Concepts inGeometric constraints solving: some tracks
Coordinate-free
A coordinate-free, or component-free, treatment of a scientific theory or mathematical topic develops its ideas without reference to any particular coordinate system. Coordinate-free treatments generally allow for simpler systems of equations, allowing greater mathematical elegance at the cost of some abstraction from the detailed formulae needed to evaluate these equations within a particular system of coordinates.
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Solution set
In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities. For example, for a set of polynomials over a ring, the solution set is the subset of on which the polynomials all vanish (evaluate to 0), formally
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Fractal
A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far" Fractals may be exactly the same at every scale, or as illustrated in Figure 1, they may be nearly the same at different scales.
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Geometry
Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science emerging in the West as early as Thales (6th Century BC).
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Interval arithmetic
Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s as an approach to putting bounds on rounding errors and measurement errors in mathematical computation and thus developing numerical methods that yield reliable results. Very simply put, it represents each value as a range of possibilities.
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