Patterning and Customization: Evaluating Tensor Field Generation For Mechanical Design On Free-Form Surfaces

This dissertation delivers a new computational framework for the automatic generation of geometric feature patterns for industrial design and architectural facades on free-form surfaces. Such patterns include holes in a speaker grill, showerhead holes, protrusions on ceramics or bumpy textures on a panel. These patterns play a key role in making a designed object aesthetically pleasing as well as functional. Computer Aided Design (CAD) systems currently offer tools for generating simple patterns, such as uniformly spaced rectangular or radial patterns. However, they are not applicable to more general cases required in industrial design, including arbitrarily shaped target geometry and graded feature sizes. 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. This thesis proposes a new method of taking input for a target region along with sizing metrics. It will generate feature patterns automatically in three steps: (1) packing isotropic or anisotropic cells tightly in a target region, (2) scaling features according to the specified sizing metrics, and (3) adding features on the base geometry. This approach automatically generates complex patterns that conform to the boundary of any specified region. User input of a small number of geometric features (called “seed features”) of desired size and orientation in preferred locations also can 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 the Laplace heat equation is used to generate the field over the target domain, subject to specified boundary conditions. The field represents the anisotropic pattern of the geometric features. The system is implemented as a plugin module in a commercial CAD package to add geometric features to the target region of the model using two set operations, union and subtraction. This method facilitates the creation of a complex pattern of hundreds of geometric features in minutes. All the features are accessible from the CAD system and can be manipulated individually if required by the user. This allows the industrial designer or architect to explore more alternatives by avoiding the tedious and time-consuming manual generation of these geometric patterns.