Given a vector x, this routine builds a right handed orthonormal frame x,y,z where the output x is parallel to the input x.
Copyright (1995), California Institute of Technology. U.S. Government sponsorship acknowledged.
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VARIABLE I/O DESCRIPTION -------- --- ------------------------------------------------ x I/O Input vector. A parallel unit vector on output. y O Unit vector in the plane orthogonal to x. z O Unit vector given by x X y.
x This vector is used to form the first vector of a right-handed orthonormal triple.
x, y, z form a right handed orthonormal frame, where x is now a unit vector parallel to the original input vector x. There are no special geometric properties connected to y and z (other than that they complete the right handed frame).
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Given an input vector x, this routine returns unit vectors x, y, and z such that xyz forms a right-handed orthonormal frame where the output x is parallel to the input x. This routine is intended primarily to provide a basis for the plane orthogonal to x. There are no special properties associated with y and z other than that the resulting xyz frame is right handed and orthonormal. There are an infinite collection of pairs (y,z) that could be used to this end. Even though for a given x, y and z are uniquely determined, users should regard the pair (y,z) as a random selection from this infinite collection. For instance, when attempting to determine the locus of points that make up the limb of a triaxial body, it is a straightforward matter to determine the normal to the limb plane. To find the actual parametric equation of the limb one needs to have a basis of the plane. This routine can be used to get a basis in which one can describe the curve and from which one can then determine the principal axes of the limb ellipse.
In addition to using a vector to construct a right handed frame with the x-axis aligned with the input vector, one can construct right handed frames with any of the axes aligned with the input vector. For example suppose we want a right hand frame xyz with the z-axis aligned with some vector v. Assign v to z z[0] = v[0]; z[1] = v[1]; z[2] = v[2]; Then call frame_c with the arguments x,y,z cycled so that z appears first. frame_c (z, x, y); The resulting xyz frame will be orthonormal with z parallel to the vector v. To get an xyz frame with y parallel to v perform the following y[0] = v[0]; y[1] = v[1]; y[2] = v[2]; frame_c (y, z, x);
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Error Free. 1) If x on input is the zero vector the ``standard'' frame (ijk) is returned.
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W.L. Taber (JPL) I.M. Underwood (JPL)
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-CSPICE Version 1.0.0, 26-MAR-1999 (NJB)
build a right handed coordinate frame