The Householder formula is a robust and efficient way to compute tangent and bitangent vectors given a surface normal. The computed vector fields are both locally and globally coherent. The accompanying demo illustrates the tangent vector fields of several quadratic surfaces : Ellipsoid, Elliptic Paraboloid, Hyperbolic Paraboloid, Hyperboloid of 1 sheet, Hyperboloid of 2 sheets, Elliptic Cone, Elliptical Cylinder, Hyperbolic Cylinder, and Parabolic Cylinder.
Each tangent and bitangent vector fields are calculated with the Householder formula.
D.S. Lopes, M.T. Silva, and J.A. Ambrósio, Tangent vectors to a 3-D surface normal: A geometric tool to find orthogonal vectors based on the Householder transformation, Computer-Aided Design, 45(3): 683 - 694, 2013. DOI: 10.1016/j.cad.2012.11.003
Daniel Lopes (2021). Tangent vectors to a surface normal (https://www.mathworks.com/matlabcentral/fileexchange/65627-tangent-vectors-to-a-surface-normal), MATLAB Central File Exchange. Retrieved .
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