Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of surfaces, they are not suitable for reversing aircraft wings. In this dissertation, we develop and demonstrate a new strategy for reversing a mathematical representation of an aircraft wing.
The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab.
There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions.
The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.
","abstract_html":"<p>Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of surfaces, they are not suitable for reversing aircraft wings. In this dissertation, we develop and demonstrate a new strategy for reversing a mathematical representation of an aircraft wing.</p> <p>The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab.</p> <p>There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions.</p> <p>The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.</p>","abstract_has_math":false,"creators":["Huband, Jacalyn M."],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Wu Li","John Swetits","Stanley Weinstein","Robert Smith"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1997,"date_issued":"1997-07-01T07:00:00Z","date_published":"1997-07-01T07:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Surface fitting","Aircraft wing data","Aerospace Engineering","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab.
There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions.
The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.
"]},{"key":"dc:title","label":"Title","values":["Reverse Engineering of Aircraft Wing Data Using a Partial Differential Equation Surface Model"]}]}],"canonical_facts":{"dc:contributor":["Wu Li","John Swetits","Stanley Weinstein","Robert Smith"],"dc:creator":["Huband, Jacalyn M."],"dc:date.available":["2019-06-05T07:00:00Z"],"dc:description.abstract":["Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of surfaces, they are not suitable for reversing aircraft wings. In this dissertation, we develop and demonstrate a new strategy for reversing a mathematical representation of an aircraft wing.
The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab.
There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions.
The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.
"],"dc:identifier":["9780591603859","https://digitalcommons.odu.edu/mathstat_etds/11"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Surface fitting","Aircraft wing data","Aerospace Engineering","Mathematics"],"dc:title":["Reverse Engineering of Aircraft Wing Data Using a Partial Differential Equation Surface Model"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:53Z"}