Rotation matrix in C# draws a weird shape

I'm trying to translate a point around the circumference of a circle.

To test my code I just translate the point and draw a line from the centre to the translated point for each angle increment.

This should look like a bike wheel, however it looks more like a spade. Oddly, it appears the same whether I used radians or degrees in the Math functions.

for (double degrees = 0; degrees <= 360; degrees += 1)
{
    double radians = Math.PI * degrees / 180.0;
    Console.Write("degrees = " + degrees + " radians = " + radians);
    double sx = 0.0;
    double sy = -100.0;
    sx = ((sx * Math.Cos(radians)) + (sy * Math.Sin(ra开发者_StackOverflowdians)));
    sy = (-(sx * Math.Sin(radians)) + (sy * Math.Cos(radians)));

    Console.WriteLine(", sx = " + sx + ", sy = " + sy);

    g.DrawLine(new Pen(Brushes.GhostWhite), 200, 200, (int)sx+200, (int)sy+200);
}

---

So your maths is right. You do calculate the rotation using this matrix.

[cos(r)  sin(r)]
[-sin(r) cos(r)]

But your coding is wrong!

You have already changed sx to the rotated value, before you use it to calculate sy!

You are performing calculations on x and y sequentially, whereas in a matrix, they are done simultaneously. So your y coordinate is computed incorrectly, using a sheared coordinate system, as it were...

You need to do this:

double sx = 0.0;
double sy = -100.0;
double nsx = ((sx * Math.Cos(radians)) + (sy * Math.Sin(radians)));
double nsy = (-(sx * Math.Sin(radians)) + (sy * Math.Cos(radians)));

g.DrawLine(new Pen(Brushes.GhostWhite), 200, 200, (int)nsx+200, (int)nsy+200);

---

    double radius = 200;

    for (double degrees = 0; degrees <= 360; degrees += 1)
    {
        double radians = Math.PI * degrees / 180.0;

        int sx = (int) (200 +  radius * Math.Cos(radians));
        int sy = (int) (200 +  radius * Math.Sin(radians));

        g.DrawLine(new Pen(Brushes.GhostWhite), 200, 200, sx, sy);
    }

---

I think it's purely a mathematical issue. Try:

double radius = 100;
double sx = radius * Math.Cos(radians);
double sy = radius * Math.Sin(radians);