.\"
.\" GLE Tubing & Extrusions Library Documentation 
.\"
.TH gleSpiral 3GLE "3.0" "GLE" "GLE"
.SH NAME
gleSpiral - Sweep an arbitrary contour along a helical path.
.SH SYNTAX
.nf
.LP
void gleSpiral (int ncp,
                gleDouble contour[][2],
                gleDouble cont_normal[][2],
                gleDouble up[3],
                gleDouble startRadius,     /* spiral starts in x-y plane */
                gleDouble drdTheta,        /* change in radius per revolution */
                gleDouble startZ,          /* starting z value */
                gleDouble dzdTheta,        /* change in Z per revolution */
                gleDouble startXform[2][3], /* starting contour affine xform */
                gleDouble dXformdTheta[2][3], /* tangent change xform per revoln */
                gleDouble startTheta,      /* start angle in x-y plane */
                gleDouble sweepTheta);     /* degrees to spiral around */
.fi
.SH ARGUMENTS
.IP \fIncp\fP 1i
number of contour points
.IP \fIcontour\fP 1i
2D contour
.IP \fIcont_normal\fP 1i
2D contour normals
.IP \fIup\fP 1i
up vector for contour
.IP \fIstartRadius\fP 1i
spiral starts in x-y plane
.IP \fIdrdTheta\fP 1i
change in radius per revolution
.IP \fIstartZ\fP 1i
starting z value
.IP \fIdzdTheta\fP 1i
change in Z per revolution
.IP \fIstartXform\fP 1i
starting contour affine transformation
.IP \fIdXformdTheta\fP 1i
tangent change xform per revolution
.IP \fIstartTheta\fP 1i
start angle in x-y plane
.IP \fIsweepTheta\fP 1i
degrees to spiral around
.SH DESCRIPTION

Sweep an arbitrary contour along a helical path. 

The axis of the helix lies along the modeling coordinate z-axis. 

An affine transform can be applied as the contour is swept. For most
ordinary usage, the affines should be given as NULL.

The "startXform[][]" is an affine matrix applied to the contour to
deform the contour. Thus, "startXform" of the form

     |  cos     sin    0   |
     |  -sin    cos    0   |

will rotate the contour (in the plane of the contour), while 

     |  1    0    tx   |
     |  0    1    ty   |

will translate the contour, and 

     |  sx    0    0   |
     |  0    sy    0   |

scales along the two axes of the contour. In particular, note that 

     |  1    0    0   |
     |  0    1    0   |

is the identity matrix. 

The "dXformdTheta[][]" is a differential affine matrix that is
integrated while the contour is extruded.  Note that this affine matrix
lives in the tangent space, and so it should have the form of a
generator.  Thus, dx/dt's of the form

     |  0     r    0   |
     |  -r    0    0   |

rotate the the contour as it is extruded (r == 0 implies no rotation, r
== 2*PI implies that the contour is rotated once, etc.), while

     |  0    0    tx   |
     |  0    0    ty   |

translates the contour, and 

     |  sx    0    0   |
     |  0    sy    0   |

scales it. In particular, note that 

     |  0    0    0   |
     |  0    0    0   |

is the identity matrix -- i.e. the derivatives are zero, and therefore
the integral is a constant.

.SH SEE ALSO
gleLathe
.SH AUTHOR
Linas Vepstas (linas@linas.org)