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What Is The Degree Of This Curve?


spinecad

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Does anyone know what kind of curve is this (e.g. Bezier, B-spline, or NURBS) and how many degrees are this curve?

 

Thank you

curve.jpg

Edited by spinecad
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The degree of a Bezier Curve is always 1 less than the number of control vertices. For instance a Bezier with 3 control vertices will be of Degree 2. This means that the largest exponent of the polynomial which computes the location of any point along the curve is 2.

 

A Parabola can be described by a degree 2 Bezier curve with 3 control vertices. It can also be described as:

F(x) = x^2.

 

B-Splines and NURBS are a composite type curve and, as such, can have a greater number of points for any particular degree. This piecewise/composite nature allows the points to be processed incrementally – that way a curve with more than 3 points can still be restricted to Degree 2 curvature. The polynomial computing a particular point along the curve, however, will only process 3 points at a time. The Knot Vector is the cadence for when one point is removed from the trio (in the case of a degree 2 spline) and the next in sequence is added.

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I am sorry because the image that should be attached, had not.

 

Now it's already uploaded.

 

Please take a look.

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The Properties Panel will show the degree of a spline when selected like that.

 

I read in the Properties windows, it says the degree of the curve is 3.

 

So, what kind of a curve is this (e.g. linear Bezier curve, quadratic Bezier curve, cubic Bezier curve, B-spline curve, NURBS curve)?

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By just looking at the image of the curve we could not say with complete certainty.

 

We know that NURBS curve designation is the Super Set (i.e., all AutoCAD Splines are NURBS) which contain all of the curve types you've listed. But I imagine that is not what you are getting at.

 

It has 6 control points - so if the Properties Panel says it is Degree 3 then we know it is not a Bezier (see post #2 above).

 

It may qualify as B-Spline. If it is then it has to be Non-Rational. The term Non-Rational means that all the weights for the Control Vertices are equal (usually equal to 1) If you look at the Properties Panels-Data Points-Weight and see a "-1", that indicates a Non-Rational curve. AutoCAD splines do not support negative weights - AutoCAD uses a "-1" to indicate that the curve is indeed non-rational (all the weighs are the same). If any of the CV has a weight other than 1 then the "minus sign" is removed. AutoCAD uses this convention to allow a user to know at a glance if a curve is Non-rational or not, without having to go through each vertex.

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