1 / 8

Polygon Packing

Asanka Herath Buddhika Kottahachchi. Polygon Packing. What?. Given a set of polygons, determine a layout such that the rectangle enclosing them is minimal, allowing translation and rotation. Why?. It has important applications in the apparel industry

lassie
Download Presentation

Polygon Packing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Asanka HerathBuddhika Kottahachchi Polygon Packing

  2. What? • Given a set of polygons, determine a layout such that the rectangle enclosing them is minimal, allowing translation and rotation.

  3. Why? • It has important applications in the apparel industry • Pieces of material (polygons) need to be cut out of rolls of material to be assembled together as items of clothing • Considerable amounts of material is wasted as a result of not having an optimal layout for making the cuts • NP-hard problem. • Current approaches use heuristics with varying degrees of efficiency. Room for improvement.

  4. Exploiting Parallel Processing • Process multiple candidate layouts simultaneously • Split resources to work on different approaches (…) • Fast heuristics to determine initial layouts • Slower relaxed placement methods to optimize initial layouts • Share information about current bounds and current optimal solution to reduce search space • Implementation: C and MPI

  5. Anyone been here before? • Lots of existing literature • Referred to as • Nesting Problem • Marker Maker’s Problem • Many related problems (…) • Our method would follow work done by Benny Kaejr Nielsen and Allan Odgaard (Copenhagen, Denmark) • Commercial implementations (…) • At least one attempt at a parallel library for solving nesting problems

  6. Related problems • Can be categorized as • Decision Problems • Decide whether a given set of shapes fit within a given shape • Knapsack Problem • Given a set of shapes and a region, find a placement of a subset of shapes that maximizes the utilization (area covered) of the region. • Bin packing problem. • Given a set of shapes and a set of regions, minimize the number of regions needed to place all shapes. • Strip packing problem. • Given a set of shapes and a width W, minimize the length of a rectangular region with width W such that all shapes are contained in the region.

  7. Commercial Implementations

  8. Questions?

More Related