Tangent vectors to a surface normal

Application of the Householder formula to compute tangent vector fields given the surface normals

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.
Please cite:
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