By Patria Dobbins
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The painter's algorithm sorts all the polygons in a scene by their depth and then paints them in this order, farthest to closest. It will paint over the parts that are normally not visible — thus solving the visibility problem — at the cost of having painted redundant areas of distant objects. The distant mountains are painted first, followed by the closer meadows; finally, the closest objects in this scene, the trees, are painted. Overlapping polygons can cause the algorithm to fail The algorithm can fail in some cases, including cyclic overlap or piercing polygons.
The knot vector The knot vector is a sequence of parameter values that determines where and how the control points affect the NURBS curve. The number of knots is always equal to the number of control points plus curve degree plus one. The knot vector divides the parametric space in the intervals mentioned before, usually referred to as knot spans. Each time the parameter value enters a new knot span, a new control point becomes active, while an old control point is discarded. It follows that the values in the knot vector should be in nondecreasing order, so (0, 0, 1, 2, 3, 3) is valid while (0, 0, 2, 1, 3, 3) is not.
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. The given "mesh" function is then continuously evaluated and an optimized version is produced according to a tradeoff between visual quality and performance.
3D Rendering In Computer Graphics by Patria Dobbins