Nesting algorithms are used to make the
most efficient use of material or space by evaluating many different possible combinations via
recursion
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...
.
#Linear (1-dimensional): The simplest of the
algorithms
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing c ...
illustrated here. For an existing set there is only one position where a new cut can be placed – at the end of the last cut. Validation of a combination involves a simple Stock - Yield -
Kerf
A saw is a tool consisting of a tough blade, wire, or chain with a hard toothed edge. It is used to cut through material, very often wood, though sometimes metal or stone. The cut is made by placing the toothed edge against the material and mov ...
= Scrap calculation.
#Plate (2-dimensional): These algorithms are significantly more complex. For an existing set, there may be as many as eight positions where a new cut may be introduced next to each existing cut, and if the new cut is not perfectly square then different rotations may need to be checked. Validation of a potential combination involves checking for intersections between
two-dimensional
In mathematics, a plane is a Euclidean (flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as s ...
objects.
#Packing (3-dimensional): These algorithms are the most complex illustrated here due to the larger number of possible combinations. Validation of a potential combination involves checking for intersections between
three-dimensional
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
objects.
References
Geometric algorithms
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