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Research Papers

Free Form Surface Skinning of 3D Curve Clouds for Conceptual Shape Design

[+] Author and Article Information
Erhan Batuhan Arisoy, Gunay Orbay

Levent Burak Kara1

Department of Mechanical Engineering,  Carnegie Mellon University, Pittsburgh, PA 15213lkara@andrew.cmu.edu

1

Corresponding author.

J. Comput. Inf. Sci. Eng 12(3), 031005 (Aug 09, 2012) (13 pages) doi:10.1115/1.4007152 History: Received September 13, 2011; Revised June 26, 2012; Published August 09, 2012; Online August 09, 2012

In product design, designers often create a multitude of concept sketches as part of the ideation and exploration process. Transforming such sketches to 3D digital models requires special expertise due to a lack of intuitive computer aided design (CAD) tools suitable for rapid modeling. Recent advances in sketch-based user interfaces and immersive environments have introduced novel curve design methods that facilitate the transformation of such sketches into 3D digital models. However, rapid surfacing of such data remains an open challenge. Based on the observation that a sparse network of curves is reasonably sufficient to convey the intended geometric shape, we propose a new method for creating approximate surfaces on curve clouds automatically. A notable property of our method is that it relieves many topological and geometric restrictions of 3D conventional networks such as the curves do not need to be connected to one another or gently drawn. Our method calculates a 3D guidance vector field in the space that the curve cloud appears. This guidance vector field helps drive a deformable closed surface onto the curves. During this deformation, surface smoothness is controlled through a set of surface smoothing and subdivision operations. The resulting surface can be further beautified by the user manually using selective surface modification and fairing operations. We demonstrate the effectiveness of our approach on several case examples. Our studies have shown that the proposed technique can be particularly useful for rapid visualization.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

A breakdown of our approach: (a) a curve cloud is input to the system, (b) the discretized 3D voxel image of the sketch and the guidance vector field is calculated within the domain, (c) the initial surface is deformed toward the input curves, and (d) the final surface is achieved after surface smoothing and subdivision operations

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Figure 2

(a) Input image, (b) the comparison of a gradient vector field to (d) the diffused gradient vector field. (c) The active contours cannot penetrate into the concave regions with the simple gradient field (e) whereas it can with the diffused gradient vector field.

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Figure 3

The space containing the input curves in (a) are discretized into the binary voxel images in (b).

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Figure 4

Gradient vector flow field of a car model on the specified cross sections.

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Figure 5

The surface deformation cycle of the proposed approach. The surface is deformed according to the vector field while the surface smoothness is maintained through surface fairing and subdivision operations.

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Figure 6

(a) The Laplacian and (b) the biharmonic operators

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Figure 7

A distance map is used to adjust the (a) Laplacian smoothing displacement and (b) relative weights of vector field displacement

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Figure 8

(a) User drawn 3D curve (b) selection of triangular meshes lying under the 3D curve and (c) weight calculation for edge path selection

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Figure 9

Mesh alignment example: (a) User drawn 3D curve and (b) final aligned mesh edge path

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Figure 10

(a) Triangle quality calculation and (b) and (c) edge swapping

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Figure 11

Inflation operation: (a) Region selection and (b) resulting surface after inflation

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Figure 12

V-spring smoothing gradually minimizes the variation of curvature in the surface: (a) Vspring for one vertex and (b) total Vspring effect

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Figure 13

Calculating the 3D positions of point pairs symmetric about a symmetry plane from their projections on the viewing plane

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Figure 14

Rubbing tool with Vspring operation: (a) Region selection and (b) resulting surface after Vspring opeartion

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Figure 15

Application of the proposed algorithm on simple geometries: (a) 3D input curve cloud, (b) discretized domain, and (c) resulting surfaces

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Figure 16

Different 3D curve clouds (a)–(e), resulting surfaces and curvature plots

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Figure 17

Different example cases for product form design, (a) spaceship (b) sedan car, and (c) coffee table

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Figure 18

Entire pipeline of our proposed algorithm

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