Abstract
This paper formulates the developable surface design problem in an optimal control setting. Given a regular curve bt on the unit sphere corresponding to a one-parameter family of rulings, and two base curve endpoints a0,a1∈R3, we consider the problem of constructing a base curve at such that at0=a0,at1=a1, and the resulting surface fs,t=at+sbt is developable. We formulate the base curve design problem as an optimal control problem, and derive solutions for objective functions that reflect various practical aspects of developable surface design, e.g., minimizing the arc length of the base curve, keeping the line of regression distant from the base curve, and approximating a given arbitrary ruled surface by a developable surface. By drawing upon the large body of available results for the optimal control of linear systems with quadratic criteria, our approach provides a flexible method for designing developable surfaces that are optimized for various criteria.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
