How to draw bezier curve by several points?

Question

I have several points, and I try to draw Bezier curve using code below

 PathFigure pf = new PathFigure(points.From, ps, false); //ps - list of Bezier segment         


        

Answer 1

The line you're getting is the union of three distinct Bezier curves - one for each group of three points. (One for each "Bezier segment"?)

If you want a single smooth curve, you need to pass your 9 (or more) points as a single collection of points (single "Bezier segment"?), not as groups of three points.

Edit: Apparently BezierSegment only supports three points, so no wonder this doesn't work. Even 'PolyBezierSegment' just gives a collection of Bezier segments rather than a single smooth Bezier...

So since WPF doesn't give you anything useful, I knocked something together using the maths here. It's a numeric solution, but it seems to be pretty performant even with enough points to look nice and smooth:

PolyLineSegment GetBezierApproximation(Point[] controlPoints, int outputSegmentCount)
{
    Point[] points = new Point[outputSegmentCount + 1];
    for (int i = 0; i <= outputSegmentCount; i++)
    {
        double t = (double)i / outputSegmentCount;
        points[i] = GetBezierPoint(t, controlPoints, 0, controlPoints.Length);
    }
    return new PolyLineSegment(points, true);
}

Point GetBezierPoint(double t, Point[] controlPoints, int index, int count)
{
    if (count == 1)
        return controlPoints[index];
    var P0 = GetBezierPoint(t, controlPoints, index, count - 1);
    var P1 = GetBezierPoint(t, controlPoints, index + 1, count - 1);
    return new Point((1 - t) * P0.X + t * P1.X, (1 - t) * P0.Y + t * P1.Y);
}

Using this,

private void Grid_Loaded(object sender, RoutedEventArgs e)
{
    Point[] points = new[] { 
            new Point(0, 200),
            new Point(0, 0),
            new Point(300, 0),
            new Point(350, 200),
            new Point(400, 0)
        };
    var b = GetBezierApproximation(points, 256);
    PathFigure pf = new PathFigure(b.Points[0], new[] { b }, false);
    PathFigureCollection pfc = new PathFigureCollection();
    pfc.Add(pf);
    var pge = new PathGeometry();
    pge.Figures = pfc;
    Path p = new Path();
    p.Data = pge;
    p.Stroke = new SolidColorBrush(Color.FromRgb(255, 0, 0));
    ((Grid)sender).Children.Add(p);
}

gives