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Crack Nucleation & Propagation

Two-field H design: We separate the strain energy history into two independent fields:

H_history (tight spherical seed) — feeds the AT2 phase-field PDE solver for localized damage

H_gradient (vertical gradient: strong at bottom, zero at mid-height) — provides a smooth ∇H for crack tip direction, ensuring consistent bottom→top propagation

Radial surface paths: At impact, 6 crack paths are seeded radially outward from the contact center (star pattern), with a low Z-component (z = 0.15) to keep paths near the bottom surface for immediate visibility

AT2 phase-field PDE: Variational damage model solved via Jacobi iteration. H_crack (5× H_ref) is seeded along existing crack paths as a boundary condition

Phase Field/Manifold-based Gaussian Splats Crack Simulation

Core Claim

Directly optimizing Chamfer Distance (CD) can produce worse CD values than not optimizing it at all. This is not a metric design problem — it is a gradient-structural failure.

Why It Fails (3 Propositions)

Prop 1. The unique attractor of the forward CD gradient is many-to-one collapse — multiple source points converge to the same target point

Prop 2. The reverse (t→s) term provides nonzero gradient to at most 1 of k collapsed points → the remaining k−1 are stuck in a zero-gradient deadlock

Prop 3. Local regularizers (repulsion, smoothness, DCD) cannot alter cluster-level drift — translational invariance guarantees pairwise forces cancel at the centroid

On the Structural Failure of Chamfer Distance in 3D Shape Optimization

1. Background & Motivation (Why?)

Commanding a robot to "cut the apple in half" is deceptively difficult.

Physical Complexity: Food deforms, fractures, and changes shape under pressure. Standard datasets for rigid bodies cannot capture these dynamics.

Data Scarcity: Collecting real-world data (e.g., slicing thousands of fruits) is expensive and dangerous. Previous simulations lacked physical accuracy regarding forces and friction.

Quantitative Grounding: Few existing models can understand and execute precise numerical instructions, such as "cut at the 30% mark from the right."

2. Key Solution: CulinaryCut & VLAP (How?)

CulinaryCut-VLAP: A Vision-Language-Action-Physics Framework for Food Cutting via a Force-Aware Material Point Method

TL;DR

A framework combining differentiable physics simulation and 3D Gaussian Splatting (3DGS) to achieve physically plausible and visually detailed 3D volumetric shape morphing.

Key Methodology

Resolves the instability and lack of geometric detail found in prior methods via F-space injection.

MPM-Gaussian Mapping: Syncs the MPM deformation gradient $\mathbf{F}$ with the Gaussian covariance Σ(Σ=FΣ0F⊤)\boldsymbol{\Sigma} (\boldsymbol{\Sigma} = \mathbf{F} \boldsymbol{\Sigma}_0 \mathbf{F}^\top)Σ(Σ=FΣ0​F⊤).

Control-Space (FFF) Injection: Injects rendering errors exclusively into the deformation gradient (FFF), avoiding the simulation crashes caused by modifying particle positions (xxx).

PhysMorph-GS: Render-Guided Volumetric Morphing with Differentiable Physics

TVCG Teaser Video:

Rendering results:

Sphere to Bunny & Duck to Cow:

D to Dragon:

A Differentiable Material Point Method Framework for Shape Morphing

Abstract : 

In this paper, we propose a novel approach to simultaneously express the angular and linear motion of the particle itself. During the integration process of the presented MPM (Material Point Method), a deformation gradient tensor is decomposed by polar decomposition theory to extract the rotation tensor. By applying this together with the linear motion of each particle, we can possibly depict each particle’s spin.

Rendering results:

Sand particle example:

Snow with Car:

Primitive Rectangle (vs MPM):

MPM-Based Angular Animation of Particles using Polar Decomposition Theory

Describe Lava’s localization with wax

Use Numeric Animation for Real Data in Gen AI

 Heat conduction: implementation complete, validated against benchmark scenarios.

 Heat convection: implementation complete, integrated with conduction for coupled heat transfer modeling.

 Phase change dynamics: solid–liquid transitions modeled, including latent heat effects.

 Target setup: experiments in thin domains, where geometric constraints amplify local phenomena.

 Localization analysis: leveraging High-Young’s modulus modeling to sharpen stress/strain concentration effects.

 Preconditioning techniques applied to stabilize and accelerate solvers, especially under strong stiffness contrasts.

 Observation goal: capture emergent patterns of localization during phase transitions in constrained geometries, and evaluate physical plausibility of the numeric animation framework with real-world data alignment.

Lava Simulation based on Wax