Essential Mathematics for Computational Design
Essential Mathematics for Computational Design, by Rajaa Issa (Robert McNeel & Associates), introduces to design professionals the foundation mathematical concepts that are necessary for effective development of computational methods for 3-D modeling and computer graphics. This is not meant to be a complete and comprehensive resource, but rather an overview of the basic and most commonly used concepts.
The material is directed towards designers who have little or no background in mathematics beyond high school. All concepts are explained visually using Grasshopper ® (GH), the generative modeling environment for Rhinoceros ® (Rhino).
The content is divided into three chapters. Chapter 1 discusses vector math including vector representation, vector operation, and line and plane equations. Chapter 2 reviews matrix operations and transformations. Chapter 3 includes an in-depth review of parametric curves with special focus on NURBS curves and the concepts of continuity and curvature. It also reviews NURBS surfaces and polysurfaces.
The author would like to acknowledge the excellent and thorough technical review by Dr. Dale Lear of Robert McNeel & Associates. His valuable comments were instrumental in producing this edition. I would also like to acknowledge Ms. Margaret Becker of Robert McNeel & Associates for reviewing the technical writing and formatting the document.
Contents
Vector Mathematics
Vector representation
Position vector Vectors vs. points Vector length Unit vector
Vector operations
Vector scalar operation Vector addition Vector subtraction Vector properties Vector dot product Vector dot product, lengths, and angles Dot product properties Vector cross product Cross product and angle between vectors Cross product properties
Vector equation of line
Vector equation of a plane
Tutorials
Face direction
Input Parameters Solution
Exploded box
Input Parameters Solution
Tangent spheres
Input Parameters Solution
Matrices and Transformations
Parametric Curves and Surfaces
References
Edward Angel, "Interactive Computer Graphics with OpenGL,” Addison Wesley Longman, Inc., 2000.
James D Foley, Steven K Feiner, John F Hughes, "Introduction to Computer Graphics" Addison-Wesley Publishing Company, Inc., 1997.
James Stewart, "Calculus," Wadsworth, Inc., 1991.
Kenneth Hoffman, Ray Kunze, “Linear Algebra”, Prentice-Hall, Inc., 1971
Rhinoceros® help document, Robert McNeel and Associates, 2009.
