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Research Papers: Design Automation

Automatic Generation of Anisotropic Patterns of Geometric Features for Industrial Design

[+] Author and Article Information
Diego Andrade

Department of Mechanical Engineering,
Carnegie Mellon University,
5000 Forbes Avenue,
Pittsburgh, PA 15213
e-mail: diegoandrade@gmail.com

Ved Vyas

Department of Mechanical Engineering,
Carnegie Mellon University,
5000 Forbes Avenue,
Pittsburgh, PA 15213
e-mail: vsv@andrew.cmu.edu

Kenji Shimada

Department of Mechanical Engineering,
Carnegie Mellon University,
5000 Forbes Avenue,
Pittsburgh, PA 15213
e-mail: shimada@cmu.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 19, 2015; final manuscript received November 4, 2015; published online December 14, 2015. Assoc. Editor: Rikard Söderberg.

J. Mech. Des 138(2), 021403 (Dec 14, 2015) (9 pages) Paper No: MD-15-1433; doi: 10.1115/1.4032092 History: Received June 19, 2015; Revised November 04, 2015

While modern computer aided design (CAD) systems currently offer tools for generating simple patterns, such as uniformly spaced rectangular or radial patterns, these tools are limited in several ways: (1) They cannot be applied to free-form geometries used in industrial design, (2) patterning of these features happens within a single working plane and is not applicable to highly curved surfaces, and (3) created features lack anisotropy and spatial variations, such as changes in the size and orientation of geometric features within a given region. In this paper, we introduce a novel approach for creating anisotropic patterns of geometric features on free-form surfaces. Complex patterns are generated automatically, such that they conform to the boundary of any specified target region. Furthermore, user input of a small number of geometric features (called “seed features”) of desired size and orientation in preferred locations could be specified within the target domain. These geometric seed features are then transformed into tensors and used as boundary conditions to generate a Riemannian metric tensor field. A form of Laplace's heat equation is used to produce the field over the target domain, subject to specified boundary conditions. The field represents the anisotropic pattern of geometric features. This procedure is implemented as an add-on for a commercial CAD package to add geometric features to a target region of a three-dimensional model using two set operations: union and subtraction. This method facilitates the creation of a complex pattern of hundreds of geometric features in less than 5 min. All the features are accessible from the CAD system, and if required, they are manipulable individually by the user.

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Figures

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Fig. 1

Examples of options to create pattern in current CAD systems systems: (a) rectangular pattern, (b) partial rectangular pattern, (c) circular pattern, and (d) partial circular pattern

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Fig. 2

Comparison between isotropic and anisotropic patterns on flat surfaces: (a) isotropic, (b) anisotropic, (c) isotropic and graded, and (d) anisotropic and graded

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Fig. 3

Boundary conformity is a desirable choice used for esthetic patterning by industrial designers: (a) boundary-conforming features and (b) nonboundary-conforming features

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Fig. 4

Proposed three-step pipeline for automatic anisotropic pattern generation on curved surfaces (pasta spoon)

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Fig. 5

Boundary-conforming anisotropic pattern showing user's input with changes in directionality and size across a flat surface

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Fig. 6

Transformation of a circle to a tensor ellipse with anisotropy in the Riemannian metric M, where θ  is the angle of rotation and d1 and d2 represent its semidiameters in 2D

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Fig. 8

General bubble packing criteria for a target stable distance: (a) attracting, (b) repelling, and (c) stable

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Fig. 9

Process to create a UDCS in inventor. (a) Build a tangent plane with three points and use them to create two vectors, (b) generate a normal vector from the cross-product between the previous two vectors, then the binormal as a cross-product of the first vector and the normal, forming the basis for the UDCS, and (c) seed feature, where d1 and d2 correspond to the semidiameters of an ellipsoid on a working plane.

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Fig. 12

Stanford bunny: (a) base geometry, Ωb and target region, Ωt, (b) seed features Ωt showing directions, (c) bubble packing, (d) feature orientation field, and (e) anisotropic features ϕ shaped and mapped on Ωb. The number of geometric features used in this pattern is 134.

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Fig. 13

Metal and wood ornament: (a) base geometry, Ωb and target region, Ωt, (b) seed features ϕt showing directions, (c) bubble packing, (d) feature orientation field, and (e) anisotropic features ϕ shaped and mapped on Ωb. The number of geometric features used in this pattern is 212.

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Fig. 10

Audi R3 Bang and Olufsen speaker (isotropic features): (a) base geometry, Ωb, (b) target region, Ωt, (c) bubble packing, and (d) isotropic features ϕ shaped and mapped on Ωb

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Fig. 11

Audi R3 Bang and Olufsen speaker (anisotropic features): (a) base geometry, Ωb and target region, Ωt, (b) seed features ϕt showing directions, (c) bubble packing, (d) feature orientation field, and (e) anisotropic features ϕ shaped and mapped on Ωb. The number of geometric features used in this pattern is 254.

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Fig. 14

Jewelry example, ring: (a) base geometry, Ωb and target region, Ωt, (b) seed features ϕt showing directions, (c) bubble packing, (d) feature orientation field, and (e) anisotropic features ϕ shaped and mapped on Ωb. The number of geometric features used in this pattern is 151.

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Fig. 15

Free-form decorative vase: (a) base geometry, Ωb and target region, Ωt, (b) seed features ϕt showing directions, (c) bubble packing, (d) feature orientation field, and (e) anisotropic features ϕ shaped and mapped on Ωb. The number of geometric features used in this pattern is 714.

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Fig. 16

Water bottle: (a) base geometry, Ωb and target region, Ωt, (b) seed features ϕt showing directions, (c) bubble packing, (d) feature orientation field, and (e) anisotropic features ϕ shaped and mapped on Ωb. The number of geometric features used in this pattern is 189.

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Fig. 17

Free-form water bottle: (a) base geometry, Ωb and target region, Ωt, (b) seed features ϕt showing directions, (c) bubble packing, (d) feature orientation field, and (e) anisotropic features ϕ shaped and mapped on Ωb. The number of geometric features used in this pattern is130.

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Fig. 7

Geometric seed features are expanded by a scale factor; this change in size is used to create a packing metric, meanwhile the angles and directions locally are used to create a shaping metric

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