Building an Orthonormal Basis from a 3D Unit Vector Without Normalization
نویسندگان
چکیده
منابع مشابه
Building an Orthonormal Basis from a 3D Unit Vector Without Normalization
I present two tools that save the computation of a dot product and a reciprocal square root in operations that are used frequently in the core of many rendering programs. The first tool is a formula for rotating a direction sampled around the z-axis to a direction sampled around an arbitrary unit vector. This is useful in Monte Carlo rendering techniques, such as path tracing, where directions ...
متن کاملBuilding an Orthonormal Basis, Revisited
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 ...
متن کاملImproved 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.
متن کاملOrthonormal vector polynomials in a unit circle, Part II : Completing the basis set.
Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zern...
متن کاملOrthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials.
Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made orthonorm...
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ژورنال
عنوان ژورنال: Journal of Graphics Tools
سال: 2012
ISSN: 2165-347X,2165-3488
DOI: 10.1080/2165347x.2012.689606