Programming is based on Computer Science and Computer Science as a discipline grew out of the study of Mathematics and Logic. So while computers in the commonly understood sense have only come into existence in the last few decades there are thousands of years of thought and work that provide the theoretical underpinning to what we do today.
Besides the mathematical underpinnings of modern computers themselves, most of the things that we are doing when creating an interactive 3d environment is simulating something that exists in the real world. Simulations are made using applied mathematics to model the way real systems work.
Mathematics is a huge field so it is worthwhile to focus on the particular sub-areas that are of most used for our task. Some of these are:
Geometry
Trigonometry
Calculus
Discrete Structures
Probability
Statistics
