Curves Knot vector

The entire parameter range of the curve can also be divided unequally amongst segments. Decreasing the parameter values along a knot vector is not allowed ... 

When parameter intervals along the knot vector are equal, the B-spline curve is uniform-. 

A B-spline curve represented by a knot vector in which parameter subrange values are repeated, is periodic. It can be... 

The B-spline is non-periodic when parameter ranges are equally distributed for inner segments, but intervals are repeated at the beginning and the end of the knot vector. A span may have the same parameter range as the previous span so that knot values are repeated. These are non-periodic curves. The number of repetitions is called the multiplicity. The maximum allowed number of repetitions is the class of the curve. A zero parameter range is allowed for a span. Examples of knot vectors for non-periodic B-spline curves of different degrees with the maximum allowed multiplicity are as follows ... 

Figure 1. One view of the backbone structure of the pancreatic trypsin inhibitor (left-hand side), and its simplification by disregarding the "marginal crossings". The space curve r(t) is characterized by the knot vector K, and the simplified curve rf(t) by vector Kt...

Figure 2. Schematic representation of the characterization of the folding pattern of a space curve r(t), associated with a configuration Rj. The left-hand-side drawing represents the sphere S enclosing the space curve r. To the right we indicate how the sphere can be subdivided into regions according to the shape classification of the space curve. Each of the letters indicates a different shape type of the shape descriptor (e.g., a new knot vector K).

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