Mathematics of Computer Graphics (continued)

• cosine rule

  • |v-w|^2 = |v|^2 + |w|^2 - 2|v||w|cos(A)

• |v|^2 = v.v

  • |v-w|^2 = (v-w) . (v-w) = v.v + w.w - 2v.w = |v|^2 + |w|^2 - 2v.w

• |v|^2 + |w|^2 - 2v.w = |v|^2 + |w|^2 - 2|v||w|cos(A)

  • cos(A) = (v.w)/(|v||w|)

V

W

V-W

A

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