.\"
.\" 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)