Approximate Continuity

Last Updated: July 14, 1997
Two patches are said to join with approximate continous with tolerance e if the angle between the surface normals of the two patches at any point along the common boundary is less than e.

The cubic interpolant work backwards to produce approximately continuous surfaces: It would

  1. sample a known function,
  2. fit cubic interpolant patches to the data,
  3. test the boundaries to see if the continuity condition was met.
    If not met, refine the sampling and repeat.
The condition verified numerically by sampling the boundary at multiple locations and seeing if the condition was met at these sample points.

Research

Part of the current research involves developing a better test for approximate continuity. For cubic patches, we can determine the maximum discontinuity by finding the roots of a degree 18 polynomial. We would prefer a find a less expensive technique that is accurate to a prescribed tolerance.

With a slightly different thrust, we are trying to develop a construction of approximately continuous surace patches. That is, given that we want our patches to interpolate certain data and meet with approximate continuity, how do we build patches that meet these constraints?

These ideas of approximate continuity also extend to surface pasting, where the features only meet approximately C0, and the normals are also only approximately the same.

[UP] Back one level.