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.

AUTHOR