(1) In mathematics, a curve is the set of all points that are valid solutions to a specific equation. This definition allows for infinite, fractal and disjointed curves. Mathematical curve equations may be both implicit and explicit.

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(2) In CAD, a finite one-dimensional object, which may be bent or kinked. Curves may be instances of primitive types such as lines, circles or polygons, or they may be freeform types such as polylines, beziers or nurbs.

Note that this is significantly dissimilar to the mathematical definition. In CAD, curves do not branch or contain gaps.