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curve

curve

[kurv]
curve, in mathematics, a line no part of which is straight; more generally, it is considered to be any one-dimensional collection of points, thus including the straight line as a special kind of curve. In analytic geometry a plane curve is usually considered as the graph of an equation or function, and the properties of curves are seen to depend largely on the degree of the equation in the case of algebraic curves (i.e., curves with algebraic equations) or on the particular function in the case of transcendental curves (i.e., curves whose equations are not algebraic). For examples of plane curves, see circle; ellipse; hyperbola; parabola. A twisted or skew curve is one that does not lie all in one plane, e.g., the helix, a curve having the shape of a wire spring. A thorough treatment of space curves requires the techniques of differential geometry.
Curve-fitting compaction is data compaction accomplished by replacing data to be stored or transmitted with an analytical expression.

Examples of curve-fitting compaction consisting of discretization and then interpolation are:

  1. Breaking of a continuous curve into a series of straight line segments and specifying the slope, intercept, and range for each segment
  2. Using a mathematical expression, such as a polynomial or a trigonometric function, and a single point on the corresponding curve instead of storing or transmitting the entire graphic curve or a series of points on it.

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