# Shape Design and Optimization for 3D Printing

28 Sep
Monday, 09/28/2015 12:30pm to 2:30pm
Computer Science Building, Room 142
Ph.D. Thesis Defense
Speaker: Yahan Zhou

In recent years, the 3D printing technology has become increasingly popular, with wide-spread uses in rapid prototyping, design, art, education, medical applications, food and fashion industries. It enables distributed manufacturing, allowing users to easily produce customized 3D objects in office or at home. The investment in 3D printing technology continues to drive down the cost of 3D printers, making them more affordable to consumers.

As 3D printing becomes more available, it also demands better computer algorithms to assist users in quickly and easily generating 3D content for printing. Creating 3D content often requires considerably more efforts and skills than creating 2D content. In this work, I will study several aspects of 3D shape design and optimization for 3D printing. I start by discussing my work in geometric puzzle design, which is a popular application of 3D printing in recreational math and art. Given user-provided input figures, the goal is to compute the minimum (or best) set of geometric shapes that can satisfy the given constraints (such as dissection constraints). The puzzle design also has to consider feasibility, such as avoiding interlocking pieces. I present two optimization-based algorithms to automatically generate customized 3D geometric puzzles, which can be directly printed for users to enjoy. They are also great tools for geometry education.

Next, I discuss shape optimization for printing functional tools and parts. Although current 3D modeling software allows a novice user to easily design 3D shapes, the resulting shapes are not guaranteed to meet required physical strength. For example, a poorly designed stool may easily collapse when a person sits on the stool; a poorly designed wrench may easily break under force. I study new algorithms to help users strengthen functional shapes in order to meet specific physical properties. The algorithm uses an optimization-based framework -- it performs geometric shape deformation and structural optimization iteratively to minimize mechanical stresses in the presence of forces assuming typical use scenarios. Physically-based simulation is performed at run-time to evaluate the functional properties of the shape (e.g., mechanical stresses based on finite element methods), and the optimizer makes use of this information to improve the shape. Experimental results show that my algorithm can successfully optimize various 3D shapes, such as chairs, tables, utility tools, to withstand higher forces, while preserving the original shape as much as possible.To improve the efficiency of physics simulation for general shapes, I also introduce a novel, SPH-based sampling algorithm, which can provide better tetrahedralization for use in the physics simulator. My new modeling algorithm can greatly reduce the design time, allowing users to quickly generate functional shapes that meet required physical standards.