如何解释 Math.Acos() 报告无效输入的情况？
嘿大家。我正在计算两个向量之间的角度，有时当 Math.Acos() 的输入超出余弦范围（-1 > 输入 && 输入 > 1）时，它会返回 NaN。这到底是什么意思？有人能够解释发生了什么事吗？任何帮助表示赞赏！
这是我的方法：
public double AngleBetween(vector b)
{
var dotProd = this.Dot(b);
var lenProd = this.Len*b.Len;
var divOperation = dotProd/lenProd;
// http://msdn.microsoft.com/en-us/library/system.math.acos.aspx
return Math.Acos(divOperation) * (180.0 / Math.PI);
}
这是我对 Dot 和 Len 的实现：
public double Dot(vector b)
{
// x's and y's are lattitudes and longitudes (respectively)
return ( this.From.x*b.From.x + this.From.y*b.From.y);
}
public double Len{
get
{
// geo is of type SqlGeography (MS SQL 2008 Spatial Type) with an SRID of 4326
return geo.STLength().Value;
}
}
Hey all. I'm computing the angle between two vectors, and sometimes Math.Acos() returns NaN when it's input is out of bounds (-1 > input && input > 1) for a cosine. What does that mean, exactly? Would someone be able to explain what's happening? Any help is appreciated!
Here's my method:
public double AngleBetween(vector b)
{
var dotProd = this.Dot(b);
var lenProd = this.Len*b.Len;
var divOperation = dotProd/lenProd;
// http://msdn.microsoft.com/en-us/library/system.math.acos.aspx
return Math.Acos(divOperation) * (180.0 / Math.PI);
}
Here's my implementation of Dot and Len:
public double Dot(vector b)
{
// x's and y's are lattitudes and longitudes (respectively)
return ( this.From.x*b.From.x + this.From.y*b.From.y);
}
public double Len{
get
{
// geo is of type SqlGeography (MS SQL 2008 Spatial Type) with an SRID of 4326
return geo.STLength().Value;
}
}
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您的向量
divOperation结果是divOperationdivOperationdivOperationdivOperation-1或> 1？那么我认为你应该检查你的Dot和Len的实现。You have vectors for which
divOperationturns out to be < -1 or > 1? Then I think you should check your implementations ofDotandLen.由于角度的 Cos 始终在 -1 和 +1 之间，因此无法计算该范围之外的值的反函数 (Acos)，或者这意味着您将 NaN 传递给了 ACos 函数。
我怀疑在这种情况下是后者 - 你的长度之一可能为零。
Since the Cos of an angle is always between -1 and +1 there is no way to compute the inverse function (Acos) of a value outside that range OR it means you passed NaN to the ACos function.
I suspect in this case it's the latter - one of your lengths is probably zero.
NaN 表示“不是数字”。从数学上讲，你不能取 [-1, 1] 范围之外的数字的反余弦（或者也许你可以，但结果很复杂——我不记得了）所以尝试这样做的结果是根本没有任何数字。
NaN means "not a number". Mathematically, you can't take the arccosine of a number that is outside the range [-1, 1] (or maybe you can but the result is complex -- I don't remember) so the result of trying to do that is not any number at all.