Database Manual / Reference / Query Language / Expressions

$atan2 (expression operator)（表达式运算符）

$atan2

Returns the inverse tangent (arc tangent) of y / x, where y and x are the first and second values passed to the expression respectively.返回y/x的反正切（反正切），其中y和x分别是传递给表达式的第一个和第二个值。

$atan2 has the following syntax:

{ $atan2: [ <expression 1>, <expression 2> ] }

$atan2 takes any valid expression that resolves to a number.$atan2接受任何解析为数字的有效表达式。

$atan2 returns values in radians. Use $radiansToDegrees operator to convert the output value from radians to degrees.$atan2返回以弧度为单位的值。使用$radiansToDegrees运算符将输出值从弧度转换为度数。

By default $atan2 returns values as a double. $atan2 can also return values as a 128-bit decimal as long as the <expression> resolves to a 128-bit decimal value.默认情况下，$atan2返回double值。$atan2也可以返回128位十进制的值，只要<expression>解析为128位十进制值。

For more information on expressions, see Expressions.有关表达式的详细信息，请参阅表达式。

Behavior行为

null and NaN

If either argument given to $atan2 is null, the expression returns null. If either argument is NaN, the expression returns NaN. 如果给定给$atan2的任一参数为null，则表达式返回null。如果任一参数为NaN，则表达式返回NaN。If one argument is null and the other is NaN, the expression returns null.如果一个参数为null，另一个为NaN，则表达式返回null。

Example示例Results结果
{ $atan2: [ NaN, <value> ] }NaN
{ $atan2: [ <value>, NaN ] }NaN
{ $atan2: [ null, <value> ] }null
{ $atan2: [ <value>, null ] }null
{ $atan2: [ NaN, null ] }null
{ $atan2: [ null, NaN ] }null

Example示例

Inverse Tangent of Value in Degrees以度为单位的值反正切

The trigonometry collection contains a document that stores three sides of a right-angle triangle:trigonometry集合包含一个存储直角三角形三条边的文档：

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5")
}

The following aggregation operation uses the $atan2 expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$atan2表达式计算与side_a相邻的角度，并使用$addFields管道阶段将其添加到输入文档中。

db.trigonometry.aggregate([
  {
    $addFields : {
      "angle_a" : {
        $radiansToDegrees : {
          $atan2 : [ "$side_b", "$side_a" ]
        }
      }
    }
  }
])

The $radiansToDegrees expression converts the radian value returned by $atan2 to the equivalent value in degrees.$radiansToDegrees表达式将$atan2返回的弧度值转换为等效的度数值。

The command returns the following output:该命令返回以下输出：

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5"),
  "angle_a" : Decimal128("53.13010235415597870314438744090658")
}

Since side_b and side_a are stored as 128-bit decimals, the output of $atan2 is a 128-bit decimal.由于side_b和side_a存储为128位十进制，因此$atan2的输出是128位十进制。

Inverse Tangent of Value in Radians以弧度为单位的值的反正切

The trigonometry collection contains a document that stores three sides of a right-angle triangle:trigonometry集合包含一个存储直角三角形三条边的文档：

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5")
}

The following aggregation operation uses the $atan2 expression to calculate the angle adjacent to side_a and add it to the input document using the $addFields pipeline stage.以下聚合操作使用$atan2表达式计算与side_a相邻的角度，并使用$addFields管道阶段将其添加到输入文档中。

db.trigonometry.aggregate([
  {
    $addFields : {
      "angle_a" : {
        $atan2 : [ "$side_b", "$side_a" ]
      }
    }
  }
])

The command returns the following output:该命令返回以下输出：

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "side_a" : Decimal128("3"),
  "side_b" : Decimal128("4"),
  "hypotenuse" : Decimal128("5"),
  "angle_a" : Decimal128("0.9272952180016122324285124629224287")
}

Since side_b and side_a are stored as 128-bit decimals, the output of $atan2 is a 128-bit decimal.由于side_b和side_a存储为128位十进制，因此$atan2的输出是128位十进制。