Creating a Consistent 3-D Virtual Last for Problems in the Shoe Industry

  • Dan Braha
  • Oded Maimon
Part of the Applied Optimization book series (APOP, volume 17)


In the shoe design industry, there are hundreds of standard lasts (3-D models of a foot) available [2, 3]. Shoe companies select specific lasts to serve as their models for specific sizes. Computer-aided design software for the shoe industry, then, is able to take a design (drawn on a 2-D flattened approximation of the last) and grade (scale) it to any of the numerous standard lasts. They are not able, however, to create a new pattern from an arbitrary set of measurements. In shoe design, the ability to quickly and easily customize each pair of shoes for an individual customer could be turned into a large market advantage. Many aspects of the required technology are already available (e.g., information systems, CNC machines). The problem is then reduced to one of computing the desired shoe pattern, given a person’s foot measurements and a similar prototype, such that the new pattern satisfies the measurements, but is still similar to the prototype. In such a computerized domain, there is a need for a virtual model of a last that can adjust to any desired size. In this chapter, an approach for creating a virtual last is demonstrated in which a series of 22 3-D Bezier curves are constrained to satisfy a set of measurements given by the designer. As there are typically numerous curves which can satisfy a given system of constraints, the COAST methodology for design consistency developed in Chapters 14 and 15 is implemented to ensure convergence to the intended solution.


Bezier Curve Individual Customer Connectivity Constraint Constraint Point Gradient Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    New York Times, March 20, 1996, Section D, page 1.Google Scholar
  2. 2.
    Karl C. Adrian, American Last Making, Shoe Trades Publishing, Massachusetts, 1991.Google Scholar
  3. 3.
    Michael H. Sharp, The Pattern Cutter’s Handbook, Footwear OPEN TECH Unit, England, 1994.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Dan Braha
    • 1
  • Oded Maimon
    • 2
  1. 1.Department of Industrial EngineeringBen Gurion UniversityBeer ShevaIsrael
  2. 2.Department of Industrial EngineeringTel-Aviv UniversityTel-AvivIsrael

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