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By Patria Dobbins

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Note that within the interval the polynomial nature of the basis functions and the linearity of the construction make the curve perfectly smooth, so it is only at the knots that discontinuity can arise. The fact that a single control point only influences those intervals where it is active is a highly desirable property, known as local support. In modelling, it allows the changing of one part of a surface while keeping other parts equal. Adding more control points allows better approximation to a given curve, although only a certain class of curves can be represented exactly with a finite number of control points.

The circle is composed of four quarter circles, tied together with double knots. Although double knots in a third order NURBS curve would normally result in loss of continuity in the first derivative, the control points are positioned in such a way that the first derivative is continuous. ) The curve represents a circle exactly, but it is not exactly parametrized in the circle's arc length. This means, for example, that the point at t does not lie at (sin(t),cos(t)) (except for the start, middle and end point of each quarter circle, since the representation is symmetrical).

The first is based on subdividing the space in a finite amount of regions, each with a certain level of detail. The result is discrete amount of detail levels, from which the name Discrete LoD (DLOD). There's no way to support a smooth transition between LOD levels at this level, although alpha blending or morphing can be used to avoid visual popping. The latter considers the polygon mesh being rendered as a function which must be evaluated requiring to avoid excessive errors which are a function of some heuristic (usually distance) themselves.

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