从矩阵变换计算角度

Question

我有以下代码行:我在不知道值(多少度)的情况下对矩形应用了少量旋转.现在我想在2D中获得旋转或元素角度.

Rectangle element = (Rectangle)sender;
MatrixTransform xform = element.RenderTransform as MatrixTransform;
Matrix matrix = xform.Matrix;
third.Content = (Math.Atan(matrix.M21 / matrix.M22)*(180/Math.PI)).ToString();

and the matrix is like following
|M11 M12 0|
|M21 M22 0|
|dx  dy  1|  which is Transformation Matrix I guess !!

这似乎不是正确的价值.我希望得到0到360度的角度

Answer 1

你可以用这个:

var x = new Vector(1, 0);
Vector rotated = Vector.Multiply(x, matrix);
double angleBetween = Vector.AngleBetween(x, rotated);

这个想法是:

1. 我们创建了一个tempvector(1,0)
2. 我们在矢量上应用矩阵变换并获得旋转的临时矢量
3. 我们计算原始和旋转的临时矢量之间的角度

你可以玩这个:

[TestCase(0,0)]
[TestCase(90,90)]
[TestCase(180,180)]
[TestCase(270,-90)]
[TestCase(-90, -90)]
public void GetAngleTest(int angle, int expected)
{
    var matrix = new RotateTransform(angle).Value;
    var x = new Vector(1, 0);
    Vector rotated = Vector.Multiply(x, matrix);
    double angleBetween = Vector.AngleBetween(x, rotated);
    Assert.AreEqual(expected,(int)angleBetween);
}

Answer 2

备查:

这将为您提供以弧度为单位的变换矩阵的旋转角度:

var radians = Math.Atan2(matrix.M21, matrix.M11);

如果需要,你可以将弧度转换为度数:

var degrees = radians * 180 / Math.PI;