NDLI: Skinning cubic Bézier splines and Catmull-Clark subdivision surfaces

Content Provider	ACM Digital Library
Author	Jacobson, Alec Gingold, Yotam Liu, Songrun
Copyright Year	2014
Abstract	Smooth space deformation has become a vital tool for the animation and design of 2D and 3D shapes. Linear methods, under the umbrella term of "linear blend skinning", are the de facto standard for 3D animations. Unfortunately such approaches do not trivially extend to deforming vector graphics, such as the cubic Bézier splines prevalent in 2D or subdivision surfaces in 3D. We propose a variational approach to reposition the control points of cubic Bézier splines and Catmull-Clark subdivision surfaces---or any linear subdivision curves or surfaces---to produce curves or surfaces which match a linear blend skinning deformation as closely as possible. Exploiting the linearity of linear blend skinning, we show how this optimization collapses neatly into the repeated multiplication of a matrix per handle. We support $C^{0},$ $C^{1},$ $G^{1},$ and fixed-angle continuity constraints between adjacent Bézier curves in a spline. Complexity scales linearly with respect to the number of input curves and run-time performance is fast enough for real-time editing and animation of high-resolution shapes.
Starting Page	1
Ending Page	9
Page Count	9
File Format	PDF
ISSN	07300301
e-ISSN	15577368
DOI	10.1145/2661229.2661270
Volume Number	33
Issue Number	6
Journal	ACM Transactions on Graphics (TOG)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-11-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Image warping Linear blend skinning Skeletal shape deformation Spline Subdivision Vector graphics
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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