GPGPU Programming for Games and Science

322 GPGPU Programming for Games and Science

is responsible for keeping the distinction in his head and enforcing the rules ac-

cordingly. In my last commercial endeavor I attempted to build a very general

homogeneous algebra system, supporting linear algebra, affine algebra, and

homogeneous operations, while at the same time having as much compiler

support and runtime support for enforcing the rules. In the end, the program-

mers using the system still found ways to violate the point-vector distinction

although not intentionally. My conclusion was that the effort spent trying

to protect a programmer from inadvertently making errors was not justified

by the maintenance costs. The bottom line is: You must understand and be

adept at the mathematical abstracti ...