A circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range [0, 2π). A circular distribution is often a continuous probability distribution, and hence has a probability density, but such distributions can also be discrete, in which case they are called…

CircularLatticeDistribution.swift

/*
A circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range [0, 2π). A circular distribution is often a continuous probability distribution, and hence has a probability density, but such distributions can also be discrete, in which case they are called circular lattice distributions. Circular distributions can be used even when the variables concerned are not explicitly angles: the main consideration is that there is not usually any real distinction between events occurring at the opposite ends of the range, and the division of the range could notionally be made at any point.
*/

// https://en.wikipedia.org/wiki/Circular_distribution

import SwiftUI

func scale(oldMin: Double, oldMax: Double, value: Double, newMin: Double, newMax: Double) -> Double {
	return ((value - oldMin) / (oldMax - oldMin)) * (newMax - newMin) + newMin
}

struct ContentView: View {
	@State private var firstAngles: [Double] = []
	@State private var secondAngles: [Double] = []
	@State private var minusThresholdAngles: [Double] = []
	@State private var plusThresholdAngles: [Double] = []
	@State private var differences: [Double] = []
	let threshold: Double = 45.0

	var body: some View {
		VStack {
			Button(action: generateAngles) {
				Text("Generate Angles")
			}
			List(0 ..< firstAngles.count, id: \.self) { index in
				VStack(alignment: .leading) {
					Text("\(Int(minusThresholdAngles[index]))° < \(Int(firstAngles[index]))° < \(Int(plusThresholdAngles[index]))° = \(Int(differences[index]))°")
					Text("\(scale(oldMin: 0.0, oldMax: 360.0, value: firstAngles[index], newMin: 0.0, newMax: 1.0))")
					Text("\(scale(oldMin: 0.0, oldMax: 360.0, value: differences[index], newMin: 0.0, newMax: 1.0))")
				}
			}
		}
		.padding()
	}

	private func generateAngles() {
		firstAngles = (0 ..< 10).map { _ in generateRandomAngle(max: 360.0) }
		secondAngles = (0 ..< 10).map { i in generateRandomAngle(max: firstAngles[i]) }
		minusThresholdAngles = firstAngles.map { wrapAngle($0 - threshold) }
		plusThresholdAngles = firstAngles.map { wrapAngle($0 + threshold) }
		differences = zip(secondAngles, zip(minusThresholdAngles, plusThresholdAngles)).map { calculateShortestDifference($0, $1.0, $1.1) }
		differences = (0 ..< 10).map { i in wrapAngle(differences[i] + firstAngles[i]) }
	}

	private func generateRandomAngle(max: Double) -> Double {
		return Double.random(in: 0 ... max)
	}

	private func calculateShortestDifference(_ angle2: Double, _ minusThreshold: Double, _ plusThreshold: Double) -> Double {
		let diffMinusThreshold = calculateShortestDistance(angle2, minusThreshold)
		let diffPlusThreshold = calculateShortestDistance(angle2, plusThreshold)

		return max(diffMinusThreshold, diffPlusThreshold)
	}

	private func calculateShortestDistance(_ angle1: Double, _ angle2: Double) -> Double {
		let diff = abs(angle1 - angle2)
		return min(diff, 360 - diff)
	}

	private func wrapAngle(_ angle: Double) -> Double {
		let wrapped = angle.truncatingRemainder(dividingBy: 360)
		return wrapped >= 0 ? wrapped : wrapped + 360
	}
}

#Preview {
	ContentView()
		.preferredColorScheme(.dark)
}