Detail-Preserving Variational Surface Design With Multiresolution Constraints

[+] Author and Article Information
Ioana Boier-Martin

 IBM T. J. Watson Research Center, Hawthorne, New Yorkioana@us.ibm.com

Remi Ronfard

 INRIA Rhône-Alpes, Montbonnot, Franceremi.ronfard@inrialpes.fr

Fausto Bernardini

 IBM T.J. Watson Research Center, Hawthorne, New Yorkfausto@us.ibm.com

J. Comput. Inf. Sci. Eng 5(2), 104-110 (Feb 23, 2005) (7 pages) doi:10.1115/1.1891824 History: Received September 02, 2004; Revised February 23, 2005

We present a variational framework for rapid shape prototyping. The modeled shape is represented as a Catmull-Clark multiresolution subdivision surface which is interactively deformed by direct user input. Free-form design goals are formulated as constraints on the shape and the modeling problem is cast into a constrained optimization one. The focus of this paper is on handling multiresolution constraints of different kinds and on preserving surface details throughout the deformation process. Our approach eliminates the need for an explicit decomposition of the input model into frequency bands and the overhead associated with saving and restoring high-frequency detail after global shape fairing. Instead, we define a deformation vector field over the model and we optimize its energy. Surface details are considered as part of the rest shape and are preserved during free-form model editing. We explore approximating the solution of the optimization problem to various degrees to balance trade-offs between interactivity and accuracy of the results.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

(a) Input model. (b) Coarse-scale edits affect the global shape. (c) Fine scale edit with local effect (patch structure of underlying surface representation is shown). Dots indicate constraints.

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Figure 2

The natural parametrization of a subdivision surface

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Figure 3

Local quadratic interpolant used to approximate first- and second-order derivatives

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Figure 4

Constraint propagation from a fine level (left) to coarser ones. Constrained vertices are shown as squares. The target value of the constraint is marked with a circle.

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Figure 5

Linear constraints are generated on coarse levels using the Catmull-Clark masks according to the expression listed in Table 1

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Figure 6

Modeling with detail preservation. (a) Original model. (b) Deformation under point constraints. (c) Normal constraints. (d) Constraints along an arbitrary curve on the surface (left) are used to rigidly deform the surface in the vicinity of the curve (right).

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Figure 7

Top: approximating energy minimization. (a) Input model. (b) Fast solution obtained using Catmull-Clark smoothing. (c) Improved solution obtained via multigrid energy minimization. Bottom: (d)–(f) the optimized control mesh and the constraints at levels 2–4 during multigrid.

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Figure 8

(a) Input model. (b) Surface after rotating the inner boundary curve and energy optimization. (c) Input model with details at multiple resolutions. (d) The model in (c) after variational editing.



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