About Approximation

This section deals with basic concepts you should know before beginning with approximating geometry.

With the options of the Approximation tab you can compute curve approximation for selected surface edges as well as any curves, depending on the approximation type set. The approximation has direct influence on the addenda. If, for example, face edge segments are selected as guides, the approximation allows to reduce the number of segments and thus the postprocessing to smooth the surface matchings.

See Also
Approximation Tab

The approximation is computed in two steps:

  1. Creation of an initial B-Spline

    With the first step, for each selected curve is created an initial B-Spline, defining the parametrization and the number of control points, but not their values. The B-Spline results from the B-Spline of the curve to be approximated as well as from the minimum and maximum values of the order and the number of segments specified by the user:

    Order and number of segments of the B-Spline are taken from the curve to be approximated, if they are within the specified minimum and maximum ranges. Otherwise, they are increased or reduced to the corresponding minimum or maximum value.

    Note: If in the selected geometry G2 discontinuities are found, they are transferred as sharp bends to the initial B-Spline. In this case, the initial B-Spline may contain more segments than the maximum value specified for the segmentation.

  2. Iterations

    After the creation of the initial B-Spline, the actual approximation is computed in the second step. This is realized by a three-step iteration:

    1. Iteration (a)

      In the first iteration, the (optimal) values of the control points of the B-Spline are computed using a Newton method. The control points allow the computation of the maximum deviation between the computed approximation curve and the original curve. If this value is smaller than the tolerance value specified by the user, the iteration is terminated successfully.

    2. Iteration (b) + (c)

      If the computed deviation is larger than the tolerance specified, the B-Spline will be modified by increasing order and number of segments, and the iteration (a) is restarted.

      Independent from the approximation type set, first the order and then the number of segments is increased. This way, the number of segments of the created curves can be minimized.

Structure View of the Approximation