Graduation Year


Document Type




Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Computer Science and Engineering

Major Professor

Les A. Piegl, Ph.D.

Committee Member

Brian Curtin, Ph.D.

Committee Member

Jay Ligatti, Ph.D.

Committee Member

Susana Lai-Yuen, Ph.D.

Committee Member

Rafael Perez, Ph.D.


Additive Manufacturing, Bézier, Curve Fitting, Moore Neighborhoods, NURBS, Tessellation


Various industries have embraced 3D printing for manufacturing on-demand, custom printed parts. However, 3D printing requires intelligent data processing and algorithms to go from CAD model to machine instructions. One of the most crucial steps in the process is the slicing of the object. Most 3D printers build parts by accumulating material layers by layer. 3D printing software needs to calculate these layers for manufacturing by slicing a model and calculating the intersections. Finding exact solutions of intersections on the original model is mathematically complicated and computationally demanding. A preprocessing stage of tessellation has become the standard practice for slicing models. Calculating intersections with tessellations of the original model is computationally simple but can introduce inaccuracies and errors that can ruin the final print.

This dissertation shows that a point cloud approach to preprocessing and slicing models is robust and accurate. The point cloud approach to object slicing avoids the complexities of directly slicing models while evading the error-prone tessellation stage. An algorithm developed for this dissertation generates point clouds and slices models within a tolerance. The algorithm uses the original NURBS model and converts the model into a point cloud, based on layer thickness and accuracy requirements. The algorithm then uses a gridding structure to calculate where intersections happen and fit B-spline curves to those intersections.

This algorithm finds accurate intersections and can ignore certain anomalies and error from the modeling process. The primary point evaluation is stable and computationally inexpensive. This algorithm provides an alternative to challenges of both the direct and tessellated slicing methods that have been the focus of the 3D printing industry.