1gleSpiral(3GLE)                       GLE                      gleSpiral(3GLE)
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NAME

6       gleSpiral - Sweep an arbitrary contour along a helical path.
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SYNTAX

9       void gleSpiral (int ncp,
10                       gleDouble contour[][2],
11                       gleDouble cont_normal[][2],
12                       gleDouble up[3],
13                       gleDouble startRadius,     /* spiral starts in x-y plane */
14                       gleDouble drdTheta,        /* change in radius per revolution */
15                       gleDouble startZ,          /* starting z value */
16                       gleDouble dzdTheta,        /* change in Z per revolution */
17                       gleDouble startXform[2][3], /* starting contour affine xform */
18                       gleDouble dXformdTheta[2][3], /* tangent change xform per revoln */
19                       gleDouble startTheta,      /* start angle in x-y plane */
20                       gleDouble sweepTheta);     /* degrees to spiral around */
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ARGUMENTS

23       ncp       number of contour points
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25       contour   2D contour
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27       cont_normal
28                 2D contour normals
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30       up        up vector for contour
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32       startRadius
33                 spiral starts in x-y plane
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35       drdTheta  change in radius per revolution
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37       startZ    starting z value
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39       dzdTheta  change in Z per revolution
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41       startXform
42                 starting contour affine transformation
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44       dXformdTheta
45                 tangent change xform per revolution
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47       startTheta
48                 start angle in x-y plane
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50       sweepTheta
51                 degrees to spiral around
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DESCRIPTION

54       Sweep an arbitrary contour along a helical path.
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56       The axis of the helix lies along the modeling coordinate z-axis.
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58       An  affine  transform  can be applied as the contour is swept. For most
59       ordinary usage, the affines should be given as NULL.
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61       The "startXform[][]" is an affine matrix  applied  to  the  contour  to
62       deform the contour. Thus, "startXform" of the form
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64            |  cos     sin    0   |
65            |  -sin    cos    0   |
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67       will rotate the contour (in the plane of the contour), while
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69            |  1    0    tx   |
70            |  0    1    ty   |
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72       will translate the contour, and
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74            |  sx    0    0   |
75            |  0    sy    0   |
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77       scales along the two axes of the contour. In particular, note that
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79            |  1    0    0   |
80            |  0    1    0   |
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82       is the identity matrix.
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84       The  "dXformdTheta[][]"  is  a differential affine matrix that is inte‐
85       grated while the contour is extruded.  Note  that  this  affine  matrix
86       lives in the tangent space, and so it should have the form of a genera‐
87       tor.  Thus, dx/dt's of the form
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89            |  0     r    0   |
90            |  -r    0    0   |
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92       rotate the the contour as it is extruded (r == 0 implies no rotation, r
93       == 2*PI implies that the contour is rotated once, etc.), while
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95            |  0    0    tx   |
96            |  0    0    ty   |
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98       translates the contour, and
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100            |  sx    0    0   |
101            |  0    sy    0   |
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103       scales it. In particular, note that
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105            |  0    0    0   |
106            |  0    0    0   |
107
108       is  the identity matrix -- i.e. the derivatives are zero, and therefore
109       the integral is a constant.
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SEE ALSO

113       gleLathe
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AUTHOR

116       Linas Vepstas (linas@linas.org)
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120GLE                                   3.0                      gleSpiral(3GLE)