Interactive Control of Deformable-object Animations through Control

Metaphor Pattern Adherence

Shane Transue and Min-Hyung Choi

Department of Computer Science and Engineering, University of Colorado Denver, Denver, U.S.A.

Keywords:

Physically-based Simulation, Animation Control.

Abstract:

In this paper we present an adaptive and intuitive methodology for controlling the localized deformations

of physically simulated objects using an intuitive pattern-based control interface. To maximize the interac-

tive component presented in this approach we consolidate existing feedback mechanisms in deformable-body

control techniques to provide intuitive editing metaphors for stretching, bending, twisting, and compressing

simulated objects. The resulting movements created by these control metaphors are validated using imposed

behavior evaluation and the effectiveness of this approach is demonstrated through interactively generated

compound movements that introduce complex local deformations of objects in existing physical animations.

1 INTRODUCTION

Controlling the behaviors of deformable objects in

physically-based simulations is an area within com-

puter animation that has recently received extensive

attention. In this ﬁeld, notable progress has been

made in the development of intuitive control tech-

niques that can be used to effectively generate and

target deformation behaviors in physical animations.

Effective approaches in this domain include goal ori-

ented behaviors derived from optimizations in inverse

dynamics (Murray-Smith, 2000) and constraint-based

techniques (Witkin and Welch, 1990). These ap-

proaches are based on methods that effectively con-

trol deformable-object behavior by interpolating be-

tween statically deﬁned deformation states. This pro-

vides an artist with the ability to generate physically

plausible animations of deformable objects by deﬁn-

ing this sequence of deformation states. Despite the

impressive results that can be achieved using these

techniques, there remains a segment within the do-

main of physically-based animation control that re-

quires the translation of high-level control behaviors

into the physical motions of simulated objects to de-

rive realistic deformations. The ability to effectively

interpret and map deformation behaviors to a simu-

lated object provides animation artists with a higher

level of control over the motions that can be expressed

in physical animations. Extending this precise control

to localized deformations, realistic motions from de-

formable models can be obtained (see Figure 1).

Figure 1: Natural deformation behavior derived from the

application of a twist control metaphor. Starting from the

rest state (top-left), the application of the twist control

metaphor produces a localized deformation (bottom-right).

In this paper we present an approach to uti-

lizing precisely controlled external forces to gener-

ate localized deformations in existing animations of

both Mass-Spring Systems (MSS) and Finite Element

Models (FEM) using high-level control metaphors.

Control metaphors introduce an abstraction for high-

level deformation patterns that can be imposed on de-

formable objects to obtain artist directed behaviors.

Unlike prior techniques where intermediate motion

is not explicitly controlled by an artist, we provide

294

Transue S. and Choi M..

Interactive Control of Deformable-object Animations through Control Metaphor Pattern Adherence.

DOI: 10.5220/0005311702940305

In Proceedings of the 10th International Conference on Computer Graphics Theory and Applications (GRAPP-2015), pages 294-305

ISBN: 978-989-758-087-1

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

a set of controls that allow an artist to continuously

interact with the physical state of a simulated object.

Speciﬁcally, we look at how control metaphors can be

used to stretch, bend, twist, and compress localized

regions of simulated deformable objects. We then in-

tegrate this editing process into an intuitive animation

interface that allows for an artist to iteratively reﬁne

deformation behaviors through the use of interactive

control widgets. The objective of our approach to de-

formation control is to provide a set of tools that can

be effectively used to generate deformations based on

predeﬁned control metaphor behaviors and precisely

control deformations within existing animations. This

tool-set includes real-time simulation recording, the

ability to generate dynamic simulation previews, and

the introduction of interactive force curves for precise

deformation control with motion blending.

The effectiveness of our approach is explored

through the application of control metaphors to exist-

ing node-based models to generate explicit deforma-

tion behaviors. From the resulting animations gener-

ated with this proposed method, we illustrate that con-

trol metaphors can be used to effectivelyimpose phys-

ically plausible localized deformationsat any physical

time-step within an existing animation. To further il-

lustrate the utility of this proposed technique, we also

demonstrate that the subsequent application of control

metaphors can be used to deﬁne compound localized

deformation behaviors.

2 RELATED WORK

Several generalized control techniques in goal ori-

ented optimization (Popovi´c et al., 2000), dynamic

key-framing (Hildebrandt et al., 2012), space-time

optimization (Barbiˇc et al., 2009), and inversedynam-

ics (Jeon and Choi, 2007), (Twigg and James, 2008)

have been developed to provide effective techniques

for generating accurately controlled animations. The

common tie between these approaches is that they

are directed at the derivation of physically plausi-

ble motion deﬁned between statically deﬁned defor-

mation states. Similarly, recent developments in ex-

ample driven deformations by (Martin et al., 2011)

and methods using internal elasticity potentials intro-

duced by (Coros et al., 2012) can be used to direct

global deformations form predeﬁned static deforma-

tion states or transformation goals. These approaches

represent a ﬁeld of deformation control techniques

that utilize constraint-based optimizations that can be

used to effectively generate targeted deformation be-

haviors. However, these approaches lack ﬂexibility

in the control of behaviors within intermediate states

generated during this optimization process. This can

be attributed to the to the difﬁculties in creating an

intuitive connection between artistic intent and opti-

mization control parameters.

To modify the deformation behavior between ex-

ample or goal states using current techniques, the so-

lution involves the introduction of additionalstatic ex-

amples that further reﬁne the description of the de-

sired behavior (Chai and Hodgins, 2007). However

the introduction of these additional constraints in-

creases the number of required example deformation

states that an artist must provide. Upon doing so, an

artist must consider that the accuracy of these input

states can signiﬁcantly affect the physical plausibility

of the resulting animation (Arikan and Forsyth, 2002).

In prior rigid-body control techniques based on

physical parameter optimization (Popovi´c et al.,

2000), these intermediate states can be derived from

global transformations. However, providing these

additional key-frames for deformable objects repre-

sents an additional challenge due to the inherent difﬁ-

culty in accurately deﬁning static deformation states.

This problem is exacerbated for objects with complex

topologies or highly-dynamic models such as articu-

lated ﬁgures or cloth. While many of these introduced

techniques are well suited for generating the interme-

diate motions between static deformations, an artist is

left to provide these initial input states, a non-trivial

task. Additionally, the introduction of these new con-

straints requires a regeneration of all intermediate mo-

tions, thus eliminating prior deformation behaviors.

This is an undesirable effect if the original deforma-

tion behavior was close to the desired result.

Alternative techniques for interactively editing

deformable simulations proposed by (Barbiˇc et al.,

2012) and (Huang et al., 2011) aim to maintain the

original behavioralcharacteristics of a deformableob-

ject within the provided animation. This provides an

effective platform for interactively controlling defor-

mations and introduces the ability to alter object be-

haviors within existing animations.

These contributions substantially improve the in-

teractive editing process used by artists to control ob-

ject deformations while preserving existing animated

behaviors. Our work is related to these contributions

and aims to provide an interactive editing environ-

ment that can facilitate real-time editing of localized

deformations. We propose that generalized high-level

control metaphors can be used in cooperation with

existing techniques to both generate static deforma-

tion states as key-frames, introduce localized defor-

mations in existing animations, and provide tweaks

to existing cage-based animation techniques (Joshi

et al., 2007), (Ju et al., 2008).

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3 METHOD OVERVIEW

The input to our interactive animation system is based

on MSS and FEM node-based deformation models

as individual rest state objects or as part of an exist-

ing physically-drivenanimation. In both instances the

dynamics model driving the deformation behavior is

orthogonal to our approach and does not contribute

to the requirements of our editing tools. Rather, the

only assumptions made about a provided nodal sys-

tem is that it is composed of n interconnected nodes

that deﬁne a shell or tetrahedral topology and can be

directly integrated into an existing dynamics model.

If an animated MSS or FEM model is provided, the

animation is discretized into states that correspond to

individual time-steps within the underlying dynam-

ics model driving the physical simulation. In using

precisely targeted external forces, we can effectively

limit the requirement of our approach to dynamics

models that support the application of these forces

to arbitrary nodes. In our implementation we utilize

the VegaFEM physics library (Barbiˇc and Schroeder,

2009) with an implicit Euler integration scheme.

The foundation of our editing approach is based

on the development of several components that are

required to facilitate this form of force-based editing

in an interactive environment. These requirements

include (1) reliable local coordinate systems for de-

formable models to facilitate targeted deformations,

(2) the ability to record physical simulations in real-

time, (3) the efﬁcient generation of dynamic simula-

tion previews for interactive feedback, and (4) a set

of intuitive control metaphors that impose intuitive

pattern-based deformation behaviors. We consolidate

these components within an interactive editing envi-

ronment that allows an artist to effectively deﬁne new

animations and reﬁne the deformation behaviors ex-

hibited by objects within existing animations. In this

section we provide the derivation for each of these

components and establish how each contributes to this

intuitive animation editing framework.

3.1 Local Coordinates

To provide an effective mapping between the imple-

mented control metaphors and the deformable objects

upon which they operate, we have introduced a ro-

bust technique for estimating local coordinate trans-

formations for deformable-bodies. Building on this

development, we introduce the notion of control co-

ordinates that allow metaphors to be directly targeted

to localized regions within a deformable object. As

these objects are simulated, these coordinate systems

maintain the application of a control metaphor to the

exact region deﬁned by an artist. This allows us to

provide consistency in localized deformations, even

for objects that exhibit complex global trajectories. In

this section we provide an overviewof our method for

identifying a unique origin and orthogonal set of vec-

tors that can be used to represent the local coordinate

transformation of a deformable-body.

Initially considering the position of a deformable

object, we simply select the center of mass C as an

accurate representation of the objects global position.

To identify the orthogonal set of vectors that will rep-

resent the rotation of the deformable object we con-

sider two objectives: (1) the initial orientation should

be aligned to the objects geometric deﬁnition and (2)

the mapping should accurately represent the rotation

of the object, even during large scale deformations.

In our approach we have devised a two stage pro-

cess for identifying this coordinate system. In an ini-

tial pre-processing stage we calculateC and the orien-

tation of the coordinate system that best matches the

geometric representation of the object through Princi-

ple Component Analysis (PCA). As the objects defor-

mation changes during each simulation time-step, we

recalculate C and update the orthogonal axes vectors

to match the new rotation of the object. The com-

plete derivation of this local coordinate system utiliz-

ing PCA and averaged deformable mass distribution

is detailed in (Transue, 2014).

Figure 2: Local and control coordinate systems for a simple

deformable object. The selected node of the deformable

object represents the origin of the control coordinate system

and deﬁnes the localized region that will be inﬂuenced by

the external forces introduced by a control metaphor.

To produce a localized deformation using a con-

trol metaphor we must also provide an intuitive way

of selecting the affected region. Therefore to attach a

control metaphor to a deformable model at a speciﬁc

location, we employ a simple node selection tech-

nique. The selection of an individual node within the

object will weld a control metaphor to this node so it

can then be used to perform localized deformations.

The image in Figure 2 illustrates the selection of an

individual node that will deﬁne the location of the ap-

plied deformation behavior.

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3.2 Simulation Recording

The generation of new animations and the support for

modifying existing animations requires a complete set

of controls for both real-time recording and playback.

In our approach we provide the standard set of mul-

timedia controls as part of an interactive time-line

that allows an artist to effectively navigate through

the collection of frames within the active animation.

Providing the ability to use this interactive time-line

to scroll through object deformations throughout the

recorded animation presents a critical feedback sys-

tem that allows an artist to closely analyze each defor-

mation state of all animated objects. This presents an

artist with the ability to iteratively reﬁne the motion

exhibited by the simulated objects until the desired

outcome has been reached. In our approach, the abil-

ity to reﬁne the deformation behavior using real-time

playback allows for a higher level of artistic control

when compared to techniques that utilize inverse dy-

namics to generate a ﬁxed result. This is simply due

to the interactive nature of our proposed approach.

3.3 Dynamic Simulation Previews

Unlike optimization techniques that require the use of

a secondary deformation state that an artist deﬁnes

as a dynamic key-frame of the object, our approach

does not explicitly deﬁne the ﬁnal position of a de-

formable object but rather it is generated during the

application of the control metaphor. Therefore in us-

ing our method an artist does not immediately know

how the changes they have imposed on a deformable

object will affect the resulting motion of the object.

To address this problem we introduce the ability to

dynamically generate simulation previews. The im-

age in Figure 3 illustrates the dynamic preview of a

falling cloth model before and after a bend metaphor

has been applied.

Figure 3: Dynamic preview of a cloth model (for three se-

lected states) as a bend control metaphor is applied. The

original animation (left) illustrates the cloth with a uniform

decent due to gravity. The application of a bend metaphor

(right) provides a realistic animation of the falling cloth.

The generation of a simulation preview does not

affect the current animation but illustrates a select

number of future states for every object within the an-

imation. This provides an artist with immediate feed-

back as to how the current conﬁguration of control

metaphors applied to various objects will affect both

local deformations and global trajectories of all ob-

jects within the animation.

4 CONTROL METAPHORS

The fundamental component that we introduce with

the proposed method of deformable object control is

the notion of high-level control metaphors. These

metaphors represent a mapping between a control

widget that speciﬁes a motion, pattern, or behavior

and the physical implementation of that motion by a

simulated object or region within the objects surface.

This provides an artist with a generalized and exten-

sible control methodology for introducing localized

deformations in animated objects. In this section we

introduce the components that formally deﬁne a con-

trol metaphor and illustrate the ﬂexibility of our pro-

posed technique by demonstrating that these compo-

nents can be easily interchanged to provide an exten-

sible set of deformation controls.

The implementation of a control metaphor is re-

sponsible for providing deﬁnitions to the following

components: (1) the identiﬁcation of the control re-

gions that indicate the nodes are inﬂuenced by the

control, (2) the orientation of the external forces the

control produces, (3) the interactive widget that pro-

vides a visual representation of the controls behav-

ioral pattern, and (4) the deﬁnition of a force curve

that deﬁnes applied force magnitude over time.

The consolidation of these four components pro-

vides the formal basis of the abstract control metaphor

deﬁnition: given a control metaphor M, the composi-

tion of these components into a control metaphor is

deﬁned as follows:

M = (R,O,V, F)

Where R represents the discrete set of bounding

volumes that identify the regions inﬂuenced by this

control, the set of normalized vectors O represents

the external force orientations applied to the object

in within each region, the set of three-dimensional

primitives V that provides the visual representation of

the control, and the scalar list F represents the force

magnitudes that deﬁne the application time and dura-

tion of the control. Providing a unique deﬁnition for

component allows for an unbound number of poten-

tial control metaphors with this extensible design.

Through the implementation of each component

we can derive high-level controls that can easily be

conﬁgured by an artist to introduce pattern-based de-

formations (such as bending, twisting, stretching, and

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Figure 4: Illustrations (top and front views) of the widget that represents the bend control metaphor as seen within our

interactive editing environment. Each sphere identiﬁes one of the control regions that are deﬁned by the bend metaphor.

compression). Additionally, every control metaphor

instance contains a unique transformation that deﬁnes

its relative position and orientation to the geometry

of the controlled object. This allows an artist to in-

troduce both global and targeted localized deforma-

tions to deﬁne new animation or adjust the behaviors

of simulated objects within existing animations.

4.1 Control Regions

Control metaphors drive localized deformation pat-

terns based on the set of control regions R that de-

ﬁne which nodes within a simulated object are inﬂu-

enced by the introduced external forces. Speciﬁcally,

we aim to derive high level control patterns from a

collection of primitive regions such that each region

r ∈ R, in part, contributes to the global behavior of

the control. From this, we can deﬁne the control re-

gions of a pattern-based metaphor as a set of bound-

ing volumes that evaluate a boolean function for the

selection of the nodes involved in the deformation.

Depending on the complexity of the desired defor-

mation, a control metaphor may contain several con-

trol regions; however to avoid unnecessary complex-

ity in the usability of each control we utilize a lim-

ited number of geometric primitives to identify these

control regions. If a node resides within any of the

control regions within R, it will be highlighted in size

and color to indicate its participation within the defor-

mation (see Figure 4). This presents a clean interface

that effectively communicates which nodes contained

within a simulated model will drive the imposed de-

formation.

4.2 Force Orientation

The selection of the nodes that will contribute to a

localized deformation is interactively deﬁned by the

set of artist conﬁgured control regions R. Therefore

for each control region r ∈ R, we must deﬁne an as-

sociated vector ﬁeld o ∈ O that deﬁnes the orienta-

tions of the external forces applied to each node en-

capsulated within r. The orientations of the applied

external forces provide the deﬁning characteristics of

the deformation pattern that will be imposed on the

controlled object, and can be deﬁned through a sim-

ple force diagram. A control metaphor force diagram

simply provides the deﬁnition of the spatial conﬁgu-

ration of the regions that contain the vector ﬁelds that

deﬁne the orientations of the controls external forces.

While the deﬁnition of each regions vector ﬁeld is

unbound, uniform vector ﬁelds are sufﬁcient for the

derivation of most primitive deformation behaviors.

4.3 Visual Representation

To effectively communicate the location and orienta-

tion of how a deformation will be applied to a sim-

ulated object, we introduce a three-dimensional in-

teractive widget that deﬁnes the control regions and

structure of the control metaphor. In our approach

we provide an interactive widget for each control

metaphor that provides an artist with the ability to

conﬁgure the selection of the effected nodes, the ori-

entation of the applied forces, and the control position

of the deformation (Figure 4).

Each interactive widget is represented by a col-

lection of geometric primitives that allow an artist to

easily conﬁgure the properties of the applied control

metaphor. The conﬁguration of these interactive con-

trol widgets is obtained by allowing an artist to per-

form adjustments by selecting the primitive compo-

nent within the widget and then modifying its parame-

ters (real-time interaction is facilitated though mouse-

based gestures). The parameter adjustments that we

provide for each control metaphor include the abil-

ity to scale and translate each component within the

widget. This provides a high-level of ﬂexibility in an

artistic control of the provided control metaphors.

4.4 Force Curves

Control metaphors and the associated widgets we

have developed provide an intuitive way of effec-

tively imposing a behavioral pattern on a simulated

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object within an interactive environment; however in

the context of physically-based animation several ad-

ditional parameters must be provided to completely

deﬁne the resulting deformation. These parameters

include the deﬁnition of the instance in time when the

external forces will be imposed, the duration of this

application, and the magnitudeof the forces applied to

the nodes within each control region of the metaphor.

Here we formally introduce the deﬁnition of a force

curve that provides the required functionality to de-

ﬁne all of these properties through a simple interac-

tive curve editor. A force curve f is deﬁned as a dis-

crete set of two-dimensional points that approximate

a function that deﬁnes the magnitude of the external

forces applied through a selected control metaphor. In

the instance where multiple control metaphors are ap-

plied to an individual object, each maintains its own

corresponding force curve. This provides an artist

with the ability to create several deformations exhibit-

ing unique characteristics on an individual object.

Time-line Discretization. Force curves approximate

a function that deﬁnes the magnitude of the exter-

nal forces required to generate a physical deformation

through control metaphors by supplyinga scalar value

that determines the strength of this deformation. To

provide these values in the context of a physical simu-

lation that employs a control metaphor,a force magni-

tude value must be provided for each simulation time-

step. This constraint is implicitly enforced through

the approximation of the curve that deﬁnes these mag-

nitude values. Let the set A represent the set of dis-

crete set of points that approximate the force curve

f and let (F

begin

end

) represent the simulation time-

steps that correspond to the application of a control

metaphor. The following constraint is then placed on

the approximated representation of this force curve:

|A| = (F

end

− F

begin

). This will guarantee that for

each simulation time-step the magnitude of the ex-

ternal forces introduced by a control metaphor is de-

ﬁned.

Curve Control. The implementation of the interac-

tive interface provided to an artist is based on an or-

thographic projection of a force curve approximated

by a Bezier curve. This representation also allows us

to provide control points that allow an artist to easily

control the shape of the approximated function. An

artist can interactively control the position of the end

and control points by simply dragging them to the de-

sired location. This provides an accurate method of

introduce precise deﬁnition of the speciﬁc instance an

artist would like interject a deformation. An illustra-

tion of the curve editor provided within our applica-

tion is illustrated in Figure 5.

Figure 5: Screenshot of the interactive force curve editor

that deﬁnes the magnitude of the applied forces over time.

With the proposed curve editing technique, com-

mon animation features such as motion blending

can be achieved. Motion blending can be achieved

through smooth gradients deﬁned within the force

curve. These gradients translate to gradual deforma-

tions that can be used to blend multiple deformations

together smoothly. This also provides an artist with

the ability to reﬁne imposed deformations by utilizing

multiple control metaphors to derive blended com-

pound deformations.

Force Magnitude-deformation Correlation. The

process of determining the magnitude of the applied

external forces required to derive the desired defor-

mation is a challenging process. In an effort to assist

an artist in the deﬁnition of the force curve that will

derive the desired behavior we employ dynamic pre-

views. As an artist modiﬁes the force curve to gener-

ate a deformation, a dynamic preview can be gener-

ated to illustrate the resulting behavior. This provides

an interactive feedback loop to an artist to iterate on

the motion generated with our approach. Once the

desired deformation behavior has been achieved, the

simulation can be recorded to make the change to the

resulting animation. While this does not resolve the

possibility of introducing externalforces that generate

undesirable or unstable behaviors, it presents an itera-

tive process that allows an artist to visualizeand reﬁne

the behaviors imposed by our control metaphors.

4.5 Deformation Controls

The deﬁnition of each component within this sec-

tion provides the basis upon which primitive defor-

mation behaviors can be created. The unique set of

components deﬁned by a control metaphor can eas-

ily be deﬁned to generate commonly required defor-

mation behaviors including bend operations, twisting,

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stretching, and compression. In this section we pro-

vide the formal deﬁnition for these primitive pattern-

based motions and illustrate how these formaliza-

tions demonstrate the desired deformation behaviors

on primitive geometric objects.

Stretch Deformation. To derive the behavior im-

posed by the stretch control metaphor we simply as-

sert that this operation will attempt to separate two

regions within an objects geometric deﬁnition. These

individual regions are separated by a division plane

that effectivelysegments the bounded regions into left

and right selection intervals deﬁned within two cylin-

drical control regions: {L

, R

}. The orientation of

the external forces is simply constrained to the X-axis

of the controls coordinate system. The node set L

external force orientation is deﬁned by a negative unit

vector along this axis:

−

, and the orientation of the

forces acting upon the node set R

is deﬁned by a

positive unit vector along this axis:

. Given these

components we formalize the deﬁnition of a generic

stretch control metaphor:

S = ({L

}, {

−

}, V, F)

The visual component V of the stretch metaphor is

simply deﬁned by the two cylindrical control regions

that correspond to the metaphors control regions. To

further reﬁne the control provided to an artist, we pro-

vide an interactive means of reﬁning the minimum

and maximum effect distance from the controls sepa-

ration plane and allow the radius of these cylindrical

regions to be dynamically adjusted. From this for-

mal deﬁnition we have also derived the components

required for a compression-based deformation. In the

application of this control, an artist can simply deﬁne

a negative force curve which will inverse the orienta-

tion of the applied forces, thus compressing the left

and right node sets to the origin of the control.

Twist Deformation. The implementation of the twist

control metaphor allows for separate regions of a

deformable-body, deﬁned by a division plane, to be

rotated in opposing directions. The formal deﬁnition

of this control metaphor closely resembles the stretch

control with the exception of of the vector ﬁeld de-

ﬁned with the cylindrical control regions. Here we de-

ﬁne these vector ﬁelds as a function of rotation about

the controls primary axis where R(L

) and R(R

) rep-

resent rotation functions operating on the nodes iden-

tiﬁed within each control region:

T = ({L

}, {R

−

),R

)},V, F)

The visual component of this control metaphor is

identical to that of the stretch control and can be in-

teractively customized in the same way by adjusting

the nodes contained within the provided control re-

gions. The application of a negative force curve to

this control will effectively inverse the rotation func-

tions providing the orientations of the external forces.

Bend Deformation. Considering the implementation

of a pivot-based bend deformation control, we deﬁne

three separate control regions, each containing an as-

sociated (uniform) force orientation vector ﬁeld. The

Joint-Bend-Force (pivot force), denoted O, deﬁnes the

direction of the force that opposes the Left- (

) and

Right- (

) Bend-Forces to impose a bend deforma-

tion based on the selected nodes contained within the

controlled object. The opposing deformations cre-

ated by the imposed external forces combined with

the provided offset creates the desired deformation

behavior at the center of this control metaphor. An

illustration of the spherical control regions and force

orientations for this control is presented in Figure 6.

Figure 6: Force diagram illustrating the orientations of the

external forces that are applied within each of the three con-

trol regions used to generate a pivot-based bend deforma-

tion.

From this force diagram and the provided set of

spherical control regions, the formal deﬁnition of this

pivot-based bend control metaphor can be derived:

B = ({O,L

}, {

}, V, F)

The visual component V is composed of three

sphere-based control regions identiﬁed in the controls

force diagram. To provide the ability to further reﬁne

the conﬁguration of this control metaphor,we provide

a customizable joint-angle θ that deﬁnes the angle be-

tween the L

and R

node sets and allow the radius

of each control region to be adjusted. Additionally,

we provide the ability to extend the distance between

each of the control regions to adjust the length of the

resulting bend deformation.

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Figure 7: Screenshot of our interactive animation editing environment with media controls, time-line, and loaded scene con-

taining a high-resolution deformable dragon. Three bend metaphors have been applied to achieve the displayed deformations.

5 EDITING ENVIRONMENT

To facilitate the generation of new animations within

an interactive editing environment, our approach re-

lies on the animation studio software we have created

to facilitate the required functionalities listed in Sec-

tion 3. This editing environment provides the core

functionality required to view, generate, and record

physically-based animations. The ability to interac-

tively introduce control metaphors and edit deforma-

tion behaviors is facilitated through the main studio

interface of our animation editing application.

This implementation provides the ability to ani-

mate multiple objects within a scene, facilitates inter-

active deformation views, and manages conﬁguration

of multiple control metaphors per simulated object.

The image in Figure 7 provides a screen-shot of our

application with a loaded animation. This interactive

interface is deﬁned by three main components: (1) the

main scene viewports that allowan artist to effectively

view the deformation behaviors imposed by the se-

lected control metaphors, (2) the animation time-line

which allows for the recorded animation to be dynam-

ically viewed, and (3) the list of control metaphors

applied to the currently selected object.

The resulting deformations that we have obtained

were generated using our approach facilitated through

this provided editing interface. In the next sec-

tion look at several demonstrations of the localized

pattern-based deformations introduced by our pro-

posed control metaphors conﬁgured and employed

within this interactive editing environment.

6 RESULTS

To clearly demonstrate the utility and ﬂexibility of our

approach we provide several illustrations of primitive

pattern-based motions, localized surface control, and

compound deformations obtained through the appli-

cation of multiple control metaphors. We show how

each of the introduced control metaphors can con-

tribute to a ﬂexible animation tool-set that can al-

low artists the create new animations of deformable

models and reﬁne the behaviors of simulated objects

within existing animations.

The implementations of our pattern-based control

metaphors introduce a basic set of deformation oper-

ations that provide the required foundation for creat-

ing complex animations of deformable models. These

results are based on the primitive deformation oper-

ations such as compression, bending, and twisting.

Here we demonstrate the resulting deformations that

can be obtained using these controls individually.

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Compression Deformation Result. A compression

deformation can be derived by applying a stretch con-

trol metaphor with a negative force curve. The image

in Figure 8 illustrates how this metaphor can effec-

tively compress a tessellated cylindrical model.

Figure 8: Resulting application of a control metaphor im-

posing a compression behavior. The orange lines indicate

both the orientation and magnitude of the applied forces.

While the desired compression is obtained, we note

the slight twist to the topology of the models surface.

This effect is due to the uneven selection of the nodes

involved in this deformation. We discuss the poten-

tial deformation side-effects that can be created from

misaligned control metaphors in Section 7.4.

Bend Deformation Result. The application of a bend

control metaphor to a cylindrical model provides the

expected results when applied to the length of the ob-

ject. The image in Figure 9 illustrates the effective-

ness of this control metaphor in this instance. How-

ever, when performing a global deformation with a

bend metaphor,we ensure that the selected control re-

gions are balanced with respect to the bend pivot.

Figure 9: Global pivot-based bend deformation.

The success rate of applying this control metaphor to

an object to derive a global deformation is based on

the material stiffness coefﬁcients that deﬁne the elas-

ticity of the model. When the bend control metaphor

is applied to a rigid model, an uneven distribution of

forces will incur an unintended torque on the object.

Localized Deformations. Control metaphors can ef-

fectively introduce localized deformations based on

the control coordinate system we have created to pro-

vide an artist with the ability to target a region within

a deformable model. The two examples illustrated in

Figure 10 illustrate these targeted deformations.

Figure 10: Twist (left) and stretch (right) control metaphors

applied to models to derive localized (to the position of the

enlarged node) deformation behaviors.

Compound Deformations. The process of apply-

ing multiple control metaphors to an individual de-

formable model provides the ability to derive com-

plex secondary behaviors within the topology of the

model. The illustration of the two control metaphors

applied to the Stanford bunny mesh in Figure 11 rep-

resents an application of two control metaphors used

to derive a compound deformation.

Figure 11: Control metaphor compound deformation. The

twist metaphor turns the rabbits head (left) and a bend

metaphor controls the rabbits ear (right).

The resulting deformation (see Figure 12) imposed by

the application of both control metaphors induces a

naturally blended motion between both operations. A

more complex compound deformation utilizing three

control metaphors is provided in Figure 13.

Figure 12: Compound deformation result created from the

control metaphors illustrated in Figure 11 (throughout 180

simulation time-steps).

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Figure 13: Compound deformations of a dragon raising its wings and rotating its head. The imposed deformations are created

from the localized application of four control metaphors. The animated result is displayed left to right.

7 EVALUATION AND

DISCUSSION

The evaluation of an artists ability to effectively for-

malize and translate the result of a desired localized

behavior to an object within a physical simulation is

a challenging task. The applicability of the provided

set of control metaphors depends on several critical

factors including: (1) the artist’s ability to effectively

identify a node that represents the desired location of

the deformation, (2) the selection of an appropriate

predeﬁned control metaphor, and (3) the process of

properly conﬁguring the provided control widget to

derive to desired behavior. To objectively evaluate the

effectiveness of our approach, we analyze the integra-

tion of our force-based metaphor technique into the

existing set of deformable object control methodolo-

gies introduced in Section 2. In this section we de-

ﬁne how our approach is framed to borrow key con-

cepts from these existing methods and identify how

our technique can contribute to an artists ability to

effectively generate localized deformation behaviors

within existing animations. Additionally, we also

consider drawbacks imposed by the set of reoccur-

ring problems (such as deformation oscillations and

induced torque) that are introduced when utilizing ex-

ternal forces to drive deformation behaviors.

7.1 Inverse-dynamics

Inverse dynamics is an animation technique that pro-

vides an artist with a high-level of control of an ob-

jects deformation states. The ability to deﬁne the ex-

act state that will be achieved by a deformable object

provides an artist with a powerful tool that can be used

to effectively produce targeted animations. This tech-

nique effectivelyreduces the time required to generate

a targeted animation of deformable object by simply

interpolating dynamic key-frames. This is achieved

by calculating the forces required to match the con-

straints imposed by the dynamic state of the object

for each key-frame during the animation. However,

utilizing a set of key-frames that deﬁne static states of

a deformable body as the input to a dynamic system

presents a large challenge to an artist: derive a set of

complex dynamic states for an object undergoing an

deformation such that the interpolated behavior will

represent a realistic and physically plausible motion.

While the task of deﬁning the dynamic states of an

object (node position, velocity, etc.) may be achiev-

able for models with a simple geometric composi-

tion, objects with complex deformation states such as

cloth will present an artist with the challenging task

of deriving the intermediate states of this deforma-

tion. Manually obtaining this state with a high level of

ﬁdelity for these complex objects is extremely chal-

lenging and generally requires an additional tool-set

(such as cage-based controls) to assist in this process.

Furthermore, even if the deﬁnitions of these dynamic

states are given, we are not guaranteed that the result-

ing motion provided by the interpolation process will

represent a ﬂuid or natural behavior. This will lead an

artist to the process of iteratively reﬁning the included

dynamic key-frames to obtain the desired behavior.

This is where we emphasize the ability of our

technique to generate physically plausible behaviors

based on high-level deformation patterns. The motion

naturally inspired by the application of external forces

can provide a resulting deformation behavior with a

high level of ﬁdelity that can be used to deﬁne a dy-

namic key-frame. Additionally, our technique can be

used to address unrealistic motions that may be gener-

ated through the inverse-dynamics interpolation pro-

cess. This can be achieved by introducing a control

metaphor that acts upon the object within the existing

animation reﬁne the resulting behavior. Therefore the

our method of creating localized deformations com-

plements this approach and can be used to improve

the quality of the generated animations.

7.2 Cage-based Control

Cage-based deformation control introduces the ability

to manipulate complex model topologies by utilizing

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a reduced set of representative nodes that form an in-

ﬂated cage around a deformable object. The nodes

of this superimposed cage can then be explicitly con-

trolled by an artist to implicitly direct the deforma-

tions of the complex underlying surface. The primary

concept introduced by cage-based deformation con-

trol techniques is that they greatly reduce the level of

control presented to an artist, thus the complexity of

the deformation editing process is greatly reduced.

This form of deformation control is generally uti-

lized as the solution to deriving physical plausible dy-

namic key-frames. However, this process does not ad-

dress the generation of physically-based motions over

time. This solution to deformation control must rely

on other techniques (such as an inverse-dynamics ap-

proach or rest-shape adaptation) to derive the inter-

mediate motion states required for an animation. This

is due to the fact that the key contribution from this

technique is a representative functional mapping be-

tween the nodes of the superimposed cage and the

nodes within the controlled deformable body.

This mapping however, provides an effective

means of imposing a high-level behavior on a com-

plex deformable model. We borrow the application

of this concept and extend it to represent dynamic be-

haviors imposed by our high-level control metaphors.

Therefore we can effectively provide a higher level

of control to an artist to accurately convey the be-

havior of the intended deformation. The control re-

gions deﬁned within each control metaphor deﬁne

the bounded region that acts as dynamic cages that

closely adhere to the global trajectory of the simulated

object. This forms the basis of our control technique

for translating high-level deformation patterns to the

underlying representative geometry.

7.3 Rest-shape Adaptations

The development the technique pioneered by (Coros

et al., 2012) that utilizes internal elastic potential

between static deformation states to derive motion

from internal forces, introduces an effective means

of animating deformable objects through example-

and goal-oriented objectives. This technique effec-

tively eliminates reoccurring problems with external

force-based techniques (such as oscillations and in-

duced torque) and also introduces the notion of the an-

imated object developing a persona due to the intrin-

sic derivation of internal forces, making them seem

lifelike.

The lifelike effect introduced by this technique

however may not be desirable in all instances. In the

development of our force-based technique, we pro-

pose a more generalized method of applying defor-

mations to simulated objects. Throughthe subsequent

application of localized deformations using control

metaphors, our approach can approximate lifelike

movements of deformable objects (as shown in Fig-

ure 13); however the incurred artistic labor is more

extensive than that required by this rest-shape adap-

tation technique. In our approach, multiple control

metaphors are required.

7.4 Metaphor Alignment

The correct application of a control metaphor depends

on the intended result desired by an artist imposing

the behavior. To adhere to the original intent of the

control metaphor, it must be properly aligned with the

geometry of the simulated object it will deform. Even

with the simpliﬁed form of interactivecontrol widgets

provided to the user, the applied external forces can

fail to produce the intended deformation.

Control metaphors are subject to several condi-

tions that must be met for the desired behavior to be

achieved. This indicates that there are several factors

that can contribute to an invalid conﬁguration of the

applied control metaphor that may lead to an undesir-

able or unstable deformation behavior. These factors

include: misaligned control widgets, an inadequate

external force magnitude, and the incorrect param-

eter conﬁguration for the applied control metaphor.

The image in Figure 14 illustrates an instance where

a bend metaphor has not been properly aligned to the

underlying geometry of the simulated object. Specif-

ically, we note the lack of the selected nodes with

two of the provided control regions. Therefore, the

only external forces that will be applied to this ob-

ject reside within the joint set of this metaphor. The

resulting deformation will not match the intended re-

sult provided by this metaphor due to the misaligned

widget conﬁguration.

Figure 14: Invalid alignment of an applied bend metaphor

where only one set of nodes is properly identiﬁed. This

will result in an incorrect deformation behavior due to the

incorrect widget orientation.

The implications of these requirements however

are not without their own merits. The ﬂexibility pro-

vided to an artist through the selection of the local-

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304

ized region, the orientation of the control, and conﬁg-

uration of the parameters speciﬁc to the applied con-

trol, can produce unwanted deformations; however

this also provides freedom to an artist to use the pro-

vided tool-set in alternativeways. As shown in the ex-

ample deformation in Figure (dragon result), the head

of the dragon can be turned using a bend deformation

rather than a twist control metaphor.

8 CONCLUSION

In this paper we have presented an effective way

to impose pattern-based deformations on simulated

MSS- or FEM-based deformable models. We have il-

lustrated that the targeted application of the proposed

high-level control metaphors can effectively generate

physically plausible deformations in new animations

and can be used to modify the behavior of objects

within existing animations.

In this results of this paper we have demonstrated

that in using the method of controlling targeted de-

formations we have introduced, localized deforma-

tions can effectively be imposed on simulated objects

and we preserve an artists ability to iteratively reﬁne

the resulting behavior. We have also deﬁned the out-

line of the interactive editing environment that was

used to create these desired deformations. Addition-

ally, through the subsequent application of the prim-

itive control metaphors introduced in our approach,

we have demonstrated that compound behaviors can

be effectively generated to create complex anima-

tions. Our deformation control technique has also

been compared to other leading approaches and we

have discussed the potential contributions and prob-

lems associated with this approach.

While this technique contains the commonly reoc-

curring challenges associated with the application of

external forces, the resulting deformation behaviors

provide physically plausible results that can be used

to effective generate realistic animations.

9 FUTURE WORK

The accurate control of deformable objects in simu-

lated environments for the generation of physically

plausible animations continues to present a challeng-

ing task. In this work we have identiﬁed a generalized

method for imposing pattern-based deformation be-

haviors on simulated objects; yet several of the promi-

nent reoccurring problems with the application of ex-

ternal forces remain, including oscillations, imposed

torque, and unbound force magnitudes.

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