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frame_c

 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

Procedure

frame_c ( Build a right handed coordinate frame )

void frame_c ( SpiceDouble x,
SpiceDouble y,
SpiceDouble z )

Abstract

Build a right handed orthonormal frame (x,y,z) from a
3-dimensional input vector, where the X-axis of the resulting
frame is parallel to the original input vector.

None.

AXES
FRAME

Brief_I/O

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 the cross product <x,y>.

Detailed_Input

x           is a 3-dimensional vector used to form the first vector
of a right-handed orthonormal triple.

Detailed_Output

x,
y,
z           are the 3-dimensional unit vectors that form a right
handed orthonormal frame, where `x' is now a unit vector
parallel to the original input vector in `x'. There are no
special geometric properties connected to `y' and `z' (other
than that they complete the right handed frame).

None.

Exceptions

Error free.

1)  If `x' on input is the zero vector the "standard" frame (ijk)
is returned.

None.

Particulars

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.

Examples

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 = v;
z = v;
z = v;

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 = v;
y = v;
y = v;

frame_c (y, z, x);

None.

None.

Author_and_Institution

N.J. Bachman        (JPL)
J. Diaz del Rio     (ODC Space)

Version

-CSPICE Version 1.0.1, 03-JUL-2021 (JDR)

Edited the header to comply with NAIF standard.

-CSPICE Version 1.0.0, 26-MAR-1999 (NJB)

Index_Entries

build a right handed coordinate frame
Fri Dec 31 18:41:06 2021