MongoDB $atan Operator

Posted in mongoDB Tutorial

Updated on Nov 24, 2024

By Mari Selvan

👁️ 21 - Views

⏳ 4 mins

💬 1 Comment

Photo Credit to CodeToFun

🙋 Introduction

In MongoDB's aggregation framework, the $atan operator offers a powerful tool for performing trigonometric computations on numerical data. By computing the arctangent (inverse tangent) of a given number, this operator enables a wide range of applications in fields such as geometry, physics, and engineering.

Let's dive into the details of how the $atan operator can be effectively utilized within MongoDB's aggregation pipelines.

💡 Syntax

The syntax for the $atan method is straightforward:

syntax.js

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{ $atan: <expression> }

$atan: This operator indicates that the subsequent operation will involve computing the arctangent.
<expression>: This represents the numerical expression for which the arctangent will be calculated. It could be a field reference, a mathematical expression, or a value.

📝 Example

⌨️ Input

Consider a collection named vectors containing documents with fields x and y, representing vector components. Here are sample documents from the vectors collection:

Input

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[
  { "_id": ObjectId("609c26812e9274a86871bc6a"), "x": 3, "y": 4 },
  { "_id": ObjectId("609c26812e9274a86871bc6b"), "x": -2, "y": 2 },
  { "_id": ObjectId("609c26812e9274a86871bc6c"), "x": 1, "y": -1 }
]

🔄 Aggregation

Suppose we want to calculate the angle (in radians) of each vector relative to the x-axis. Here's how you can achieve this using the $atan operator:

example.js

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db.vectors.aggregate([
  {
    $project: {
      angleRadians: { $atan: { $divide: ["$y", "$x"] } }
    }
  }
])

🧩 Explanation

$project: This stage reshapes documents to include computed fields.
$divide: This divides the y component by the x component to compute the slope of the vector.
$atan: Computes the arctangent of the result, yielding the angle (in radians) relative to the x-axis.

When discussing how the above aggregation works:

For the first document:
- x: 3 and y: 4
- angleRadians: atan(4/3) ≈ 0.93 radians
For the second document:
- x: -2 and y: 2
- angleRadians: atan(2/-2) ≈ -0.79 radians
For the third document:
- x: 1 and y: -1
- angleRadians: atan(-1/1) ≈ -0.79 radians

💻 Output

Now, let's take a look at the output generated by the aggregation pipeline:

Output

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{ "_id": ObjectId("609c26812e9274a86871bc6a"), "angleRadians": 0.93 }
{ "_id": ObjectId("609c26812e9274a86871bc6b"), "angleRadians": -0.79 }
{ "_id": ObjectId("609c26812e9274a86871bc6c"), "angleRadians": -0.79 }

📚 Use Cases

Geometric Computations:

The $atan operator facilitates angle calculations, making it useful for various geometric applications.
Engineering Analysis:

When analyzing vectors or orientations in engineering projects, the $atan operator aids in precise computations.
Trigonometric Analysis:

MongoDB's $atan operator supports trigonometric analysis in scientific and engineering domains, contributing to tasks such as signal processing and data visualization.

🎉 Conclusion

The $atan operator in MongoDB's aggregation framework offers a valuable solution for computing arctangents within aggregation pipelines. Whether you're analyzing geometric data, engineering simulations, or scientific experiments, mastering the usage of $atan enhances your ability to perform accurate trigonometric computations and gain deeper insights into your datasets.

With its intuitive syntax and versatile applications, the $atan operator proves to be an indispensable asset for handling numerical data effectively within MongoDB. Incorporate it into your aggregation pipelines to unlock new dimensions of data analysis and achieve greater precision in your computations.