Application To Computer Graphics
A common problem in computer graphics is to generate a non-zero vector in R3 that is orthogonal to a given non-zero one. There is no single continuous function that can do this for all non-zero vector inputs. This is a corollary of the hairy ball theorem. To see this, consider the given vector as the radius of a sphere and note that finding a non-zero vector orthogonal to the given one is equivalent to finding a non-zero vector that is tangent to the surface of that sphere. However, the hairy ball theorem says there exists no continuous function that can do this for every point on the sphere (i.e. every given vector).
Read more about this topic: Hairy Ball Theorem
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