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lir

Largest Interior Rectangle implementation in C# for Unity.

REQUIREMENTS

Unity.Mathematics is required for int2 and float2x2 (2D integer vectors and float 2x2 matrices, respectively).

The simplest way to get this package is to open the "Package Manager" window in Unity, click the plus icon, select "add package from git URL ..." and then enter "com.unity.mathematics" (without quotes).

USAGE

LargestInteriorRectangle.cs

the LargestInteriorRectangle class contains various static methods for processing Vector2 arrays. The primary methods are:

CalculateInteriorCells(Vector2[] vs, out float[] xs, out float[] ys, out int[,] cells)

This method takes a list of Vector2s representing a simple polygon (ordered counter-clockwise, concave, non-intersecting) and generates three output arrays : the xs (ordered, filtered unique x coordinates for all vertices), the ys (ordered, filtered, unique y coordinates for all vertices) and the 2D cells array representing each cell of the projection of the xs and ys arrays into a 2D rectangle array. Each cell is marked as exterior (0) or interior (1) based on it's position relative to the polygon.

CalculateLargestInteriorRectangle(float[] xs, float ys[], int[,] cells, out Bound2D best)

this method takes the xs, ys and cells arrays created by CalculateInteriorCells and calculates the axis-aligned Largest Interior Rectangle. The bound of this rectangle is output in best.

Along with these methods, there are a variety of other geometry processing methods:

CalculateConcavePolygon (Vector2[] vs)

Sorts a point set into an ordered array (counter-clockwise) representing a concave polygon.

CalculateConvexHull(Vector2[] vs, out Vector2[] hull_vs)

Calculates a convex hull, given a point set.

CalculateConvexPolygonArea(Vector2[] vs)

calculates the area of a convex polygon, given a CCW ordered point array representing that convex polygon.

CalculatePrimaryAxis(Vector2[] vs, out Vector2 axis, out float eigenvalue)

Given a point set in vs, calculates the primary axis, and the corresponding eigenvalue. The primary axis is the line through the point set representing the largest variance.

CalculateEigenValues(float2x2 mat, out float v1, out float v2)

Given a 2x2 matrix, calculates the eigenvalues.

CalculateEigenVector(float 2x2 A, float eigenvalue)

Given a 2x2 matrix and an eigenvalue, calculates an eigenvector.

Bound2D.cs

This class represents a 2D bound. The bound is not required to be axis aligned. The bound is constructed from a centre point, a 2D size and the primary axis (the first element of the 2D size).

Extensions.cs

This class contains some Vector2 extension methods to simplify the code (Rotate for simple 2D rotations, and F3() to make logging more concise).

LargestInteriorRectangleTests.cs

This class contains a selection of tests across the LargestInteriorRectangle methods.

BACKGROUND READING

please see https://www.evryway.com/largest-interior/ for background details.