Introduction Our Approach The Force Density Method Results

Fast Simulation of Skin Sliding

Xiaosong Yang, Richard Southern and Jian Jun Zhang

Bournemouth University

Computer Animation and Social Agents, 2009

Introduction Our Approach The Force Density Method Results

Outline

1 Introduction

2 Our Approach

3 The Force Density Method

4 Results

Introduction Our Approach The Force Density Method Results

The Problem

The human body is acomplex multi-layeredorganism.

Each layer has differentelasticity properties.

In particular skin is quitetaut, while the fat whichconnects it to muscle andbone is loose.

Introduction Our Approach The Force Density Method Results

The Problem

Other approaches

Can be simulated with physically based systems, such asFinite Element Method or Mass Spring systems.

These are difficult to set up and slow to solve.

Simple muscle simulations do not take fat layer intoaccount.

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tattoo_bad.aviMedia File (video/avi)

Introduction Our Approach The Force Density Method Results

Desired Behaviour

Why skin sliding?

We want to give the impression of the muscle movingunderneath the taut skin surface.

Without skin sliding the muscle sticks to the skin.

Introduction Our Approach The Force Density Method Results

Desired Behaviour

GoalsDevelop a method that approximates the behaviour ofmuscles moving under skin.

The method should be independent of the deformation.

It should be simple to set up.

It has to be fast.

It must fit into the standard animation pipeline.

Introduction Our Approach The Force Density Method Results

Our Approach

Method OverviewSelect a region on the surface which is to slide.

Introduction Our Approach The Force Density Method Results

Our Approach

Method OverviewSelect a region on the surface which is to slide.

Embed the original mesh into a 2D domain.

Introduction Our Approach The Force Density Method Results

Our Approach

Method OverviewSelect a region on the surface which is to slide.

Embed the original mesh into a 2D domain.

Embed the deformed mesh into a 2D domain.

Introduction Our Approach The Force Density Method Results

Our Approach

Method OverviewSelect a region on the surface which is to slide.

Embed the original mesh into a 2D domain.

Embed the deformed mesh into a 2D domain.

Resample the deformed mesh based on the original meshembedding.

Introduction Our Approach The Force Density Method Results

Result

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elbow.aviMedia File (video/avi)

Introduction Our Approach The Force Density Method Results

Discussion

Alternative approaches

Why not slide the texture coordinates?

Introduction Our Approach The Force Density Method Results

Discussion

Alternative approaches

Why not slide the texture coordinates?

Texture boundary is discontinuous

Introduction Our Approach The Force Density Method Results

Discussion

Quality of resampling depends on:

The shape of the selected patch.

How the surface is interpolated.

How the surface is embedded in 2D.

Introduction Our Approach The Force Density Method Results

Discussion

Quality of resampling depends on:

The shape of the selected patch.

How the surface is interpolated.

How the surface is embedded in 2D.

Use quadrilateral patches: simple to define.

Introduction Our Approach The Force Density Method Results

Discussion

Quality of resampling depends on:

The shape of the selected patch.

How the surface is interpolated.

How the surface is embedded in 2D.

Non-quadrilateral patches may sometimes be useful.

Introduction Our Approach The Force Density Method Results

Discussion

Quality of resampling depends on:

The shape of the selected patch.

How the surface is interpolated.

How the surface is embedded in 2D.

Use triangular or generalized barycentric coordinates.

Introduction Our Approach The Force Density Method Results

Discussion

Quality of resampling depends on:

The shape of the selected patch.

How the surface is interpolated.

How the surface is embedded in 2D.

Use the Force Density Method.

Introduction Our Approach The Force Density Method Results

The Force Density Method: Introduction

History

A non-iterative method to find the form of cable networks.

Developed for the roof of the 1972 Munich Olympiccomplex.

Linearises shape analysis of tensile structures.

Introduction Our Approach The Force Density Method Results

The Force Density Method: Definition

Components of the FDM

The force density of a cable element i is approximated byqi = Fi/Li.

The cable network is defined by a branchnode matrix C.

The load vector applied to each node given by(CTQC)X = R.

Cf Cu1 2 3 4 5 6 7 8

a 1 -1 . . . . . .b . 1 -1 . . . . .c . . 1 -1 . . . .d 1 . . -1 . . . .e 1 . . . -1 . . .f . 1 . . . -1 . .g . . 1 . . . -1 .h . . . 1 . . . -1i . . . . 1 -1 . .j . . . . . 1 -1 .k . . . . . . 1 -1l . . . . 1 . . -1

Introduction Our Approach The Force Density Method Results

Force Density Method: Embedding

To determine the form:Define fixed (Xf ) and unfixed (Xu)nodes.

Seperate C into Cf and Cu respectively.

Unfixed nodes can be computed bysolving for Xu in

(

CTu QCTu

)

Xu = (

CTu QCTf

)

Xf .

Introduction Our Approach The Force Density Method Results

Force Density Method: Embedding

To determine the form:Define fixed (Xf ) and unfixed (Xu)nodes.

Seperate C into Cf and Cu respectively.

Unfixed nodes can be computed bysolving for Xu in

(

CTu QCTu

)

Xu = (

CTu QCTf

)

Xf .

Embedding computed by using Xf R2

around edge of parameteric domain.

Xf

Xu

Introduction Our Approach The Force Density Method Results

Force Density Method: Embedding

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embed.aviMedia File (video/avi)

Introduction Our Approach The Force Density Method Results

Force Density Method: Properties

Properties1 It is a sparse linear system.2 It is foldover free.3 It is defined only by edge properties.4 It is stable under motion.

Quickly solved with Conjugate Gradient Method.

Introduction Our Approach The Force Density Method Results

Force Density Method: Properties

Properties1 It is a sparse linear system.2 It is foldover free.3 It is defined only by edge properties.4 It is stable under motion.

No foldover ifqi > 0, and

Xf is defined on the boundary of theparameter space.

Introduction Our Approach The Force Density Method Results

Force Density Method: Properties

Properties1 It is a sparse linear system.2 It is foldover free.3 It is defined only by edge properties.4 It is stable under motion.

It ignores differential surface properties, so does notminimize distortion.

Introduction Our Approach The Force Density Method Results

Force Density Method: Properties

Properties1 It is a sparse linear system.2 It is foldover free.3 It is defined only by edge properties.4 It is stable under motion.

It jiggles less than surface based methods.

Introduction Our Approach The Force Density Method Results

Force Density Method: Properties

Stability under motion

Rotate vertices of a face around the surface of a sphere.

Measure the magnitude of the vector cone from original todeformed vertices (units of jiggle).

Introduction Our Approach The Force Density Method Results

Force Density Method: Properties

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embed_compare.aviMedia File (video/avi)

Introduction Our Approach The Force Density Method Results

Texture sliding

Introduction Our Approach The Force Density Method Results

Tattoo example

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tattoo_good.aviMedia File (video/avi)

Introduction Our Approach The Force Density Method Results

Timings

vertices edges embed original embed deformed Lookup Tex FPSelbow 51 90 3 0 1 1000bicep 163 299 18 4 1 200face 316 593 53 8 2 100

elephant 431 1218 110 15 3 55finger 538 1060 153 12 2 72

Introduction Our Approach The Force Density Method Results

Conclusions

We have presented a method to simulate skinsliding that:

is easy to specify,

is realtime,

works with any deformation technique, and therefore,

fits into any animation production pipeline.

In the future

Introduction Our Approach The Force Density Method Results

Conclusions

We have presented a method to simulate skinsliding that:

is easy to specify,

is realtime,

works with any deformation technique, and therefore,

fits into any animation production pipeline.

In the futureOverlapping patches?

Introduction Our Approach The Force Density Method Results

Conclusions

We have presented a method to simulate skinsliding that:

is easy to specify,

is realtime,

works with any deformation technique, and therefore,

fits into any animation production pipeline.

In the futureOverlapping patches?

Weight painting?

Introduction Our Approach The Force Density Method Results

Conclusions

We have presented a method to simulate skinsliding that:

is easy to specify,

is realtime,

works with any deformation technique, and therefore,

fits into any animation production pipeline.

In the futureOverlapping patches?

Weight painting?

Wrinkles?

Introduction Our Approach The Force Density Method Results

The End

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Questions?

elephant.aviMedia File (video/avi)

Force Density Optimizations

Choosing qiMost systems find qi = 1/Li produces satisfactory results.

For performance reasons we approximate the force densitywith

qi = maxj

|ej|2 |ei|

2 + ,

where is a very small value used to prevent degeneratecases.

Speeding up interpolation

Interpolation

Interpolation with barycentric coordinates requires us tofind the facet in which a point lies.

The embedding of the deformed surface is rendered,different colors for each facet.

A 3 3 grid is tested around the point to find the facet.

Embedding examples

IntroductionOur ApproachThe Force Density MethodResultsAppendix