This is the webpage for the course Geometry and Algorithms in Three-Dimensional Modeling at Oklahoma State University.

Classes will consist of lectures on the mathematical underpinnings of 3D design software, and "workshop classes", spent learning the use of the software and working on projects. We will also use the 3D printing lab, MSCS 421. Students in the class will have 24 hour keycard access to the lab with their university ID card.


We will cover a number of sections from the course text, Applied Geometry for Computer Graphics and CAD (Springer Undergraduate Mathematics Series) 2nd Edition, by Duncan Marsh. (The text is freely available in electronic form from We will go through parts of chapters 1-3 (transformations, homogeneous coordinates), and chapters 6-7 (Bézier curves).


Homeworks will consist of standard problem sets to be handed in during class, and virtual 3D models/animations/interactive content to be handed in via Canvas, or real-life 3D printed models to be submitted in class.


You cannot effectively learn how to use a piece of software by listening to lectures. You have to use the software. The modelling homework sets and projects will give concrete goals to guide exploration of the software. Students will also follow tutorials.


There will be two take home midterms, with tentative due dates March 9 and April 13. There will be no final exam.


There will be three major projects due throughout the semester. The following schedule and topics are tentative.

Project 1: Goblet

Design and 3D print a goblet. This will likely be a surface of revolution (although if you wish you may depart from this). The goblet should hold precisely 100ml of water. The shape should be interesting in some way, either mathematically, culturally, and/or aesthetically. Along with the 3D print, students will complete a writeup on the mathematics, including a calculation of the volume of the goblet, and other relevant details of the design and present their work to the class.

Project 2: Oklahoma map project

The OSU Museum of Art a planning a show on Geometry/Math for October-December 2023. For the second project, the class will divide up the map of the state of Oklahoma, each taking some collection of counties. I will supply files with the terrain and county boundaries. Your job is to add a landmark, building, or other relevant features to your subset of the state, designed using some form of mathematics or programming. We will agree on a scale to print at so that all of the prints can be assembled together, giving a decorated map of Oklahoma that will be displayed in the art exhibition.

Project 3: Illustrate something mathematical

Produce a model (or animation, or interactive demonstration) illustrating a mathematical object, process, algorithm etc. The model may be drawn from your previous mathematics classes, or (even better) mathematics that is new to you. I can give you references to read. For example there are many ideas in symmetry or knot theory or other areas of mathematics that are accessible and would be good to illustrate with a 3D model.


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