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Continuity with Four Sided Surfaces
& Avoiding Singularities
By Jeremy Birn

The Surfaces > Four Sided function is another vital link in assembling models for SurfaceContinuityManager+. The following tutorial shows a basic example of their use, and also shows how to resolve a problem with SurfaceContinuityManager+ and singularities.

Singularities are areas of your models where a whole row of points are drawn together into the same location, as commonly seen at the top and bottom of a primitive sphere. SurfaceContinuityManager+ can cause distortion and fail to achieve continuity if applied to groups of surfaces containing singularities.

1. Get > Primitive > Sphere. Choose Cubic NURBS, with a radius of 5 units, a U count of 8, and a V count of 8.

2. Draw > Cut and slice the sphere along the equator. Delete the lower half so that you only have the top half of the sphere left in the scene.

3. From the top view, Draw > Cut the sphere four times, into four quarters. The cut-lines will line-up with the axis lines running horizontally and vertically through the top view.

4. Open a Schematic view, and delete any uncut or partially cut surfaces, so that only the four quarters are left in the scene.

The four quarters are already seamless before SurfaceContinuityManager+ is applied.

5. At this point, your four quarters will fit together seamlessly (without Surface Continuity Manager.) In the shaded view, you won't be able to tell that they are four separate objects.

6. Multi-select the four objects, and choose Deformation > SurfaceContinuityManager+. The plug-in will badly mangle a formerly-smooth area of your model, making it clear why SurfaceContinuityManager+ is listed in the "Deformation" menu.

The SurfaceContinuityManager+ effect corrupts the singularity.

7. Delete the bandage icon to get rid of the SurfaceContinuityManager+ effect. Deleting the icon will reset the models to their pre-SurfaceContinuityManager+ state.

NOTE: After deleting the SurfaceContinuityManager+ icon, you will see the wireframe immediately restored, while the shaded view may not be refreshed, even if you press the r key. If this happens, you can force the shaded view to re-tessellate all the geometry it displays by clicking the SETUP button in the top of a shaded window, and changing the value labeled "Surface Precision." For example, if the number is 0, change it to 1, and click OK. You can click SETUP again and change it back to 0 afterwards, but the geometry will still have been refreshed by the process

8. To remove the singularity, select one of the four surfaces, and Draw > Cut the surface at the location of 5.5 in the V direction. Repeat for each of the four surfaces.

9. Open a Schematic view, and delete any uncut or partially cut surfaces, so that a round hole appears in the center of the four quarters.

Cutting the four surfaces eliminates the singularity.

10. Select one of the quarters, and Draw > Extract the interior curve along the edge that you just cut. Repeat for each quarter, so you have four NURBS curves tracing the edge of the hole.

11. In the top view, Multi-select the top two curves, such that the curves around half of the hole are selected. Effect > Inverse the two curves. This will insure that opposite sides of the Four Sided surface do not become crossed-over.

Inverse the top two extracted curves.

12. Select Surface > Four Sided and click each of the four curves running clockwise. Choose "Uniform" for the type of parameterization.

13. Apply SurfaceContinuityManager+ again to unite the five surfaces.

 

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This tutorial copyright © 1999 by Jeremy Birn.
Please do not duplicate any part fo this tutorial without written permission.