What Kind Of A Bezier Curve Is This?

[SEANT]

Look at the circles posted here:

 

http://www.cadtutor.net/forum/showthread.php?32338-Splined-Circles&p=211259&viewfull=1#post211259

 

 

These are examples of Nurbs curve that cannot be made via Bezier or B-Splines. The splined circles incorporate the “Non-uniform” and “Rational” qualifications that can only be expressed as NURBS.

 

 

The drawing file attached to this post also has examples of Non-Uniform (though the CYAN one is Uniform). They are Fit Point Splines that have had different Knot Parameterization applied.

 

 

Some data points are represented more accurately by the different parameterization. Likewise, a programmer may be inclined to set the parameters such that subsequent analysis of the curve is more easily predictable. For the 4 lobe circle I could have used 0,0,0,1,1,2,2,3,3,4,4,4 but the location on the curve was more easily predicted with the knot sequence 0,0,0,π/2, π/2, π, π, 3π/2, 3π/2, 2π, 2π, 2π.* Now a point on the curve has a parameter equal to the angle.

 

* 2π = 2Pi

Parameterization.dwg

Edited April 3, 2013 by SEANT

[spinecad]

How to define the knot vector?

[SEANT]

Similar to the question I asked here:

http://www.cadtutor.net/forum/showthread.php?78226-What-Kind-Of-A-Bezier-Curve-Is-This&p=528657&viewfull=1#post528657

 

Are you trying to define the Knot Vector via Programming? Perhaps while using the Managed ARX API as required by the Spline constructor:

 

public unsafe Spline(

int degree,

[MarshalAs(UnmanagedType.U1)] bool rational,

[MarshalAs(UnmanagedType.U1)] bool closed,

[MarshalAs(UnmanagedType.U1)] bool periodic,

Point3dCollection controlPoints,

DoubleCollection knots,

DoubleCollection weights,

double controlPointTolerance,

double knotTolerance

);

 

if so, there are numerous factors involved. All very specific to what is required by the programmer.

 

 

If an AutoCAD user (i.e., while drafting/modeling) needs control over the knot sequence definition, there are only a couple of options. While using the “Method = Fit” option of the Spline command, there is another option listing “Knots”. The three options there are Chord, Square root, and Uniform. Each method would produce different Knot sequences, and the Shape Manager module at the core of AutoCAD programming would calculate the appropriate Control Vertices to match the Fit Points. The difference in the Knot sequence is usually of no concern to the drafter/modeler, as long as the curve matches what is required for the drawing.

 

 

All splines created by the drafter/modeler via the “Method = CV” option of the Spline command will have a knot sequence that progresses in a uniform/incremental fashion. But, again, not really a concern for the drafter/modeler.

 

To avoid my posting irrelevant information, please specify the ultimate goal you are looking to achieve.