Given a normalized 3D vector, here’s an efficient method for computing a full basis. The computed basis is axis aligned if the input vector is axis aligned. void ComputeBasis(const Vec& a, Vec* b, Vec* c) { // Suppose vector a has all equal components and is a unit vector: // a = (s, s, s) // Then 3*s*s = 1, s = sqrt(1/3) = 0.57735. This means that at // least one component of a unit vector must be greater or equal // to 0.
