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The fair polygon partitioning problem [20] is to partition a (convex) polygon into (convex) pieces with an equal perimeter and equal area (this is a special case of fair cake-cutting). Any convex polygon can be easily cut into any number n of convex pieces with an area of exactly 1/n. However, ensuring that the pieces have both equal area and ...
Breaking a polygon into monotone polygons. A simple polygon is monotone with respect to a line L, if any line orthogonal to L intersects the polygon at most twice. A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone.
Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given: A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers ...
However, other volume based representations (e.g. constructive solid geometry) or point based representations (point clouds) can be used to represent shape. Once the objects are given, either by modeling (computer-aided design), by scanning or by extracting shape from 2D or 3D images, they have to be simplified before a comparison can be achieved.
David Kennison's Polypack, a FORTRAN library based on the Vatti algorithm. Klamer Schutte's Clippoly, a polygon clipper written in C++. Michael Leonov's poly_Boolean, a C++ library, which extends the Schutte algorithm. Angus Johnson's Clipper, an open-source freeware library (written in Delphi, C++ and C#) that's based on the Vatti algorithm.
Binary space partitioning is a generic process of recursively dividing a scene into two until the partitioning satisfies one or more requirements. It can be seen as a generalization of other spatial tree structures such as k -d trees and quadtrees , one where hyperplanes that partition the space may have any orientation, rather than being ...
In order to cut a shape into smaller pieces, you'll simply need to click and hold as you drag your mouse across the screen, letting go after you've created a straight line.
This was an open problem until 2007, when an efficient algorithm based on dynamic programming was published. [ 14 ] The minimum number of knife changes problem (for the one-dimensional problem): this is concerned with sequencing and permuting the patterns so as to minimise the number of times the slitting knives have to be moved.