Physics-Inspired Adaptive Fracture Refinement Zhili Chen, Miaojun Yao, Renguo Feng, Huamin Wang The Ohio State University
Fracture Animation • Physically simulated fracture Physically accurate X Stability issue X Slow in high resolution O’brien , et.al. 1999 • Pre-defined fracture pattern Easier artistic control Fast and robust X Difficult to create physically plausible detail Müller, et.al. 2013 1
Physics-Inspired Fracture Refinement • Physically plausible – Material property and stress variation • Fast and stable – Generate refined result in seconds • Easy artistic control – Can use low-resolution animation as preview 2
Low-Res Animation Input animation in low resolution 3
Low-Res Surface Extraction Animation Low-resolution fracture surface 4
Low-Res Surface Surface Adaptive Extraction Animation Evolution Remeshing Evolve fracture surface to higher resolution 5
Low-Res Surface Surface Adaptive High-Res Extraction Animation Animation Evolution Remeshing Transfer deformation to high-resolution fracture surface 6
Physics-Inspired Fracture Refinement Surface Refinement Low-Res Surface Surface Adaptive High-Res Animation Extraction Evolution Remeshing Animation Iterative 7
Fracture Surface Extraction 1s 1s 2s 2s 4s 4s 3s 3s 4s 4s 3s 3s 4s 4s 5s 5s 2s 2s 1s 1s Material space in final frame 8
Fracture Surface Extraction 1s 2s 4 s 3s 4s 3 s 4s 5s 2 s 1 s Material space in final frame 9
Physics-Inspired Fracture Refinement Surface Refinement Low-Res Surface Surface Adaptive High-Res Animation Extraction Evolution Remeshing Animation Iterative 10
Fracture Surface Evolution • How to advect vertices? – Towards where the material most likely breaks – Define Separation Field in high resolution – Vertices advect in separation field 11
Separation Field Material Strength Field Some locations within the object are more likely to break due to material property/structure Stress Field The object is more likely to break at where the stress is large 12
Material Strength Field Darker – > Easier to break – Volumetric field as user input • Procedurally generated solid texture • Volumetric data from CT scan, etc. • Voxelization of 3D mesh 13
Stress Field Brighter – > Higher stress Approximation: • The closer to low-res fracture surface, the higher the stress 14
Separation Field - = W1* W2* Stress Field Material Strength Field Separation Field 15
Discrete Gradient Descent Flow S Evolve surface to minimize y ( x ) ( ) separation field Gradient descent for each vertex i ´ n j æ ö y ( x ) f i ( x ) ds - e j d x i dt = - 1 å ò ò Ñ x i y ( x ) ds ç ÷ A i 2 A j è ø S j S j j Î N i Delaunoy, A., and Prados, E. 2011. 16
Discrete Gradient Descent Flow S Evolve surface to minimize y ( x ) ( ) separation field Gradient descent for each vertex i ´ n j 3 A j Ñ y ( x i ) - e j d x i dt = - 1 1 ( ) å å y ( x k ) A i 2 A j j Î N i k Î T j y ( x ) Approximation: varies linearly within triangle plane 17
Gradient Computation ? 18
Gradient Computation 19
Constraints • Fracture boundary – Vertices on exterior surface only move on exterior surface 20
Constraints • Fracture boundary – Vertices on exterior surface only move on exterior surface 21
Constraints • Fracture boundary – Vertices on exterior surface only move on exterior surface • Intersection free – Fracture surfaces do not intersect with each other or themselves 22
Physics-Inspired Fracture Refinement Surface Refinement Low-Res Surface Surface Adaptive High-Res Animation Extraction Evolution Remeshing Animation Iterative 23
Adaptive Remeshing • Random candidate vertices 24
Adaptive Remeshing • Random candidate vertices 25
Adaptive Remeshing • Random candidate vertices • Select and insert candidates • Edge flipping optimization 26
Fracture Surface Refinement 27
Physics-Inspired Fracture Refinement Surface Refinement Low-Res Surface Surface Adaptive High-Res Animation Extraction Evolution Remeshing Animation Iterative 28
High-resolution Animation Generation Deformation • Transfer from low-res to high-res Fracture time (Different for Fracture surface and Exterior surface) 29
Fracture Surface Generation Transfer deformation from corresponding point on fracture surface 30
Exterior Surface Generation 31
Exterior Surface Generation 32
Exterior Surface Generation 33
Exterior Surface Generation Transfer deformation from closet point that belongs to the same partition 34
Exterior Surface Generation Transfer deformation from closet point that belongs to the same partition 35
Exterior Surface Generation Transfer deformation from closet point that belongs to the same partition 36
Exterior Surface Generation Transfer deformation from closet point that belongs to the same partition 37
Examples 38
Bunny Bunny Generation Time Generation Time 11.7 s 11.7 s Refined vertex count Refined vertex count 174 k 174 k 39
Tree Tree Generation Time Generation Time 5.1 s 5.1 s Refined vertex count Refined vertex count 123 k 123 k 40
Jello Jello Generation Time Generation Time 3.0 s 3.0 s Refined vertex count Refined vertex count 32 k 32 k 41
Plastic clay Plastic clay Generation Time Generation Time 3.0 s 3.0 s Refined vertex count Refined vertex count 40 k 40 k 42
Summary • PRO – Physically plausible – Fast and stable – Easy artistic control 43
Summary • PRO – Physically plausible – Fast and stable Early fracture – Easy artistic control • CON – Issue with nonlinear deformation near fracture boundary 44
Limitations • PRO – Physically plausible – Fast and stable – Easy artistic control • CON – Issue with nonlinear deformation near fracture boundary – New collisions from refined surface not resolved 45
Limitations • PRO – Physically plausible – Fast and stable 1 2 – Easy artistic control • CON 3 – Issue with nonlinear deformation 5 6 near fracture boundary 4 – New collisions from refined surface not resolved – Does not create new fracture pieces 46
Acknowledgement 47
Thank you! 48
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