Rotate a point around another point

Question

I have a task to draw a specific graphic. As part of this task I need to rotate some dot's on 45 degrees.

I've spent already 2 days trying to calculate a formula, but just couldn't get it right. I've been searching all over the place including this particular website, I'm getting very close, but I'm still not there.

Here it is: I need to draw 4 different points

I have a specific formula to calculate there position, which is out of scope of the question, but here is what I'm getting as a result of it:

int radius = 576; int diameter = radius * 2; Point blueA = new Point(561, 273); Point greenB = new Point(273, 561); Point yellowC = new Point (849, 561); Point redD = new Point (561, 849); 

Now I need to rotate this dots on 45 degrees. I use the following code to achieve it:

double rotationAngle = 45; double rotationRadians = rotationAngle * (Math.PI / 180); int center = radius;     result.X = (int)(Math.Cos(rotationRadians) * ((double)result.X - (double)center) - (double)Math.Sin(rotationRadians) * ((double)result.Y - center) + (double)center); result.Y = (int)(Math.Sin(rotationRadians) * ((double)result.X - (double)center) + (double)Math.Cos(rotationRadians) * ((double)result.Y - center) + (double)center); 

But that's what I'm getting:

Any help would be much appreciated

Answer 1

The problem is int center = radius which you are setting int radius = 576. This doesn't make sense as surely you are rotating about a point that should have an x and y location.

Given you are rotating around the origin the center x and y should both be 0 not 576.

So, given that, try this.

/// <summary> /// Rotates one point around another /// </summary> /// <param name="pointToRotate">The point to rotate.</param> /// <param name="centerPoint">The center point of rotation.</param> /// <param name="angleInDegrees">The rotation angle in degrees.</param> /// <returns>Rotated point</returns> static Point RotatePoint(Point pointToRotate, Point centerPoint, double angleInDegrees) {     double angleInRadians = angleInDegrees * (Math.PI / 180);     double cosTheta = Math.Cos(angleInRadians);     double sinTheta = Math.Sin(angleInRadians);     return new Point     {         X =             (int)             (cosTheta * (pointToRotate.X - centerPoint.X) -             sinTheta * (pointToRotate.Y - centerPoint.Y) + centerPoint.X),         Y =             (int)             (sinTheta * (pointToRotate.X - centerPoint.X) +             cosTheta * (pointToRotate.Y - centerPoint.Y) + centerPoint.Y)     }; } 

Use like so.

Point center = new Point(0, 0);  Point newPoint = RotatePoint(blueA, center, 45); 

Obviously if the center point is always 0,0 then you can simplify the function accordingly, or else make the center point optional via a default parameter, or by overloading the method. You would also probably want to encapsulate some of the reusable math into other static methods too.

e.g.

/// <summary> /// Converts an angle in decimal degress to radians. /// </summary> /// <param name="angleInDegrees">The angle in degrees to convert.</param> /// <returns>Angle in radians</returns> static double DegreesToRadians(double angleInDegrees) {    return angleInDegrees * (Math.PI / 180); }  /// <summary> /// Rotates a point around the origin /// </summary> /// <param name="pointToRotate">The point to rotate.</param> /// <param name="angleInDegrees">The rotation angle in degrees.</param> /// <returns>Rotated point</returns> static Point RotatePoint(Point pointToRotate, double angleInDegrees) {    return RotatePoint(pointToRotate, new Point(0, 0), angleInDegrees); } 

Use like so.

Point newPoint = RotatePoint(blueA, 45); 

Finally, if you are using the GDI you can also simply do a RotateTransform. See: http://msdn.microsoft.com/en-us/library/a0z3f662.aspx

Graphics g = this.CreateGraphics(); g.TranslateTransform(blueA); g.RotateTransform(45); 

Answer 2

You're math looks weird to me. I think dx = r*Cos(theta) and dy = r*Sin(theta).

Here's a little program I wrote because this was bothering me, and I haven't done math is years.

Point center = new Point() { X = 576, Y = 576 };  Point previous = new Point() { X = 849, Y=561 }; double rotation = 45; double rotationRadians = rotation * (Math.PI / 180);  //get radius based on the previous point and r squared = a squared + b squared double r = Math.Sqrt(Math.Pow(previous.X - center.X, 2) + Math.Pow(previous.Y - center.Y, 2)); Console.WriteLine("r = " + r.ToString());  //calculate previous angle double previousAngle = Math.Atan((previous.Y - center.Y) / (previous.X - center.X)); Console.WriteLine("Previous angle: " + previousAngle.ToString());  double newAngle = previousAngle + rotationRadians;  Point newP = new Point(); newP.X = center.X + r * Math.Cos(newAngle); newP.Y = center.Y + r * Math.Sin(newAngle);  Console.WriteLine("(" + newP.X.ToString() + ", " + newP.Y.ToString() + ")");  Console.ReadLine();