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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 ...
If the array abstraction does not support true negative indices (as for example the arrays of Ada and Pascal do), then negative indices for the bounds of the slice for a given dimension are sometimes used to specify an offset from the end of the array in that dimension. In 1-based schemes, -1 generally would indicate the second-to-last item ...
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.
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 ...
Let p be an interior point of the disk, and let n be a multiple of 4 that is greater than or equal to 8. Form n sectors of the disk with equal angles by choosing an arbitrary line through p, rotating the line n / 2 − 1 times by an angle of 2 π / n radians, and slicing the disk on each of the resulting n / 2 lines.
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.
A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packing must be without overlaps between goods and other goods or the container walls.
One can make a polyhedral Voronoi diagram mesh by dualizing a Delaunay triangulation simplicial mesh. One can create a cubical mesh by generating an arrangement of surfaces and dualizing the intersection graph; see spatial twist continuum. Sometimes both the primal mesh and its dual mesh are used in the same simulation; see Hodge star operator.