This concise textbook teaches readers how to turn geometry into an image on a computer screen.

The exciting journey begins in the schools of the ancient Greek philosophers and describes the major events that changed people’s perceptions of geometry. Readers will learn how to see geometry and colors beyond simple mathematical formulas and how to represent geometric shapes, transformations and motions by digital sampling of various mathematical functions. Special multiplatform visualization software developed by the author will allow readers to explore the exciting world of visual immersive mathematics, and the book software repository will provide a starting point for their own sophisticated visualization applications.

Topics and features now include:

• a section on interactive artistic shape modeling
• an extended section on interactive shape modeling with ShapeExplorer
• a section on creating models of virtual objects
• experiments in shape modeling using generative AI 

Making Images with Mathematics serves as a self-contained text for a one-semester computer graphics and visualization course for computer science and engineering students, as well as a reference manual for researchers and developers.

Dr. Alexei Sourin is an associate professor at Nanyang Technological University, Singapore, and is on the editorial board of the Springer journal, The Visual Computer.

Alexei Sourin is an established scientist in several areas of computer graphics. He began his research in 1980 with his master’s and PhD projects in computer animation. From 1988, he focused on problems in scientific visualization in physics. In 1993, Dr. Sourin joined the faculty of the renowned Nanyang Technological University in Singapore to teach and conduct research in computer graphics, function representation in solid modeling, virtual reality, human–computer interaction and artificial intelligence in computer vision.

In 2006, Professor Sourin was awarded the title of Senior Member of the IEEE. In 2012-2018, he served as Chair of the Working Group “Computer Graphics and Virtual Reality” of the International Federation for Information Processing. He is the creator and coordinator of the annual international conference on Cyberworlds, which focuses on various aspects of immersive virtual communities. For a number of years, he has been a member of the Editorial Board of The Visual Computer journal (Springer Nature). He has written several books and book chapters on computer graphics and virtual reality.