围绕另一个点旋转一个点

Question

我有一个绘制特定图形的任务。作为这项任务的一部分，我需要在45度旋转一些点。

我已经花了2天时间尝试计算一个公式，但却无法做到正确。 我一直在寻找这个地方，包括这个特定的网站，我已经非常接近，但我仍然不在那里。

这是： 我需要绘制4个不同的点

我有一个特定的公式来计算位置，这超出了问题的范围，但这是我得到的结果：

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);

现在我需要将这个点旋转45度。我使用以下代码来实现它：

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);

但这就是我所得到的：

非常感谢任何帮助

Answer 1

问题是int center = radius您正在设置int radius = 576。这没有意义，因为你肯定在一个应该有x和y位置的点上旋转。

鉴于您在原点周围转动，中心x和y都应为0而不是576。

所以，考虑到这一点，试试这个。

/// <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)
    };
}

像这样使用。

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

显然，如果中心点始终为0,0，那么您可以相应地简化功能，或者通过默认参数或通过重载方法使中心点可选。您也可能希望将一些可重用的数学封装到其他静态方法中。

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);
}

像这样使用。

Point newPoint = RotatePoint(blueA, 45);

最后，如果您使用GDI，您也可以简单地执行RotateTransform。 请参阅：http://msdn.microsoft.com/en-us/library/a0z3f662.aspx

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

Answer 2

你的数学对我来说很奇怪。我认为dx = r * Cos（theta）和dy = r * Sin（theta）。

这是我写的一个小程序，因为这让我感到困扰，而且我没有做数学就是多年。

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();