Rotate Point around pivot Point repeatedly

Question

For a while now I've been using the following function to rotate a series of Points around a pivot point in various programs of mine.

private Point RotatePoint(Point point, Point pivot, double radians)
{
    var cosTheta = Math.Cos(radians);
    var sinTheta = Math.Sin(radians);

    var x = (cosTheta * (point.X - pivot.X) - sinTheta * (point.Y - pivot.Y) + pivot.X);
    var y = (sinTheta * (point.X - pivot.X) + cosTheta * (point.Y - pivot.Y) + pivot.Y);

    return new Point((int)x, (int)y);
}

This has always worked great, until I tried to rotate a shape repeatedly by small amounts. For example, this is what I get from calling it for 45° on a rectangular polygon made up of 4 points:

foreach (var point in points)
    Rotate(point, center, Math.PI / 180f * 45);

But this is what I get by calling rotate 45 times for 1°:

for (var i = 0; i < 45; ++i)
    foreach (var point in points)
        Rotate(point, center, Math.PI / 180f * 1)

As long as I call it only once it's fine, and it also seems like it gets gradually worse the lower the rotation degree is. Is there some flaw in the function, or am I misunderstanding something fundamental about what this function does?

How could I rotate repeatedly by small amounts? I could save the base points and use them to update the current points whenever the rotation changes, but is that the only way?

Answer 1

Your Point position measure is off because of the integer rounding generated by the RotatePoint() method.

A simple correction in the method returned value, using float coordinates, will produce the correct measure:

To test it, create a Timer and register its Tick event as RotateTimerTick():

Added a rotation spin increment (see the rotationSpin Field) to emphasize the motion effect.

PointF pivotPoint = new PointF(100F, 100F);
PointF rotatingPoint = new PointF(50F, 100F);
double rotationSpin = 0D;

private PointF RotatePoint(PointF point, PointF pivot, double radians)
{
    var cosTheta = Math.Cos(radians);
    var sinTheta = Math.Sin(radians);

    var x = (cosTheta * (point.X - pivot.X) - sinTheta * (point.Y - pivot.Y) + pivot.X);
    var y = (sinTheta * (point.X - pivot.X) + cosTheta * (point.Y - pivot.Y) + pivot.Y);

    return new PointF((float)x, (float)y);
}

private void RotateTimerTick(object sender, EventArgs e)
{
    rotationSpin += .5;
    
    if (rotationSpin > 90) rotationSpin = 0;
    rotatingPoint = RotatePoint(rotatingPoint, pivotPoint, (Math.PI / 180f) * rotationSpin);
    Panel1.Invalidate(new Rectangle(new Point(50,50), new Size(110, 110)));
}

private void Panel1_Paint(object sender, PaintEventArgs e)
{
    e.Graphics.SmoothingMode = SmoothingMode.AntiAlias;
    e.Graphics.FillEllipse(Brushes.White, new RectangleF(100, 100, 8, 8));
    e.Graphics.FillEllipse(Brushes.Yellow, new RectangleF(rotatingPoint, new SizeF(8, 8)));
}

This is the result using float values:

And this is what happens using integer values: