3D Graphics in Calculus (UMAP)

This module helps students to strengthen their multidimensional visual intuition and their ability to solve problems that involve multidimensional concepts in calculus and in linear algebra. The vehicle is an application familiar to students: three-dimensional graphics, studied only with elementary concepts from multivariable calculus and linear algebra. The challenges against which students may measure their progress are to design and modify algorithms for three-dimensional graphics.

Table of Contents:

INTRODUCTION

ORTHOGONAL PROJECTIONS IN SPACE
The Pythagorean Theorem
Dot Products and Perpendicularity
Orthonormal Bases and Orthogonal Projections

AXONOMETRIES
The Geometric Concept of Axonometry
Algorithms to Calculate Axonometries

GRAPHICS
An Algorithm to Plot Spatial Curves
An Algorithm to Plot Wire Frames on Graphs

RENDERING
Expanding Horizons to Remove Hidden Lines
Ray Tracing to Remove Hidden Lines and Shade Surfaces

TERM PROJECTS
From Computer Programs to Number Theory
Perspectives without Projective Geometry
Geometric Perspectives on History
2-D Graphics in Flatland

SOLUTIONS TO THE EXERCISES

REFERENCES

ACKNOWLEDGMENTS

ABOUT THE AUTHOR