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Crack Nucleation & Propagation

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

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

1. Background & Motivation (Why?) Traditional shape morphing techniques have suffered from a fundamental problem known as the "Rendering Gap."

Physics Simulation (MPM): Efficient because it uses sparse particles, but it lacks sufficient surface detail for high-quality visuals.

Rendering: Typically requires dense surface information to display high-fidelity images.

The Problem: The process connecting these two domains was non-differentiable. This meant that rendering errors couldn't be used to correct or optimize the underlying physical motion.

2. Key Idea: PhysMorph-GS (How?) The researchers proposed a new pipeline that establishes a bidirectional coupling between Differentiable MPM (Physics) and 3D Gaussian Splatting (Rendering). Core Mechanisms 1) Deformation-Aware Upsampling

Instead of relying solely on the sparse "Anchor Particles" from the physics engine, the system generates virtual "Child Particles" specifically for rendering.

PhysMorph-GS: Differentiable Shape Morphing via Joint Optimization of Physics and Rendering Objectives

TVCG Teaser Video:

Rendering results:

Sphere to Bunny & Duck to Cow:

D to Dragon:

A Differentiable Material Point Method Framework for Shape Morphing

Abstract : 

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

Lava Simulation based on Wax