Mathematics for Computer Graphics (Appendix)
Computer graphics works in vector space Rn
- Rn - set of all ordered n-tuple of real numbers
- We typically consider points in space as column vectors in R2, R3, and R4
- Two basic operations
- Vector addition
- Scalar multiplication
- Vector properties (u and v are vectors)
- Addition is commutative - u+v = v+u
- Addition is associative - u+(v+w) = (u+v)+w
- Addition identity - v+0 = v
- Addition must have inverse - v+w = 0 implies w = -v
- Multiplication must satisfy (a and b are scalars):
- (a*b)*v = a*(b*v)
- 1*v = v
- (a+b)*v = a*v + b*v
- a*(u+v) = a*u + a*v