drygaq.blogg.se - Vb.net draw smooth curve

public static void GetCurveControlPoints(Point knots, / /// array must contain at least two points. / /// Get open-ended Bezier Spline Control Points.

Bezier Curve RepresentationĪ Bezier curve on a single interval is expressed as: Here, we'll deal with open-ended curves, but the same approach could be applied to the closed curves. I spent some time Googling for a code in any C-like language for a Bezier spline, but couldn't found any cool, ready-to-use code. The trick to making it a spline is to calculate control points in such a way that the whole spline curve has two continuous derivatives. Bezier curves start and end with two points often named “knots” the form of the curve is controlled by two more points known as “control points”.īezier spline is a sequence of individual Bezier curves joined to form a whole curve.

Bezier curve is a special representation of a cubic polynomial expressed in the parametric form (so it isn't the subject of single valued function restriction). On the other hand, the platform provides us with a suite of Bezier curve drawing methods. This implies that the function is single valued it isn't always appropriate.

Cubic spline algorithms are usually designed to deal with functions in the Cartesian coordinates, y=f(x).

So, to draw that spline, we have to invent an effective algorithm to approximate a cubic polynomial with polyline, which isn't trivial (word “effective” is a point!). NET Forms, or WPF do not provide methods to draw a piecewise cubic polynomial curve.

Cubic spline is a cubic polynomial, but Win32.

We could use it and draw the result of the interpolation, but there are some nasty drawbacks: The cubic spline variations, for example, give satisfactory results in most cases. And, very often, all we need is to draw the curve which passes through the points given and is smooth enough. Very often, we don't have any data to evaluate these additional parameters. Yes, we can draw a polyline, Bezier polyline, or a piece-wise cardinal spline, but they are all not what is desired: polyline isn't smooth with Bezier and cardinal spline, we have a headache with additional parameters like Bezier control points or tension. From time to time, I am faced with the question: how to draw a smooth curve through a set of 2D points? It seems strange, but we don't have out of the box primitives to do so.