import UIKit
import simd
import Accelerate

extension CGPoint {
    init(simd3: SIMD3<Double>) {
        self.init(x: simd3.x, y: simd3.y)
    }
}

extension simd_double3 {
    init(point: CGPoint) {
        self.init(x: Double(point.x), y: Double(point.y), z: Double(1))
    }
}

struct CGLine {
    let start: CGPoint
    let end: CGPoint

    var norm: CGPoint {
        let dy = end.y - start.y
        let dx = end.x - start.x
        return CGPoint(x: start.x + dy, y: start.y - dx)
    }
}

extension CGAffineTransform {
    init(from initialLine: CGLine, to transformedLine: CGLine) {
        let initMat = simd_double3x3(
            simd_double3(point: initialLine.start),
            simd_double3(point: initialLine.end),
            simd_double3(point: initialLine.norm)
        ).transpose

        let transformedMat = simd_double3x3(
            simd_double3(point: transformedLine.start),
            simd_double3(point: transformedLine.end),
            simd_double3(point: transformedLine.norm)
        ).transpose

        let transMat = simd_mul(initMat.inverse, transformedMat).transpose

        self.init(
            a: CGFloat(transMat.columns.0.x), b: CGFloat(transMat.columns.0.y),
            c: CGFloat(transMat.columns.1.x), d: CGFloat(transMat.columns.1.y),
            tx: CGFloat(transMat.columns.2.x), ty: CGFloat(transMat.columns.2.y)
        )
    }
}