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control polygons
Key for improvement is developing methods to calculate tangent vectors and two coefficients for intermediate Bezier points, which allow higher flexibility of the control polygons than that of the Bezier spline fitting.
      
Furthermore, using those linear non-self-intersecting offsets as the legs of NURBS control polygons, NURBS-format tool paths can be smoothly reconstructed with G1-continuity, no overcutting, no cusps, and global error control.
      
The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form
      
This paper presents a short, simple, and general proof showing that the control polygons generated by subdivision and degree elevation converge to the underlying splines, box-splines, or multivariate Bézier polynomials, respectively.
      
Bernstein bases, control polygons and corner-cutting algorithms are defined for C1 Merrien's curves introduced in [7].
      
It is known that the sequence of control polygons of a Bézier-De Casteljau curve or surface obtained by the "degree elevation" process converges towards the underlying curve and surface.
      
It is known that non-self-intersecting regular Bézier curves have non-self-intersecting control polygons, after sufficiently many uniform subdivisions.
      
A more general property is fairness,, which refers to the overall smoothness of the curves resulting from arbitrary control polygons.
      
As stated, linear interpolation of the control polygons and control meshes of freeform curves and surfaces is a common practice.
      
Figure 5 on the next page shows 4 control polygons and their corresponding zier curves.
      
However, figure 7a shows how removal of the LCA can lead to ambiguity problems if the original control polygons only contains three control points.
      
One highly desirable property of a spline is that all control polygons yield interpolating curves.
      
Removal of the LCA can lead to ambiguity problems if the original control polygons only contains three control points.
      
The functions also map the original control polygon to the control polygons that generate each of the two subcurves.
      
The roundness property only applies to control polygons with points lying on a common circular arc.
      
Unfortunately, the percent cover of the weed-control polygons collected by field crews is generally not known and not constant.
      
 

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