Computer Aided Design (CAD) is a powerful tool for designing
parametric geometry. However, many CAD models of current
configurations are constructed in previous generations of CAD
systems, which represent the configuration simply as a collection of
surfaces instead of as a parametrized solid model. But since many
modern analysis techniques take advantage of a parametrization, one
often has to re-engineer the configuration into a parametric
model. The objective here is to generate an efficient, robust, and
accurate method for fitting parametric models to a cloud of
points. The process uses a gradient-based optimization technique,
which is applied to the whole cloud, without the need to segment or
classify the points in the cloud a priori.
First, for the points associated with any component, a variant of
the Levenberg-Marquardt gradient-based optimization method (ILM) is
used to find the set of model parameters that minimizes the
least-square errors between the model and the points. The
efficiency of the ILM algorithm is greatly improved through the use
of analytic geometric sensitivities and sparse matrix techniques.
Second, for cases in which one does not know a priori the
correspondences between points in the cloud and the geometry model\u27s
components, an efficient initialization and classification algorithm
is introduced. While this technique works well once the
configuration is close enough, it occasionally fails when the
initial parametrized configuration is too far from the cloud of
points. To circumvent this problem, the objective function is
modified, which has yielded good results for all cases tested.
This technique is applied to a series of increasingly complex
configurations. The final configuration represents a full transport
aircraft configuration, with a wing, fuselage, empennage, and
engines. Although only applied to aerospace applications, the
technique is general enough to be applicable in any domain for which
basic parametrized models are available
