Building an Orthonormal Basis, Revisited
نویسندگان
چکیده
Frisvad [2012b] describes a widely-used computational method for efficiently augmenting a given single unit vector with two other vectors to produce an orthonormal frame in three dimensions, a useful operation for any physically based renderer. However, the implementation has a precision problem: as the z component of the input vector approaches −1, floating point cancellation causes the frame to lose all precision. This paper introduces a solution to the precision problem and shows how to implement the resulting function in C++ with performance comparable to the original.
منابع مشابه
Improved accuracy when building an orthonormal basis
Frisvad’s method for building a 3D orthonormal basis from a unit vector has accuracy problems in its published floating point form. These problems are investigated and a partial fix is suggested, by replacing the threshold 0.9999999 by the threshold -0.999805696, which decreases the maximum error in the orthonormality conditions from 0.623 to 0.0062.
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