C# 将角度（以度为单位）转换为向量
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Convert an angle in degrees, to a vector
提问by Rory Becker
I'm doing some game programming. FWIW I'm using XNA, but I'm doubtful that this is relevant.
我正在做一些游戏编程。FWIW 我正在使用 XNA，但我怀疑这是否相关。
I'd like to convert degrees to a directional vector (ie X and Y) with magnitude 1.
我想将度数转换为幅度为 1 的方向向量（即 X 和 Y）。
My origin (0,0) is in the upper left.
我的原点 (0,0) 在左上角。
So I'd like 0 degrees to convert to [0, -1]
所以我想将 0 度转换为 [0, -1]
I thought the best way to do this was to take my definition of North/Up and rotate it using a matrix, but this does not seem to be working.
我认为最好的方法是采用我对北/上的定义并使用矩阵旋转它，但这似乎不起作用。
Here is the Code...
这是代码...
public class Conversion
{
public static Vector2 GetDirectionVectorFromDegrees(float Degrees)
{
Vector2 North= new Vector2(0, -1);
float Radians = MathHelper.ToRadians(Degrees);
var RotationMatrix = Matrix.CreateRotationZ(Radians);
return Vector2.Transform(North, RotationMatrix);
}
}
... and here are my unit tests...
...这是我的单元测试...
[TestFixture]
public class Turning_Tests
{
[Test]
public void Degrees0_Tests()
{
Vector2 result = Conversion.GetDirectionVectorFromDegrees(0);
Assert.AreEqual(0, result.X);
Assert.AreEqual(-1, result.Y);
}
[Test]
public void Degrees90_Tests()
{
Vector2 result = Conversion.GetDirectionVectorFromDegrees(90);
Assert.AreEqual(1, result.X);
Assert.AreEqual(0, result.Y);
}
[Test]
public void Degrees180_Tests()
{
Vector2 result = Conversion.GetDirectionVectorFromDegrees(180);
Assert.AreEqual(0, result.X);
Assert.AreEqual(1, result.Y);
}
[Test]
public void Degrees270_Tests()
{
Vector2 result = Conversion.GetDirectionVectorFromDegrees(270);
Assert.AreEqual(-1, result.X);
Assert.AreEqual(0, result.Y);
}
}
Am I approaching this all wrong? Should I be using a matrix? Have I screwed up and converted from degrees to radians in the wrong place?
我这样做是错的吗？我应该使用矩阵吗？我是否在错误的地方搞砸并从度数转换为弧度？
I've seen suggestions that this can be done using code like:
我已经看到可以使用以下代码完成此操作的建议：
new Vector2((float)Math.Cos(Angle), (float)Math.Sin(Angle));
...or sometimes...
……或者有时……
new Vector2((float)Math.Sin(Angle), (float)Math.Cos(Angle));
However these don't seem to work either
然而，这些似乎也不起作用
Can someone put me on the right path... or better yet give me some code which causes the 4 provided unit tests to path?
有人可以让我走上正确的道路......或者更好地给我一些代码，导致 4 个提供的单元测试通过？
Many thanks in advance.
提前谢谢了。
采纳答案by Jeppe Stig Nielsen
Just use:
只需使用：
new Vector2((float)Math.Cos(radians), (float)Math.Sin(radians))
Be sure to convert from degrees to radians with this approach too.
一定要使用这种方法将度数转换为弧度。
This uses the mathematician's convention of starting from [1, 0]and going in the direction towards [0, 1](that is counter-clockwise with the orientation that mathematicians use for the two axes).
这使用了数学家的惯例，即从[1, 0]朝向的方向开始和前进[0, 1]（即逆时针方向，数学家用于两个轴的方向）。
To use instead your convention (starting from [0, -1]and going in the direction of [1, 0]) you need:
要使用您的约定（从 开始[0, -1]并朝着 方向[1, 0]），您需要：
new Vector2((float)Math.Sin(radians), -(float)Math.Cos(radians))
Note that your conversion from degrees to radians can never be exact (it involves something with π). You should allow for some tolerance in your tests. Also, if you use doubleinstead of floatfor the radians, you will have some extra precision in the intermediate calculation.
请注意，从度数到弧度的转换永远不可能精确（它涉及到π）。您应该在测试中允许一些容忍度。此外，如果您使用double而不是floatfor radians，您将在中间计算中获得一些额外的精度。
