Date of Award

June 2017

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


John F. Dannenhoffer

Second Advisor

Sinéad C. Mac Namara

Subject Categories



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's

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.


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