A Completely Generalized and Algorithmic Approach to Identifying the Maximum Area Inscribing Ellipse of an Asymmetric Convex Quadrangle

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Creator: 

Copeland, Zachary Alexander

Date: 

2017

Abstract: 

An algorithm is developed herein using the projective extension of the Euclidean plane which will always generate the entire one-parameter family of inscribing ellipses, and directly identify the area maximizing one of any given convex quadrangle, within a metric space. Given four bounding points, no three of which are collinear, four line equations are generated which describe a convex quadrangle. Alongside the definition of a specific polar point, these five constraints identify a pencil of inscribing line conics, which is then transformed into its point conic dual for visualisation and plotting. The pencil of point conics then has its area optimised with respect to the value of its polar point, at which juncture the maximum area inscribing ellipse may be identified from the pencil of inscribing conics.

Subject: 

Engineering - Mechanical

Language: 

English

Publisher: 

Carleton University

Thesis Degree Name: 

Master of Applied Science: 
M.App.Sc.

Thesis Degree Level: 

Master's

Thesis Degree Discipline: 

Engineering, Mechanical

Parent Collection: 

Theses and Dissertations

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