How to Normalize a Two-Dimensional NumPy Array by Adjusting Minimum Coordinates to Zero

Описание: Learn an elegant and efficient method to normalize 2D coordinate arrays in Python using NumPy by adjusting minimum x and y values to zero.
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This video is based on the question https://stackoverflow.com/q/79473651/ asked by the user 'Paul St George' ( https://stackoverflow.com/u/9842773/ ) and on the answer https://stackoverflow.com/a/79474022/ provided by the user 'jared' ( https://stackoverflow.com/u/12131013/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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The Problem: Normalizing 2D Coordinate Arrays

When working with 2D coordinate data—such as the vertices of a shape—you might want to shift all points so that the minimum x and y values become zero. This effectively normalizes the data to start at the origin (0,0), eliminating negative coordinates and simplifying further processing.

Common but Verbose Approach

A typical approach can be verbose:

Extract x and y values separately.

Find their minimums.

Calculate offsets.

Create a new array.

Loop through all points to apply the offset.

For example, manually extracting values and looping through each element makes the code longer and harder to maintain.

Elegant NumPy Solution

NumPy allows you to perform this normalization concisely and efficiently in one line:

[[See Video to Reveal this Text or Code Snippet]]

Explanation:

pa.min(axis=0) computes the minimum for each column (x and y separately).

Subtracting this minimum from the entire array shifts all coordinates so the smallest x and y become zero.

This leverages NumPy's vectorized operations, removing the need for explicit loops or complex array reconstruction.

Example

[[See Video to Reveal this Text or Code Snippet]]

Output:

[[See Video to Reveal this Text or Code Snippet]]

Summary

Use pa.min(axis=0) to get minimums of each coordinate axis efficiently.

Subtract these from the original array to normalize.

This approach is concise, fast, and easy to maintain.

This method works for any 2D NumPy array representing coordinate points, making it ideal for normalizing shapes and trapeziums to non-negative space.