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gleSpiral

NAME

gleSpiral - Sweep an arbitrary contour along a helical path.

SYNTAX

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 */

ARGUMENTS

ncp

number of contour points

contour

2D contour

cont_normal

2D contour normals

up

up vector for contour

startRadius

spiral starts in x-y plane

drdTheta

change in radius per revolution

startZ

starting z value

dzdTheta

change in Z per revolution

startXform

starting contour affine transformation

dXformdTheta

tangent change xform per revolution

startTheta

start angle in x-y plane

sweepTheta

degrees to spiral around

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.

SEE ALSO

gleLathe

AUTHOR

Linas Vepstas (linas AT linas DOT org)

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