Automatic Generation of a Pattern of Geometric Features for Industrial Design

7/27/2019 Automatic Generation of a Pattern of Geometric Features for Industrial Design

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Automatic Generation of a Pattern of Geometric

Features for Industrial Design

Diego F. Andrade Mechanical Engineering Department

Carnegie Mellon University5000 Forbes Avenue

Pittsburgh, Pennsylvania 15213, USA Email: [email protected]

Prof. Kenji Shimada Mechanical Engineering Department

Carnegie Mellon University5000 Forbes Avenue

Pittsburgh, Pennsylvania 15213, USA Email: [email protected]

ABSTRACT

This paper presents a new computational method for the automatic generation of geometric feature

patterns for industrial design. Such patterns include speaker holes, shower head holes, and bumpy

textures on a grip, and they play a key role in making a designed object aesthetically pleasing and

also functional. While modern CAD packages support the automated creation of basic patterns,

rectangular grids and radial grids, they are not applicable to more general cases required in

industrial design, including arbitrarily shaped target geometry and graded feature sizes. The

proposed computational method takes as input a target region along with sizing metrics and

generates feature patterns automatically in three steps: (1) packing circles tightly in the target

region, (2) scaling features according to the specified sizing metrics, and (3) adding features on the

base geometry. The proposed method is installed as a plugin module to a commercial CAD

package, and a pattern of hundreds of features can be added to a 3D CAD model in less than five

minutes. This allows the industrial designer to explore more design alternatives by avoiding the

tedious and time-consuming manual generation of patterns.


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1. INTRODUCTION

Many product shapes are designed and modeled by first defining a base geometry and then adding

local geometric features. For example the base geometry of a home phones handset can be modeled

as a prism, and local geometric features, such as speaker holes, LCD display, and push keys, can beadded to the base geometry to yield the final product shape. Some of the local geometric features

are repeated on the base geometry, forming a particular pattern, as illustrated in Fig. 1. These

patterns can be classified into three types: (1) uniform and isotropic (Fig.1 (a)), (2) graded or

anisotropic (Fig 1(b)), and (3) graded and anisotropic (Fig. 1(c)).

(a) Uniform, isotopic pattern (b) Graded or anisotropic

pattern

(c) Graded and

anisotropic pattern

Figure 1. Examples of geometric feature patterns used in product design

While modern CAD systems offer automatic feature-pattern generation, their functionality is

quite limited, supporting only two simple types of patterns: (1) rectangular grid patterns, and (2)

radial grid patterns, as illustrated in Fig.2. They are useful in designing typical mechanical parts

such as brackets and flanges, as their geometry often contains repeating rectangular or radial grid

patterns. The current CAD packages, however, do not support the generation of more general


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patterns required in industrial design such as patterns with arbitrarily shaped target regions, graded

feature sizes, oriented features, anisotropic feature shapes, and so on.

The ultimate goal of our research project is to develop a versatile computational method for

the automatic generation of geometric-feature patterns for industrial design. In this paper, as thefirst step toward that goal, we will focus on isotropic patterns of local geometric features and

demonstrate that such patterns can be generated automatically. The process and algorithms

proposed in this paper are designed so that they can be later extended to graded and/or anisotropic

feature patterns.

(a) Rectangular grid pattern (b) Radial grid pattern

Figure 2 Two automated pattern generation methods available incommercial CAD packages

The proposed pattern-generation method takes as input a target region along with sizing

metrics and generates feature patterns automatically in three steps: (1) packing circles tightly in the

target region, (2) scaling features according to the specified sizing metrics, and (3) adding features

on the base geometry. The first step is achieved by a physically based tight packing of cells, or

bubbles, in the target region. While this cell packing method, called bubble packing, was originally

developed for mesh generation for Finite Element Method (FEM), it has never been applied to

pattern generation for industrial design [2,7-8].

The proposed method is realized as a plugin module in a commercial CAD package. With

this new tool, an industrial designer can create hundreds of features laid out in an aesthetically

pleasing way within five minutes without tedious and time-consuming manual pattern generation.

This allows the designer to explore numerous design alternatives easily and focus on creative work.


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The rest of the paper is organized as follows: Section 2 presents the detailed problem

statement, Section 3 describes the overview and details of the proposed computational method

including the integration of the proposed pattern-generation method with a commercial CAD

package. Section 4 then presents the results and discussion. Section 5 examines related work to the proposed pattern generation method, and Section 6 presents conclusions.

2. PROBLEM STATEMENT

Let us first define key terminology used in the rest of the paper. The overall product shape with no

geometric features is called Base Geometry and denoted as b. Geometric Features, or simply

Features, are small local geometries such as holes and protrusions and denoted as . Features are

often arranged in a distinct pattern within Target Region, t. Feature patterns can be further

characterized by two factors: (1) packing how Features are positioned, or packed, inside the

Target Region; and (2) shaping how each of the Features is shaped. These characteristics of a

feature pattern are specified respectively by: Packing Metrics, M p, and Shaping Metrics, M s, both of

which are defined as a 3 3 metric tensor field over the Target Region. The definition and the usage

of the 3 3 metric tensor field can be found in previous mesh generation literatures [1-5].

While the ultimate goal of the project is generate general anisotropic patterns such as the

ones illustrated in Fig. 1(c), this paper focuses on uniform and graded feature patterns. These

limited target feature patterns do not require full 3 3 metric tensors for Packing Metrics and

Shaping Metrics representations; they require only a scalar field defined over the Target Region.

The uniform and graded feature pattern generation method takes as input Base Geometry, b,

Target Region, t, and two scalar fields, M p and M s, and automatically generates a set of Geometric

Features, , added to Base Geometry in a hexagonal arrangement. The three key requirements of

this automated process are: Requirement 1: Features are arranged on Base Geometry according to

the specified packing metrics, Requirement 2: Features are shaped/sized according to the specified

shaping metrics, and Requirement 3: Features are arranged in a way that they respect the boundary

of the Target Region. The last requirement is particularly difficult to satisfy for an arbitrarily


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shaped Target Region. Fig. 3 shows two types of patterns: non-boundary conforming patterns (Fig.

3 (a)) and boundary conforming patterns (Fig.3 (b)). It is critical that the proposed method generate

boundary-conforming patterns.

(a) Non boundary conforming features (b) Boundary conforming features

Figure 3 Boundary conforming features are more preferable in industrial design.

Figure 4 Proposed three-step computational method for automatic pattern generation

3. PROPOSED COMPUTATIONAL METHOD

Once the user, or the industrial designer, specifies the Target Region for feature pattern generation

along with the Packing Metrics and Shaping Metrics, the proposed computational method generates

the feature patterns and adds them to the Base Geometry automatically. The process consists of

three steps as illustrated in Fig. 4.: In Step 1, the Target Region will be filled with tightly packed

bubbles whose sizes are specified by Packing Metrics. Each bubble represents the territory or

neighborhood for a geometric feature. In Step 2, each and every bubble is converted to a feature by

scaling the bubble according to Shaping Metrics. Finally in Step 3, a set of generated features is

added to the Base Geometry to complete the process. Sections 3.1, 3.2 and 3.3 describe the details


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of Steps 1, 2, and 3 respectively.

3.1. Step 1: Packing Bubbles

We consider, r ! , to be a stable distance between two adjacent bubbles. The inter-bubble force f is

similar to the intermolecular van der Waals force, and usually the Lennard-Jones form is used to

describe the interaction force between molecules [6-9]. These forces are attractive when two

bubbles are farther apart than the stable distance r ! or repulsive when they are less than the stable

distance r ! . The force, f, is defined as a bounded cubic function of the distance r satisfying the

following boundary conditions:

f r =a r

! + b r ! + cr + d

0

0 r 1 .5 r !r < 0 1 .5 r !

Automatic Generation of a Pattern of Geometric Features for Industrial Design

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