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Perspective Division

Implement a perspective division to project a 3D point onto a 2D plane, which is a fundamental concept in 3D to 2D Projections. This process is crucial in understanding how pinhole cameras form images.

The concept of perspective division is based on the idea that the projection of a 3D point $(X, Y, Z)$ onto a 2D plane results in a 2D point $(x, y)$ , where $x$ and $y$ are calculated using the formulas $x = \frac{X}{Z}$ and $y = \frac{Y}{Z}$ .

Start with a 3D point $(X, Y, Z)$ .
Apply the perspective division formula to obtain the 2D coordinates.

x = \frac{X}{Z}, \quad y = \frac{Y}{Z}

This technique is widely used in computer vision applications.

Example:

Input:

perspective_divide([10, 20, 5])

Output:

[2.0, 4.0]

Reasoning:

The input point is $(X, Y, Z) = (10, 20, 5)$ .
Apply perspective division to get the 2D $x$ coordinate: $x = \dfrac{X}{Z} = \dfrac{10}{5} = 2.0$ .
Apply perspective division to get the 2D $y$ coordinate: $y = \dfrac{Y}{Z} = \dfrac{20}{5} = 4.0$ .
Combine these to form the output 2D point: [2.0, 4.0].

Constraints:

Z > 0 (point is in front of camera)
Return [x, y] rounded to 4 decimal places

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.

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