Mathematics for Computer Graphics (continued)
Computer graphics works in vector space Rn (continued)
- Vector properties (u and v are vectors, a and b are scalars) (continued)
- Linear combination - a1*v1 + a2*v2 + Ö + an*vn
- Dot product - v . w = v1*w1 + v2*w2 + Ö + vn*wn
- Properties
- v.w = w.v
- v.v = 0 iff v = 0
- v.(u+a*w) = v.u + a*(v.w)
- Length - vector v = denoted by |v|
- length v = = distance from point x,y to origin = sqrt(x^2+y^2)
- In general length v = |v| = sqrt(v1^2 + v2^2 +Ö+ vn^2) = sqrt(v.v)
- Vector normalisation (unit vector has length = 1)
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