Spline Motion Transitions in Linear Subspaces

彬彬

Abstract

We develop a novel system to concatenate motions with a smooth

transition involving natural, redundant movements which cannot be

obtained using traditional motion blending technique. Our basic

idea is to apply a spline interpolation in a linear subspace in which

each input motion is represented as a low-dimensional curve. By

connecting the curves via a spline interpolation, a transition motion

is synthesized according to a shape of the spline curve while

preserving correlations among joints of input motions. Our system

allows users to create a variety of transition motions with simple

control of the spline parameters.

1 Introduction

Motion concatenation technique is widely used for generating a

long stream of character animation from a collection of short motion

clips. Most existing methods employ a problem formulation of

energy minimization to create a smooth transition from one clip to

another. A common approach creates a transition motion by blending

input motions with an ease-in and ease-out interpolation. The

blending-based method generates a transition motion so as to minimize

dissimilarity between the transition motion and the input motions.

The dissimilarity is further reduced by optimizing a transition

length [Wang and Bodenheimer 2008] or by using dynamic timewarping

[Kovar and Gleicher 2003], both of which reduce temporal

misalignment of the input motions. Another approach uses a spacetime

optimization to generate a transition motion based on physical

low [Rose et al. 1996]. The spacetime method minimizes joint

torque required for the transition, which results in a physically realistic

motion. These energy-minimization techniques successfully

generate a smooth and rapid motion transition.

However, a natural transition is sometimes obtained with redundant

movement. Jumping motion for example, a blending-based

technique generates a rapid transition from landing to jumping.

Moreover, we can make it more visually appealing by adding two

movements; squatting down after landing and taking arms back

∗e-mail: tmki@acm.org

before jumping, which correspond to a basic principle of ’followthorough’

and that of ’anticipation’, respectively. These movements

are effective to exaggerate the jumping motion although they are redundant

in terms of efficient transition. Existing methods, however,

are not applicable to generate such redundant movement because

they minimize a certain type of energy function.

The goal of our work is to develop a motion concatenation technique

to generate a natural transition which involves redundant

movement. In our preliminary experiment, we used a spline interpolation

for concatenating motion curves of each joint. By controlling

a shape of the interpolation curve with spline parameters, we

could obtain redundant movements of joint rotation such as overshoot

and oscillation. Such a per-joint operation, however, often

broke correlations among joints and damaged original style of input

motions.

Inspired by [Ye and Liu 2010], we developed a system to concatenate

motions via a spline interpolation in a low-dimensional,

linear subspace in which each input motion is represented as a lowdimensional

curve as shown in Figure 1(b). The spline interpolation

is used to connect the low-dimensional curves, and a transition

motion is recons***cted from the connecting spline curve. We can

create a variety of transition motions by changing a shape of the

spline curve as shown in Figure 1(c) and (d). Arbitrary shape of

the spline generates a possible transition because the subspace is

cons***cted to reflect correlations among joints of input motions.

Consequently, our system provides a flexible generation of natural

motion transition which involves redundant movements. Users can

easily control the degree of the redundancy with spline parameters

while visually checking the shape of the spline in the subspace.

彬彬

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