gleSpiral(3gle)

NAME

gleSpiral - Sweep an arbitrary contour along a helical path.

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 */

ncp number of contour points

contour 2D contour

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.

Linas Vepstas (linas@linas.org)