I posted a previous question about generating a bezier curve based on only the start and end points, and I was able thanks to the answers in that create a bezier curve using the information I have.
This is the code that allows me to draw the types of curve that I want on a form.
private void Form1_Paint(object sender, System.Windows.Forms.PaintEventArgs e)
{
Random rnd = new Random();
Point startp = new Point(rnd.Next(0, this.Width), rnd.Next(0, this.Height));
Point endp = new Point(rnd.Next(0, this.Width), rnd.Next(0, this.Height));
int xMod = 0;
int yMod = 0;
if (startp.X > endp.X) {
xMod = -1;
} else {
xMod = 1;
}
if (startp.Y > endp.Y) {
yMod = 1;
} else {
yMod = -1;
}
Point control1p = new Point(endp.X + (rnd.Next(20, 50) * xMod), endp.Y + (rnd.Next(20, 50) * yMod));
Point control2p = new Point(endp.X + (rnd.Next(5, 20) * xMod), endp.Y + (rnd.Next(5, 20) * yMod));
Point[] pts = {
startp,
control1p,
control2p,
endp
};
Pen dashed_pen = new Pen(Color.Black, 0);
dashed_pen.DashStyle = Drawing2D.DashStyle.Dash;
for (int i = 0; i <= 2; i++) {
e.Graphics.DrawLine(dashed_pen, pts(i), pts(i + 1));
}
e.Graphics.SmoothingMode = Drawing2D.SmoothingMode.HighQuality;
Pen bez_pen = new Pen(Color.Black, 3);
e.Graphics.DrawBezier(bez_pen, pts(0), pts(1), pts(2), pts(3))
}
Is there a way, or can someone help me with returning all the points that form the curve? I'd like for each point of a curve calculated from those points to be returned in an array of points, but I'm having no luck figuring it out, and haven't been able to find a similar solution on stackoverflow or google in general.
Thanks.
What you want to do is to convert a Bezier Curve (Cubic from the looks of it) into a Polyline
Use the Equation on this page ...Value of t
should be between 0 to 1
...Calculate all values of Bx(t)
and By(t)
by using the equation for values of t in increments of "0, 0.01, 0.02....1"
(Convert them to integers
of course) The smaller your increments, the more accurate your points will be.
Here's a C Sample of the DeCasteljau Algorithm (almost the same procedure, but its a bit optimized i believe) :)
Maxim Shemanarev在“反谷物几何”页面: Bezier曲线的自适应细分中描述了用于创建具有最佳点数的平滑Bezier曲线的完美算法。
It may help if you use a lerp or float t derivatives in-between the draw bezier. I've found it helps with accuracy; considering the number of float calcs .
I know this is an old post, but, having found none of the current answers all that satisfying, hopefully others will get some use out of the following:
using System.Collections.Generic;
using System.Drawing;
public List<Point> CubicBezierToPoints(Point P0, Point P1, Point P2, Point P3, double step = 0.01)
{
var pointList = new List<Point>();
for (var t = 0.00; t <= 1; t += step)
{
var x = Math.Pow(1 - t, 3) * P0.X + 3 * Math.Pow(1 - t, 2) * t * P1.X +
3 * (1 - t) * Math.Pow(t, 2) * P2.X + Math.Pow(t, 3) * P3.X;
var y = Math.Pow(1 - t, 3) * P0.Y + 3 * Math.Pow(1 - t, 2) * t * P1.Y +
3 * (1 - t) * Math.Pow(t, 2) * P2.Y + Math.Pow(t, 3) * P3.Y;
pointList.Add(new Point((int)x,(int)y));
}
return pointList;
}
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