Numerical Simulation

    Background:

    • Physics-based animation often struggles with numerical instability and damping.
    • Previous integration methods for deformable solids can lead to exploding animations or undesirable energy loss.
    • Accurate simulation of deformable materials is crucial for realistic computer graphics.

    Purpose of the Study:

    • To present a novel numerical integration method for deformable solids.
    • To achieve exact energy conservation in physics-based animation.
    • To address common issues like exploding animations and numerical damping.

    Main Methods:

    • Propose Average Vector Field (AVF) integration.
    • Achieve exact energy conservation for St. Venant-Kirchhoff materials.
    • Formulate implicit update rules as a minimization problem for efficient solving.

    Main Results:

    • Demonstrate exact energy conservation without correction steps or extra parameters.
    • Animations exhibit no exploding behavior and avoid numerical damping.
    • Produce lively motion even with large time steps, suitable for practical animation.

    Conclusions:

    • AVF integration offers a stable and accurate method for simulating deformable solids.
    • The approach overcomes limitations of existing numerical integration techniques.
    • It is readily deployable in animation pipelines, supporting damping and collision response.