//
//  BezierAlgorithm.swift
//  TestExample
//
//  Created by Julia Bulantseva on 27/10/16.
//  Copyright © 2016 Julia Bulantseva. All rights reserved.
//

import Foundation
import UIKit

struct CubicCurveSegment
{
    let controlPoint1: CGPoint
    let controlPoint2: CGPoint
}

class CubicCurveAlgorithm
{
    private var firstControlPoints: [CGPoint?] = []
    private var secondControlPoints: [CGPoint?] = []
    
    func controlPointsFromPoints(dataPoints: [CGPoint]) -> [CubicCurveSegment] {        
        firstControlPoints.removeAll()
        secondControlPoints.removeAll()
        
        //Number of Segments
        let count = dataPoints.count - 1
        
        //P0, P1, P2, P3 are the points for each segment, where P0 & P3 are the knots and P1, P2 are the control points.
        if count == 1 {
            let P0 = dataPoints[0]
            let P3 = dataPoints[1]
            
            //Calculate First Control Point
            //3P1 = 2P0 + P3
            
            let P1x = (2*P0.x + P3.x)/3
            let P1y = (2*P0.y + P3.y)/3
            
            firstControlPoints.append(CGPoint(x: P1x, y: P1y))
            
            //Calculate second Control Point
            //P2 = 2P1 - P0
            let P2x = (2*P1x - P0.x)
            let P2y = (2*P1y - P0.y)
            
            secondControlPoints.append(CGPoint(x: P2x, y: P2y))
        } else {
            firstControlPoints = Array(repeating: nil, count: count)
            
            var rhsArray = [CGPoint]()
            
            //Array of Coefficients
            var a = [Double]()
            var b = [Double]()
            var c = [Double]()
            
            for i in 0 ..< count {
                
                var rhsValueX: CGFloat = 0
                var rhsValueY: CGFloat = 0
                
                let P0 = dataPoints[i];
                let P3 = dataPoints[i+1];
                
                if i==0 {
                    a.append(0)
                    b.append(2)
                    c.append(1)
                    
                    //rhs for first segment
                    rhsValueX = P0.x + 2*P3.x;
                    rhsValueY = P0.y + 2*P3.y;
                    
                } else if i == count-1 {
                    a.append(2)
                    b.append(7)
                    c.append(0)
                    
                    //rhs for last segment
                    rhsValueX = 8*P0.x + P3.x;
                    rhsValueY = 8*P0.y + P3.y;
                } else {
                    a.append(1)
                    b.append(4)
                    c.append(1)
                    
                    rhsValueX = 4*P0.x + 2*P3.x;
                    rhsValueY = 4*P0.y + 2*P3.y;
                }
                
                rhsArray.append(CGPoint(x: rhsValueX, y: rhsValueY))
            }
            
            //Solve Ax=B. Use Tridiagonal matrix algorithm a.k.a Thomas Algorithm
            
            for i in 1 ..< count {
                let rhsValueX = rhsArray[i].x
                let rhsValueY = rhsArray[i].y
                
                let prevRhsValueX = rhsArray[i-1].x
                let prevRhsValueY = rhsArray[i-1].y
                
                let m = a[i]/b[i-1]
                
                let b1 = b[i] - m * c[i-1];
                b[i] = b1
                
                let r2x = rhsValueX.f - m * prevRhsValueX.f
                let r2y = rhsValueY.f - m * prevRhsValueY.f
                
                rhsArray[i] = CGPoint(x: r2x, y: r2y)
                
            }
            
            //Get First Control Points
            
            //Last control Point
            let lastControlPointX = rhsArray[count-1].x.f/b[count-1]
            let lastControlPointY = rhsArray[count-1].y.f/b[count-1]
            
            firstControlPoints[count-1] = CGPoint(x: lastControlPointX, y: lastControlPointY)
            var i = count-2
            
            while i >= 0 {
                if let nextControlPoint = firstControlPoints[i+1] {
                    let controlPointX = (rhsArray[i].x.f - c[i] * nextControlPoint.x.f)/b[i]
                    let controlPointY = (rhsArray[i].y.f - c[i] * nextControlPoint.y.f)/b[i]
                    
                    firstControlPoints[i] = CGPoint(x: controlPointX, y: controlPointY)
                    
                }
                i -= 1
            }
            
            //Compute second Control Points from first
            
            for i in 0 ..< count {
                
                if i == count-1 {
                    let P3 = dataPoints[i+1]
                    
                    guard let P1 = firstControlPoints[i] else{
                        continue
                    }
                    
                    let controlPointX = (P3.x + P1.x)/2
                    let controlPointY = (P3.y + P1.y)/2
                    
                    secondControlPoints.append(CGPoint(x: controlPointX, y: controlPointY))
                    
                } else {
                    let P3 = dataPoints[i+1]
                    
                    guard let nextP1 = firstControlPoints[i+1] else {
                        continue
                    }
                    
                    let controlPointX = 2*P3.x - nextP1.x
                    let controlPointY = 2*P3.y - nextP1.y
                    
                    secondControlPoints.append(CGPoint(x: controlPointX, y: controlPointY))
                }
            }
        }
        
        var controlPoints = [CubicCurveSegment]()
        
        for i in 0 ..< count {
            if let firstControlPoint = firstControlPoints[i],
                let secondControlPoint = secondControlPoints[i] {
                let segment = CubicCurveSegment(controlPoint1: firstControlPoint, controlPoint2: secondControlPoint)
                controlPoints.append(segment)
            }
        }
        
        return controlPoints
    }
}

extension CGFloat {
    var f: Double {
        return Double(self)
    }
}
