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Table of Contents

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.