Sensitive Couture for Interactive Garment Modeling and Editing
Nobuyuki Umetani

Danny M. Kaufman

Takeo Igarashi

Eitan Grinspun

The University of Tokyo

Columbia University

The University of Tokyo / JST ERATO

Columbia University

Figure 1: “2D or not 2D?” This timeless question is rendered moot by Sensitive Couture, our tool for simultaneous, synchronized modelingand editing of both a 2D garment pattern (top) and its corresponding 3D drape (bottom).

Abstract
We present a novel interactive tool for garment design that enables,
for the first time, interactive bidirectional editing between 2D patterns and 3D high-fidelity simulated draped forms. This provides
a continuous, interactive, and natural design modality in which 2D
and 3D representations are simultaneously visible and seamlessly
maintain correspondence. Artists can now interactively edit 2D pattern designs and immediately obtain stable accurate feedback online, thus enabling rapid prototyping and an intuitive understandingof complex drape form.
CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling;
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V IDEOC ODEIntroduction

The multi-billion dollar fashion industry caters to every strata of
consumption, from penny socks to haute-couture pieces costing
thousands (even millions) of dollars [Sherman 2006]. Fashion’s

pervasion is rooted in clothing’s role as a medium for personal expression. Garments that “suit us” invoke a sense of confidence andsatisfaction.
Tailoring requires the insight to combine flat 2D panels of woven
textiles that, stitched together into a garment, exhibit an expressive
3D shape when worn. In the language of differential geometry, agarment is simultaneously both a 2D and a 3D object: on the one
hand, it may be viewed as the initial assembly of flat panels, eachhaving holes and curved/kinked boundaries; on the other hand, it
can be understood by its ultimate 3D form.
Classical iterative design
The garment design process involves
many iterations of drafting, synthesis, and revision that alternate
between 2D and 3D perspectives: a tentative 2D panel design iscreated from which a corresponding garment is manufactured; theresulting garment reveals desired alterations to the 3D form that, inturn, induce revisions of the 2D design; and so forth. These many
iterations consume raw materials, time, and energy.
Even veteran dressmaking teams go through many iterations where
the designer conceptualizes 3D forms in sketches and the patternmaker drafts precise 2D outlines. The drape of a garment over a
curved body is affected by frictional contact and the map from the
2D to 3D representation is complex and nonlinear. The challengein sketching 3D forms is to stay true to the wrinkles and bulges
that will be formed when a nearly-inextensible surface is draped
over a body. Vice versa, revising 2D patterns often induces not
only the expected alteration of the 3D forms but also unintended“side-effects” (pinching, buckling, tight spots) which are often only
discovered after time- and resource-consuming assembly. It takes
great effort and many attempts to bring the 2D and 3D views into
correspondence, making design an inherently iterative, painstaking
process.

While both the 2D (“intrinsic”) and 3D (“extrinsic”) perspectives
are innate aspects of garment design, existing software tools force
one view in lieu of the other. The situation is amplified in the computer animation industry. In general, artists either sculpt in 3D ordraft in 2D but not both, and the choice is typically determined by
the software used at the studio. Sculpting tools provide artists witha familiar interaction paradigm, but do not account for the special(low Gaussian curvature) structure of draped fabric, thus results appear less natural. Sometimes the 3D mesh is computationally flattened [Decaudin et al. 2006], a process that alters the 3D form andconsumes time. On the other hand, drafting tools ensure that the final form is natural, but the artist must learn to draft 2D patterns, andwait for draping computations that produce the 3D form [Volino
et al. 2005]. To sum, existing flattening (3D→2D) and draping(2D→3D) computations are akin in their effect to the time and material impediments of manual dressmaking: they divide design into
discrete tasks and inhibit a free-flowing creative process.
Figure 3: A Sensitive Couture screen snapshot.
Sensitive Couture (SC) for interactive bidirectional design

We present a novel approach to garment design, similar in spirit
to the system proposed by Volino et al. [2005]. Our software tool
provides a continuous, interactive, natural design modality. The 2D
design and 3D draped form receive equal status, are simultaneously
visible, and seamlessly maintain correspondence. The artist may
interactively edit the 2D design immediately observing how thesechanges affect 3D form.
The impact on the user is more thanmerely a quantitative acceleration of theold design loop. Consider a small metallic “brain-teaser” puzzle, in which two
linkages must be separated. Staring at
the puzzle and thinking for a long time
does not get one very far. But a little bitof manual tinkering quickly builds intuition about the “design space” and voilà!
Figure 2: Can you
In this vein, an interactive, synchronizedsolve a brain teaser
garment design process offers a qualitawithout interaction?
tive jump in the way that design is carried out, where the discrete transitions
between phases vanish: drafting, manufacturing, and critique of 3D
form are fused into one seamless, natural process.
There are several technical hurdles to incorporating online cloth
simulation in the design process: existing high-resolution simulation codes are not yet fast enough for maintaining interactiverate correspondence between the 2D and 3D views. The simulation must account for geometric nonlinearity and frictional contact
while remaining stable even under rapid user input.
To address these challenges, our design tool employs a combination of techniques, including (i) fast prediction of 3D forms
from cached shapes using sensitivity analysis and generalized moving least squares, (ii) fast invisible remeshing using positive meanvalue coordinates to accommodate arbitrary revisions of the patternboundary, and (iii) stable and accurate cloth modeling using an isometric bending model, a modified St. Venant-Kirchhoff membraneelement, and progressive refinement. The novel use of sensitivity
analysis in enabling interactive-rate synchronization of the 2D and3D perspectives is reflected in the tool’s name, Sensitive Couture.

2

Related Work

Fashion being a huge field, computer-aided garment design has
grown into an industry of its own, as evidenced by the myriad companies producing garment CAD products; spanning the five inhabited continents, companies such as AGE Technologies, AMSSys-tems, Browzwear, CADTERNSCustom Clothing Inc., Fashion
CAD, Fashion Matters, Gemini CAD, GRAFIS, Investronica Systems, Marvelous Designer, Mechanix, OptiTex, Pad Systems, Pattern Works Int’l, and others provide a variety of tools focusing on
2D pattern creation and/or 3D draping for garment design.
Sketch-Based Design
Sketch-based approaches to garment design have produced promising 2D→3D design processes that enable the mapping of fashion sketches to procedurally generated
three-dimensional garments [Decaudin et al. 2006; Igarashi andHughes 2003; Turquin et al. 2007]. These methods leverage a designer’s honed intuition about garment shape and flow. Advancesin flattening sketch space to developable patterns [Decaudin et al.
2006], placement and sliding of generated garments [Igarashi andHughes 2003], and position-based garment generation [Turquin
et al. 2007] have all enabled improved one-way work flow. However, such approaches are still hampered by the limitations of procedural, rather than physically based, garment generation and have
yet to be extended to enable bidirectional editing.
Cloth Simulation
The simulation of cloth, and more generally
shells, is a widely treated area [Bridson et al. 2003; Baraff andWitkin 1998; Goldenthal et al. 2007]. Mass-spring models generally enable fast and simple computational models for rapid cloth
simulation [Meyer et al. 2001; Choi and Ko 2002] providing responsiveness at the cost of accuracy and stability. Recent methods have also generated real-time wrinkle synthesis [Rohmer et al.
2010], as well as more generally, real-time, data-driven reduced
cloth modeling [Feng et al. 2010; Wang et al. 2010].
Interactive Cloth Design and Simulation
Physically based interactive design of clothing has long been a grand challenge forsimulation and graphics [Volino et al. 2005]. Recently, promisingframeworks have been proposed that suggest that interactive design
processes combining 2D and 3D perspectives may be in reach fortextile design [Volino et al. 2005]. Complementary developments indirect interactive editing on garment meshes [Keckeisen et al. 2004]
and the real-time coupling between edits and simulation for simple
mass-spring systems [Mori and Igarashi 2007], have likewise offered tantalizing forward progress towards seamless bidirectional
garment authoring.
Design Sensitivity Analysis
In the context of fashion, the preferences of a designer are hard to quantify and their choices difficult
to predict. Design sequences can be expected to evolve throughout the creative process, potentially requiring reliable computation

over broad ranges of design space. Thus we put offline optimization aside in favor of a sensitivity based strategy that enables a truly
interactive exploration of design.
Similar in spirit to differential manipulation [Gleicher and Witkin1991], which uses sensitivity maps to enforce geometric constraints
at interactive rates, we propose to use design sensitivity to maintainthe static equilibrium of drape pose.
In the engineering literature, this formulation is central to design
sensitivity analysis, which attempts to provide (first-order) insight
into the relationships between design and performance in either
one-off calculations or offline optimizations; Van Keulen [2005]
provides a recent survey, and Derouet-Jourdan et al. [2010] provide
a recent application to rod design.

3

Sewing/pleating
The designer can specify that two boundary
segments should be sewn. When the two segments differ in length,a pleat is formed, i.e., a sequence of attractive doubled-back folds
that gather a longer piece of fabric into a shorter length. In all cases,
SC automatically selects the boundary orientations that avoid cloth
inversion.
Symmetry
The designer may mark boundary pieces as symmetric about an axis, and subsequently SC enforces these symmetries.
Sloper parameters
We emphasize that the designer can adjust
sloper parameters (e.g., sleeve length, waist width) at any time.
These adjustments can be made by manipulating a slider, or by direct manipulation in the 3D view. For example, the user can “tug”
on a hemline to make a skirt longer (see Fig. 1, left and accompanying movie).

Interaction Tools
4

As depicted in Fig. 3 and the accompanying movie, Sensitive Couture (SC) presents the 2D and 3D design perspectives simultaneously. All selection operations are naturally at home in either the
2D or 3D window.
A typical session begins with layout of a “blank canvas.” While SC
affords from-scratch creation of patterns, designers typically begin
with a sloper (or block), a basic pattern drafted to standard measurements intended as a generic starting point [Digest 2002] (seeFig. 4). Slopers are typically parameterized by height, girth, sleeve
length, and so forth.
Whereas typical CAD tools might navigate the parametric space
using sliders, SC further allows the designer a “tangible” navigationof parameter space via direct manipulation of the 2D pattern andthe 3D draped shape, reinforcing the idea that all components aresynchronized and can be accessed in any order.
Indeed, every aspect of the SC user experience emphasizes a freeflowing (as opposed to sequential or “linear”) design process. For
instance, as the designer makes detailed alterations (“strokes”) topatterns by inserting darts, modifying boundary curves, etc., thesestrokes “ride” over the sloper, in the sense that the designer may
revisit the parameters of the sloper at any time without undoing thecreative, style-defining strokes.
If a sloper serves as blank canvas, then the rich diversity of final designs comes from the various creative strokes applied by designers.
Our research goal was to understand the under-the-hood infrastructure needed for interactive design in a real-application (practical)
context, thus we focused on a small but useful set of front-end tools
intended to stress-test the underlying simulation infrastructure:
Curve edits
The designer may alter the shape and position of
the pattern boundary, which is defined by the control degrees of
freedom (DOFs) of a spline. Positions are stored relative to thesloper, and are therefore naturally maintained over adjustment tothe underlying sloper’s dimensions.
Darts
The designer may add
or modify darts, triangular folds
or excisions that induce intrinsic
curvature (so-called cone singularities) thus “filling out” the 3D form. SC understands darts as“first-order primitives,” so they have dart-specific DOFs to control
their position, shape, and size. The designer adds a dart by drawing a line using the dart pen. If the line intersects a boundary, SC
creates a triangular dart that “rides” the boundary, i.e., the designer
may later freely slide the dart along the boundary.

Sensitive Interaction

As the user revises the design, SC must keep the 2D and 3D perspectives synchronized. The 2D and 3D configurations, each realized by a mesh of n vertices, are related by the static equilibrium
equationR(X, x) = F(X, x) − Q(X, x) = 0 ,

(1)

2n

where X ∈ R is the undeformed configuration given by the 2D
perspective, x ∈ R3n is the deformed configuration given by the 3D
perspective, and F, Q ∈ R3n are the external (e.g., gravitational)
and internal (e.g., elastic) forces, respectively. The 2D and 3D pictures are in correspondence when the residual R(X, x) ∈ R3n vanishes.
We solve (1) from scratch once for the initial drape (§7), an operation too costly to repeat at interactive rates due to the nonlinearityof (1). Fortunately, in design processes, most user input effects incremental revisions to the existing design.
Suppose that the designer alters the
2D configuration X to a nearby configuration X + ∆X. Expanding (1) to first order yields the incremental update equation
Design sensitivity analysis(∇X R(X, x)) ∆X + (∇x R(X, x)) ∆x = 0
relating the change ∆X in the 2D to the change ∆x in the 3D
picture, by a linear map S : ∆X 7→ ∆x∆x = (∇x R)−1 (∇X R)∆X = S∆X.
where S is encoded by a 3n × 2n design sensitivity matrix. In practice one applies the map by solving the incremental update equation
using a linear solver.
Note that ∇x R is the usual stiffness matrix associated with a nonlinear statics problem: if the static problem has a nonsingular stiffness matrix, then ∇x R is full rank.
Buckling, wrinkling, and static
friction all make for a nonlinear relation between the 2D design andthe 3D draped form. While linear sensitivity is a good first step, we
found that for the larger edits typical at the start of the design process, or for radical redesigns, the local model produced by sensitivity analysis (i.e., linearization about the pre-revised configuration)
does not remain valid for the full extent of the editing operation.
In short, a linear sensitivity response centered about the original
design is insufficient when the change in design is large. Therefore, we extend the basic sensitivity-based approach by accounting
for nonlinearity via coupled simulation and progressive nonlinear
modeling.
Linear sensitivity is insufficientFigure 4: Starting with just a few standard sloper templates artists can easily generate a wide variety of garments.

During idle times, such as pauses in mouse
movement, we integrate the system in time, starting from the configuration produced via sensitivity-based increments. If this werea dynamic simulation, the interruption of time integration withsensitivity-based positional updates would likely cause great instabilities or other artifacts. Fortunately, our interest in static draping
rather than inertial response allows us to use kinetic damping (§7)
and hence to be well insulated from any “spikes” that might result
from interleaving time integration with direct positional updates.
Coupled simulation

In the most crucial interactive
editing operations—those where the designer hesitates in selecting
between multiple design alternatives—the editing operation may
endure over a longer duration (a few dozen seconds), and pause
at various points in design space as options are being considered.
In these cases, SC takes advantage of the available time to evaluate and cache additional linearizations (sensitivity matrices), thusbuilding up a nonlinear model of drapes in the local design space.
Compared to an up-front precomputation, this progressive enrichment of the local model allocates computation proportionally to theinterest in a given region of design space, i.e., it is most accurate
near designs that interest the user.
Progressive nonlinear modeling

How do we aggregate the linearizations into a local model of simulation response in design space? In the context of offline optimization, some works have considered moving least squares (MLS)
interpolation [Breitkopf et al. 2005]. MLS requires dense, wellspaced samples, does not make use of derivative information, andbreaks down when the sampling pattern degenerates (i.e., there are
too few samples along one dimension). To alleviate these difficulties, Martin et al. [2010] use generalized moving least squares(GMLS), which extend MLS interpolation to incorporate derivative
information. Indeed, GMLS can make direct use of the sensitivity
matrices that we compute [Atluri et al. 1999; Fries and Matthies
2003].

When the pointer moves to position d = (d1 , d2 )T , SC can draw
upon two kinds of readily reusable data: the draped configuration
x0 ∈ R3n (i.e., zeroth-order data) at the previous pointer positionmd0 ∈ R2 , and the sensitivities sm
1 = ∂x/∂d1 , s2 = ∂x/∂d2 ofthe draped configurations xm ∈ R3n (i.e., first-order data) at thecached previous configurations dm ∈ R2 (m = 1, . . . , M ). Since
GMLS is a direct extension of MLS, it is possible to extend theusual derivations of MLS and GMLS interpolation to now accountfor a combination of zeroth- and first-order samples. In particular, following the notation of Martin et al. [2010], the interpolated
configuration field is given by x(d) = a(d)p(d) ∈ R3n , wherea ∈ R3n×3 is a coefficient matrix applied to the monomial vectorp = (1, d1 , d2 )T . At a given pointer position d, the coefficients a
are the minimizers of the least-squares error metric
MX

J(a) =w(d − dm ) kap(dm ) − xm k2

m=0
M
X

+

m=1

‚2
2 ‚
X
‚
‚ ∂p
m‚
‚
w(d − d )‚a ∂dj − sj ‚ ,m

j=1

where w is a suitably chosen weighting function. We use w(d −dm ) = 1/(kdm − dk2 + 2 ), with  a small constant guaranteeing finite weight (we use 2 = 10−3 ). As in the usual (G)MLS
derivation, we analytically minimize J with respect to a, obtaining

x(d) =MX

xm N m (d) +

m=0
m

M X
2
X
m
sm
j Nj (d),m=1 j=1T−1p(dm )w(d − dm ) ,∂p
Njm (d) = p(d)T G(d)−1w(d − dm ) ,∂dj

N (d) = p(d) G(d)drag. A simple and useful extension would be to visualize, before
the mouse is depressed, the degree of sensitivity of a screen point,
as a guide for the user.

5

Figure 5: Comparison of sensitivity strategies. Cloth is draped on asphere with respectively, from left to right, no sensitivity, linear sensitivity,
progressive sensitivity analysis with GMLS, and nonlinear (“ground truth”)
static equilibrium.

andG(d) =MX

w(d − dm )p(dm )p(dm )T

m=0

+

M
X

w(d − dm )

m=1

2
X
∂p ∂p T
j=1

∂dj ∂dj.

Consider as a canonical example a hanging cloth partly draped on a sphere, and an editing operation in which the (undeformed, 2D material-space) length of the
strip of cloth is increased. Fig. 5 and the accompanying movie
compare the result of an editing operation conducted using only
a dynamic, kinetically-damped simulation, augmented with linear
sensitivity analysis, or augmented with progressive GMLS modeling. Here Fig. 5 (a) and (b) give the cached solutions employed
by sensitivity. Observe (left to right in Fig. 5) that the dynamic
simulation lags behind the user’s edit; the formation of distracting
wrinkling artifacts can be understood by interpreting the dynamic
simulation as a process that approaches the final equilibrium state
in a fine-to-coarse manner. Linear sensitivity, which can be viewed
as a “global” or “implicit” approach, eliminates these artifacts, but,in using a linear model, does not approximate the overall draped
shape well. The GMLS interpolation exhibits stable results that
better agree with ground truth (Fig. 5, far right).
Comparing different strategies

4.1

Bidirectional Sensitivity Enables Direct 3D Editing

Sensitivity information also enables SC to interpret editing operations applied directly to the 3D form.
Consider editing a sloper parameterg ∈ R (e.g., sleeve length), as depicted in Fig. 1, left. When the
pointer is depressed over the 3D view,
SC identifies the corresponding material point (u, v) ∈ R2 on the cloth,and computes the sensitivity vector s = ∇g x(u, v) ∈ R3 , i.e., thefirst-order 3D motion of the cloth at the picked point with respect
to sloper parameter g.
The 3-vector s is projected to the screen space vector ŝ ∈ R2 , which
gives the first-order motion of the picked screen point with respect
to g. As the user drags the pointer from d ∈ R2 to d + ∆d ∈ R2 ,SC updates the sloper parameter via the incremental relation∆g = ŝ · ∆d/kŝk2 .
Observe that when kŝk is small, the selected screen point is insensitive to g; for example, the position of a shirt collar may be
independent of sleeve length. Thus, for small kŝk we neglect the

Cloth Model

In selecting a cloth model for an interactive tool, our primarydesiderata were stability and fast computation. Typical to mostcloth models, we treat bending and stretching models separately [Baraff and Witkin 1998; Bridson et al. 2003]. We chose
to work with triangle meshes, but the overall framework does notdepend on this choice.
Bending
Our final implementation uses the isometric bending
model (IBM) of Bergou et al. [2006], which has a constant energy
Hessian (force Jacobian), therefore (a) eliminating the cost of theforce Jacobian computation for implicit time integration, (b) providing a simple matrix-vector multiplication for bending force computation (which would be easy to port to the GPU), and (c) ensuring that the Hessian remains positive semi-definite for all configurations and thereby stabilizing numerics. Before adopting IBM,
we implemented a co-rotational treatment of the Discrete Kirchhoff Triangle [Batoz et al. 1980; Khosravi et al. 2007], but foundthat we needed a stronger guarantee of stability in the context of
our interactive tool. We then adopted nonlinear hinges [Bridson
et al. 2003; Grinspun et al. 2003], which lose some of the meshingindependence of DKT [Batoz et al. 1980] but increase stability. Ultimately, the cost of force Jacobian computation in the nonlinear
models drove us to use IBM, which drops the generality of an arbitrary stress-strain map in favor of increased stability and speediercomputation.
Membrane
Our final implementation uses a stabilized St.
Venant-Kirchhoff (StVK) constant strain triangle (CST). The usual
StVK CST element, when it is compressed, can induce instability [Volino et al. 2009], because its force Jacobian becomes indefinite. Similar to Teran et al. [2005], when the element is in a compressed configuration, we adjust the Jacobian entries to eliminate
negative eigenvalues. This stabilization affects only the trajectory
toward the draped configuration, but it does not alter the set of solutions of the static equilibrium equations. To sum, this stabilization
assures stability without affecting the draped shape.
We first tried a geometric model governed by changes in edge
length and triangle area [Grinspun et al. 2003]. We found that thearea term induced instabilities – the length term alone was stable,
but lacked similitude to fabric [Delingette 2008]. We therefore transitioned to the CST model, first using a corotational treatment [Bittnar and Sejnoha 1996], which was stable, but was relatively slow inconverging to the equilibrium draped shape StVK membrane, compared to our final (quartic) CST element. In hindsight, we might
have also applied the stabilization to the area term of the geometricmodel, but since the stabilized StVK CST worked well, and is aconvergent model, we were satisfied.
We have found the combination of theguaranteed positive semi-definite IBM bending and stabilized StVKCST membrane models to be more stable than other combinations
in ongoing usage of SC. Since, to our knowledge, this is the firstreport of combining these approaches, we include for reference
the results of two stability benchmarks (see Fig. 6) in which thestatic equilibrium (1) is solved with kinetic damping (see §7) starting from a random initial guess. Alternatives, discussed above, that
we tried earlier were either unstable or were slower to converge.
Robustness evaluation

polate along the boundary, and use positive mean value coordinates(PMVC) [Lipman et al. 2007] to efficiently determine the tensor
field Ψ throughout the domain. PMVC builds on mean value coordinates (MVC) [Floater 2003] by incorporating a notion of visibility, which we found enhances the coordinate’s interpolation capability in the non-convex higher genus shapes typical of 2D design
patterns. Fig. 8 compares the two linear mesh deformation models
we implemented based on MVC and PMVC, where we observedthat PMVC produces a homogenous deformation that avoids the
distortions and inversions.
Figure 6: Stability Benchmark: (top) Snapshots at initial,
third, 50th, and 200th iterations for the draping of a rectangular(membrane-dominated) textile (3K triangles, 12s total computation). (bottom) Snapshots at initial, third, 50th, and 100th iterations for static equilibrium of a rectangular (bending-dominated)thin plate with bending stiffness 100× that of textile (2K triangles,
4s total computation).

6

Mesh Updates

When the designer uses the pointer to drag 2D pattern elements(e.g., boundary vertices, darts, boundary spline tangents), SC updates the (unseen) positions of the internal vertices (see Fig. 8) thus
maintaining uniform, well-shaped elements throughout the material
domain. The concatenated change of all internal and boundary vertex positions makes up the change ∆X in the 2D configuration fed
to the sensitivity-based 3D update.
While such a mesh update might be achieved by solving equilibrium of the mass spring system, the resulting nonlinear motion withrespect to pattern element alteration makes first-order sensitivity
analysis incorrect. Instead, we adopt a coordinate-based mesh manipulation that is linear in pattern element alteration.

Figure 7: Action of Ψ for (left) translation of an interior (diamond) dart, (center) translation of a boundary dart, and (right) adjustment of boundary dart opening.

Figure 8: Our 2D pattern manipulation employs positive meanvalue coordinates (PMVC) with Delaunay smoothing. This allows for linear interpolation over a domain, while enabling a moresatisfying interpolation in nonconvex higher-genus domains. Here
we illustrate the advantages: consider (a) an undeformed mesh, (b)mesh manipulation with MVC, (c) mesh manipulation with PMVC,
and finally (d) PMVC with Delaunay smoothing.
Applying the sensitivity map
With the tensor field Ψ =[Ψ1 Ψ2 . . .]T in hand, sensitivity is calculated by mapping pointermovement to 2D mesh movement ∆X = Ψ∆d. We note thatthe typical sensitivity analysis considered in engineering design
does not involve this extra degree of mapping, since sensitivity is
typically conducted with respect to a specific boundary mesh element [Van Keulen et al. 2005].
Fast and slow remeshingOver the course of multiple large manipulations, the mesh may distort necessitating remeshing. We firstattempt Delaunay smoothing, updating mesh connectivity retaining
nodal positions. With our finite element discretization, displacement and sensitivity are stored at vertices and need not be recomputed, making this an inexpensive way to improve the mesh. Ifmesh quality (ratio of diameter of incircle against the maximum
edge length) remains poor, SC rebuilds the mesh from scratch andinterpolates the simulation state to the new mesh using barycentric
coordinates.

7
Mapping pointer movement to alterations
For each kind ofpattern element, we first define how pointer motion affects the control vertices (CVs) of a 2D pattern element; e.g., for a boundarydart, a drag centered inside the dart moves the three CVs identically, whereas a drag of the dart’s interior CV leaves the boundary
vertices stationary. Let Ψi be the 2 × 2 tensor relating pointermovement ∆d to the movement Ψi ∆d of the ith CV. Typically,
our tools use: (Fig. 7-left) Ψ = I or Ψ = 0, in which the CV follows the pointer or remains stationary, respectively; (Fig. 7-center)Ψ = eeT , in which the CV shadows the pointer movement only inthe direction e; or (Fig. 7-right) Ψ = ei eTj in which the CV moves
along ei when the pointer moves along ej .
Interpolating the alteration
Having defined Ψ at the CVs,
it remains to interpolate the motion in the remainder of the domain. Since Ψ is known at all boundary CVs, we linearly inter-

Numerics of Time Integration

SC intends to display the static drape of the cloth, consequently
any computation invested into capturing dynamics is wasted effort.
When a previous static solution is not available for an incremental
sensitive update, SC must find the static equilibrium from scratch,and do so quickly. A from-scratch solve is needed not only forthe initial drape, but also when new 2D pattern elements are added
midway through design.
One of the fastest ways we found to solve the static equilibirum (1)from scratch is to employ kinetic damping [Barnes 1988; Volino
and Magnenat-Thalmann 2007], which integrates the (undamped)
equations of motion while monitoring total kinetic energy at eachtime step. When the kinetic energy reaches a local maximum (acondition evaluated by considering three consecutive time steps),
the kinetic damping approach zeros the velocity (the kinetic energy). The intuition behind this is that in a conservative oscilla-tory system, when kinetic energy is at a maximum, potential energy is at a minimum. When the system is far from the minimal
potential, damping would slow down the approach to the minimum; when the system is close to the minimal potential, reducing the momentum helps to avoid overshooting the minimum. We
found that, in practice, kinetic damping is simple to implement, andreaches the draped configuration faster than a dynamic simulation
with Rayleigh damping, an application of gradient descent, or thestabilized Newton’s method.
We apply kinetic damping to the semi-implicit time integration
scheme proposed by Baraff and Witkin [1998]. Since the coefficient matrix of the dynamic simulation and sensitivity analysis areboth positive-definite, we solve the system using conjugate gradients preconditioned with ILU(0) [Saad 2003]. While the IBM bending model has a constant Hessian, the StVK CST membrane model
does not, and we must numerically factorize the matrix at every
time step.
The performance of ILU(0) preconditioning is (surprisingly) significantly influenced by choices in the treatment
of seams. SC sews boundaries ofcorresponding panels using Hookean
springs. In general, the boundaries do
not correspond in length—an importantfeature in dressmaking used to effectpleats and ruffles—nor in connectivity, therefore, SC connects the(“emitting”) vertices of the one panel with springs anchored at (“receiving”) boundary edges of the other panel (see Fig. 7). To avoid
gaps at the seams, the seam springs are much stiffer than textile tensile stiffness. The consequent linear system has stiff and weak components, thus the success of ILU(0) preconditioning depends on the
permutation of matrix entries [Saad 2003]. In a nutshell, ILU(0)favors permutations where large entries appear earlier (toward topleft of matrix) and small entries appear later (bottom-right). Entries
associated to emitting vertices dominate entries of receiving vertices, which in turn dominate all other vertices.
Before considering penalty-based seams, we used Lagrange multipliers, which allow for exact constraint enforcement without preselection of a spring stiffness. We were not satisfied with the increase in the linear system size and the indefiniteness of the resulting system matrix, which combined slowed convergence. We
then observed that the usual problems plaguing penalty methods
are less relevant to our context: since our problem setting is fixed(the spatial scale of the cloth designs do not vary by orders of magnitude), estimating the penalty stiffness once up-front is sufficient
to obtain a good seal at the seams. The penalty method maintains
the positive-definiteness of the system, and since the set of dominating matrix entries is given by a simple tallying of seam vertices(a set which remains constant except during exceptional stitching
events), the permutation for ILU(0) is of negligible implementationand computational cost.
Contact model SC models contact between the garment and thebody, but does not consider garment self-contact. Contact and friction between body and cloth are essential for cloth drape simulation.
We opted for speed and robustness at some expense to accuracy. As
with seaming we enforce contact constraints at mesh nodes using
penalty springs. For contact we place normal springs at collisionsites detected by a one-time, precomputed adaptive signed distancefield [Frisken et al. 2000]. We model friction using a moving anchor spring method [Hasegawa et al. 2003] that enables both staticand dynamic friction modes. Contacting nodes are connected bysprings to seeded anchors vertices placed on the contacting surface.
We then update (or release) anchor positions, with respect to nodal

movement, to ensure Coulomb’s Law is satisfied by these anchor
spring forces. This allowed us to obtain stable draping and frictional wrinkling.
In general, for a nonlinear cloth
statics problem, there exist configurations for which the stiffness
matrix is close to singular. Consider a horizontal cantilevered rectangle of sufficiently thin fabric: intuitively, it can’t hold itself up.
Quantitatively, gravity acts against the bending mode. The ratio of bending membrane stiffness of a thin plate is O(h2 ) where
h is the thickness measured relative to the object’s characteristic
length [Malvern 1969]. In principle one could select h so smallthat the configuration is near singular, with kernel corresponding tonormal displacements. In practice, we did not encounter this problem while using SC. However, for completeness, we did experimentwith the cantelevered rectangle to induce this problem. Since thekernel (must) correspond to normal displacements, the remedy is
direct: if the solver fails to converge, we recompute S with bending
stiffness corresponding to h = 1/100, which is sufficiently thickto avoid a singular matrix. The modification of the bending stiffness is local to the sensitivity computation, and does not affect thebending stiffness used in determining the ultimate static drape. We
found that this stabilization was not invoked during cloth design,
including all the examples shown in the video.
Full-rank of sensitivity matrix

7.1

Progressive Refinement

We find that as users explore design space with SC, detailed cloth
behavior is unnecessary during the sketch-like exploratory phases
where rapid-fire design choices are made. On the other hand, during
the slower, refinement-oriented phases of garment design, fine-level
details are critical. We therefore focus on progressive refinement atechnique long-used in graphical applications to provide a senseof immediacy [Hoppe 1996]. We employ the so-called Cascading
Multigrid approach [Bornemann and Deuflhard 1996]. As users
provide input, we initially solve the drape using a coarsened mesh.
If we reach convergence at the coarse-level prior to the initiationof new design edits, we then warm start our fine mesh solve withthe coarse solution. For preview we always display the fine meshrepresentation. Fine-level nodes are updated progressively: first via
barycentric coordinates from the coarsened solution and later, when
not interrupted, via direct update from the fine-level solve.

7.2

Sensitive Couture Workflow

Our approach is then best illustrated by considering a typical editing
step (see also Fig. 11):(1) Mouse click
Design sensitivity computation. The mapping
between mesh updates and XY mouse movement is computed. Sensitivity analysis then calculates the corresponding bi-modal linear
response, at the clicked point, with respect to these maps (§6).
(2) Drag
Sensitive response. While edits are performed withthe mouse button down, SC provides instantaneous linear response.
As the editing process continues progressive nonlinear modelingenriches the local model and the corresponding response (§4).
(3) Release
Time Integration. When the mouse button is released the current sensitivity configuration warm starts the nexttime-integration cycle (§7).

examplesBlue Armadillo (Fig. 4)coarsefine
stretchingarea density
bending
nodes
nodes stiffness (Nm) stiffness (N/m)(kg/m^2)-8
1682 10168
10
0.20
10

drag operations (fps)
max
min
avg
17.0 19.9
10.1

coarse solve (fps)min
avg max
17.4 20.4 15.3

fine solve (fps)
avg max min
2.4
2.7 1.9

remesh (ms)avg
233

sensitivity (ms)
GMLS interp. (ms)avg max minavg
145 17882
0.38

Man (Fig. 9)

1634

10149

10-8

10

0.20

15.0

17.2

11.1

20.4

22.7

18.8

2.4

3.2

2.0

227

316

492

170

0.36

Woman (Fig. 9)

1580

10040

10-8

10

0.20

19.5

23.0

16.0

25.1

28.5

22.9

2.9

3.8

2.6

144

310

440

155

0.38

10073

5x10-6

200

0.15

19.3

22.0

17.0

25.1

26.3

23.8

3.1

3.2

3.1

146

228

513

116

0.40

5032

3x10-4

2000

0.08

20.7

22.2

19.3

24.2

25.5

22.7

7.2 10.0

5.1

123

639

419

767

0.39

Armadillo (Fig. 9)
Heart (Fig. 10)

1600
1543

Table 1: SC session parameters, statistics, and timings: all timings were measured on an Intel Core 2 Duo 2.66 GHz laptop, 4Gb memory.

8

Results and Discussion

Figure 1 illustrates the bidirectional SC workflow for designing garments on 3D models. SC enables designer edits of both the 2D pattern (Fig. 1, right) and the 3D draped model (Fig. 1, left). Material
parameters for fabrics used are estimated both by measurement andexperiment. We measure the areal density of fabrics and then adjust stiffnesses to match simulations with on-sphere draping tests. A
video accompanying this paper demonstrates the interactive, stable
workflow provided by SC during the various phases of the garment
design process.
Building high-fidelity interactive rate simulation and editing tools
stressed a range of tried and true methods. In many cases we discovered that techniques that performed well in standard settings did
not satisfy our needs for seamless, interactive rate updates. Often obtaining working solutions required unexpected and complex
combinations of methods. Throughout our discussion we have documented both what did not work, as well as what did (and thus madeSC successful). Correspondingly we have provided comparisonsthroughout our discussion to explain these issues. These comparisons and validations can be found in Figures 5, 6, and 8, while in
Table 1 we present timing and performance statistics for a range of
SC sessions.

8.1

Garments designed in our SC sessions were then manufactured
from the generated patterns. See Figure 9 for snapshots of the editing process, the completed 2D designs, simulated final drapes, andcorresponding manufactured garments.

Conclusion

We have presented a novel interactive garment design tool, Sensitive Couture (SC), that, for the first time, offers seamless bidirectional design and editing capabilities for the generation of 2D patterns and the online simulation of drape. SC provides a continuous,interactive, natural design modality in which the 2D design and 3D
draped form receive equal status, are simultaneously visible, andseamlessly maintain correspondence. As such, artists are enabled
to interactively edit and explore 2D designs and immediately observe how these changes affect 3D form.

9.1

consider the drape of SC garments on static 3D models. Clearlya desirable extension is for a dynamic preview capability allowing
the simulation of 3D garment behavior subject to 3D model motion.

Evaluation and Garment Manufacture

Here we wish to focus on how these parts sum to a whole in SC.
As such, we have documented and captured (see our accompanying
movies) the editing process and work flow of a variety of skilled
and amateur clothing designers as they use SC to design a range of
garments (see Fig. 9).

9Figure 10: In principle, SC could be extended to many other flexible materials, enabling the design of upholstery, aluminum sculptures, or these paper sculptures. (Left to right): an artist produced
2D pattern of darts, the corresponding 3D paper simulation, andthe manufactured papercraft objects. We have yet to extend SC toincorporate the constitutive model of materials such as paper.

Future extensions to Sensitive Couture

While contact remains well-resolved for body-garment interaction,complex folding patterns will additionally require self-contact resolution. We are interested in exploring local methods of identifying
and robustly treating self-contact and intersection in the SC framework. Similarly, as in the traditional couture setting, we currently

We look forward to extending SC to a user-evaluated, fully-featured
tool targeting design professionals in both animation and fashion.
However, the design of shell-based objects also has exciting applications beyond garment design (see Fig. 10). We expect that SCtype tools can be extended to address interactive design needs inarchitecture, industrial design, and engineering, e.g., tensile structures, metal folding processes, upholstery, balloons.
In principle, the 3D editing of more than two design degrees of
freedom (DOFs) could follow the same line of thought: so long as
no more than two of the DOFs have non-negligible screen space
vectors at the drag point, the editing operation is unambiguous andstraightforward to implement. However, the likelihood that the edit
operation remains unambiguous decreases as the number of available DOFs increases, raising interesting directions for future work:(a) SC should intuitively convey to the user which DOFs are affected by the edit (information that varies over screen space), (b) isthere an intuitive (unambiguous and deterministic) way of mapping
the 2D drag to the simultaneous revision of more than two DOFs?

9.2

Future work in integrated design, simulation, andinteraction

Integrated design, simulation, and interaction (IDSI) is an outstanding challenging open problem in graphics and engineering.
SC grew out of our interest in tackling this longstanding problem.
Many application domains do not admit interactive, physics-in-theloop design solutions for problems of practically relevant complexity. In this work we identified garment design as a domain for which
IDSI was (barely) within reach for problems of real-world complexity on current hardware.

Figure 9: The SC workflow: an interactive design session leads to a final 2D pattern and corresponding 3D drape pose which is thenrealized from the pattern.

To reach interactive rates in SC required leveraging observations
shared by many potential IDSI problems. Among these are (a)faster, more stable computation of equilibrium, at the expense of
dynamics, for design of static structures; (b) synchronized editing
and bidirectionality for a seamless design process; (c) sensitivity
analysis for interactive exploration of nearby designs; and (d) adaptive enrichment of sensitivity information using GMLS to leverage users’ natural pauses and inclination to explore multiple design
variants. We hope that insights such as these, originally garneredfor SC, will prove portable to a broad range of domains, and that
SC itself will serve as a motivating example spurring research into
fusing design, simulation, and interaction for a broad range of exciting domains.

Acknowledgements
We would like to thank Charles Han for dress design, garment manufacture, and modeling; Susana Kim for dress modeling; and Brandon Arrington for SC testing, and papercraft design and manufacture. Nobuyuki Umetani was supported in part by the Funai Overseas Scholarship and the JSPS. Danny Kaufman and Eitan Grinspun
were supported in part by the Sloan Foundation, the NSF (CAREER
Award CCF-0643268, IIS-0916129), Adobe, ATI, Autodesk, Intel,
mental images, Microsoft Research, NVIDIA, Side Effects Software, the Walt Disney Company, and Weta Digital.

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