战平UIBezierPath图表曲线(Draw Graph curves with UIBezier

我画我的应用程序的图形。 我的问题是，我想画线的曲线加入顶点。 目前，我画他们UIBezierPath的功能addLineToPoint: 我想提请他们为曲线。 我很清楚地知道， UIBezierPath有以下两个功能来支持此功能。

三次曲线： addCurveToPoint:controlPoint1:controlPoint2:二次曲线： addQuadCurveToPoint:controlPoint:

但问题是，我没有控制点。 我只有两个端点。 既不我发现了一个方法/公式来确定控制点。 有人能帮我一下吗？ 我将不胜感激，如果有人能提出一些可供选择的...

Answer 1:

扩大阿比德·侯赛因的12月5日'12答案。

我Implemeted一个代码，和它的工作，但结果看上去像是：

有了小的调整，我能得到我想要的：

我所做的就是addQuadCurveToPoint到中点为好，用点中旬中期作为控制点。 下面是基于阿比德的样本代码; 希望它可以帮助别人。

+ (UIBezierPath *)quadCurvedPathWithPoints:(NSArray *)points
{
    UIBezierPath *path = [UIBezierPath bezierPath];

    NSValue *value = points[0];
    CGPoint p1 = [value CGPointValue];
    [path moveToPoint:p1];

    if (points.count == 2) {
        value = points[1];
        CGPoint p2 = [value CGPointValue];
        [path addLineToPoint:p2];
        return path;
    }

    for (NSUInteger i = 1; i < points.count; i++) {
        value = points[i];
        CGPoint p2 = [value CGPointValue];

        CGPoint midPoint = midPointForPoints(p1, p2);
        [path addQuadCurveToPoint:midPoint controlPoint:controlPointForPoints(midPoint, p1)];
        [path addQuadCurveToPoint:p2 controlPoint:controlPointForPoints(midPoint, p2)];

        p1 = p2;
    }
    return path;
}

static CGPoint midPointForPoints(CGPoint p1, CGPoint p2) {
    return CGPointMake((p1.x + p2.x) / 2, (p1.y + p2.y) / 2);
}

static CGPoint controlPointForPoints(CGPoint p1, CGPoint p2) {
    CGPoint controlPoint = midPointForPoints(p1, p2);
    CGFloat diffY = abs(p2.y - controlPoint.y);

    if (p1.y < p2.y)
        controlPoint.y += diffY;
    else if (p1.y > p2.y)
        controlPoint.y -= diffY;

    return controlPoint;
}

Answer 2:

使用@ user1244109的答案我实现斯威夫特3更好的算法。

var data: [CGFloat] = [0, 0, 0, 0, 0, 0] {
    didSet {
        setNeedsDisplay()
    }
}

func coordXFor(index: Int) -> CGFloat {
    return bounds.height - bounds.height * data[index] / (data.max() ?? 0)
}

override func draw(_ rect: CGRect) {

    let path = quadCurvedPath()

    UIColor.black.setStroke()
    path.lineWidth = 1
    path.stroke()
}

func quadCurvedPath() -> UIBezierPath {
    let path = UIBezierPath()
    let step = bounds.width / CGFloat(data.count - 1)

    var p1 = CGPoint(x: 0, y: coordXFor(index: 0))
    path.move(to: p1)

    drawPoint(point: p1, color: UIColor.red, radius: 3)

    if (data.count == 2) {
        path.addLine(to: CGPoint(x: step, y: coordXFor(index: 1)))
        return path
    }

    var oldControlP: CGPoint?

    for i in 1..<data.count {
        let p2 = CGPoint(x: step * CGFloat(i), y: coordXFor(index: i))
        drawPoint(point: p2, color: UIColor.red, radius: 3)
        var p3: CGPoint?
        if i == data.count - 1 {
            p3 = nil
        } else {
            p3 = CGPoint(x: step * CGFloat(i + 1), y: coordXFor(index: i + 1))
        }

        let newControlP = controlPointForPoints(p1: p1, p2: p2, p3: p3)

        path.addCurve(to: p2, controlPoint1: oldControlP ?? p1, controlPoint2: newControlP ?? p2)

        p1 = p2
        oldControlP = imaginFor(point1: newControlP, center: p2)
    }
    return path;
}

func imaginFor(point1: CGPoint?, center: CGPoint?) -> CGPoint? {
    guard let p1 = point1, let center = center else {
        return nil
    }
    let newX = 2 * center.x - p1.x
    let diffY = abs(p1.y - center.y)
    let newY = center.y + diffY * (p1.y < center.y ? 1 : -1)

    return CGPoint(x: newX, y: newY)
}

func midPointForPoints(p1: CGPoint, p2: CGPoint) -> CGPoint {
    return CGPoint(x: (p1.x + p2.x) / 2, y: (p1.y + p2.y) / 2);
}

func controlPointForPoints(p1: CGPoint, p2: CGPoint, p3: CGPoint?) -> CGPoint? {
    guard let p3 = p3 else {
        return nil
    }

    let leftMidPoint  = midPointForPoints(p1: p1, p2: p2)
    let rightMidPoint = midPointForPoints(p1: p2, p2: p3)

    var controlPoint = midPointForPoints(p1: leftMidPoint, p2: imaginFor(point1: rightMidPoint, center: p2)!)


    // this part needs for optimization

    if p1.y < p2.y {
        if controlPoint.y < p1.y {
            controlPoint.y = p1.y
        }
        if controlPoint.y > p2.y {
            controlPoint.y = p2.y
        }
    } else {
        if controlPoint.y > p1.y {
            controlPoint.y = p1.y
        }
        if controlPoint.y < p2.y {
            controlPoint.y = p2.y
        }
    }

    let imaginContol = imaginFor(point1: controlPoint, center: p2)!
    if p2.y < p3.y {
        if imaginContol.y < p2.y {
            controlPoint.y = p2.y
        }
        if imaginContol.y > p3.y {
            let diffY = abs(p2.y - p3.y)
            controlPoint.y = p2.y + diffY * (p3.y < p2.y ? 1 : -1)
        }
    } else {
        if imaginContol.y > p2.y {
            controlPoint.y = p2.y
        }
        if imaginContol.y < p3.y {
            let diffY = abs(p2.y - p3.y)
            controlPoint.y = p2.y + diffY * (p3.y < p2.y ? 1 : -1)
        }
    }

    return controlPoint
}

func drawPoint(point: CGPoint, color: UIColor, radius: CGFloat) {
    let ovalPath = UIBezierPath(ovalIn: CGRect(x: point.x - radius, y: point.y - radius, width: radius * 2, height: radius * 2))
    color.setFill()
    ovalPath.fill()
}

Answer 3:

如果你只有两个点，那么你真的不能推断出来成曲线。

如果有两个以上的点（沿曲线即几个点），那么你可以粗略地划出一道弧线跟着他们。

如果你这样做了以下...

OK，说你有5个点。 P1，P2，P3，P4和P5。 你需要每对点之间制定出中点。 M1 = P1和P2（等）的中点...

所以，你有M1，M2，M3和M4。

现在你可以使用中间点，作为曲线段的终点和点为四曲线的控制点...

所以...

移动到另一个点M1。 加入四曲线与P2作为控制点，以点M2。

加入四曲线与P3为控制点，以点立方米。

加入四曲线与P4为控制点，以点M4。

等等...

这将让你在曲线的两端全部拆开（不记得如何让他们在此刻，抱歉）。

Answer 4:

SO，我发现周围的基础上@ Fogmeister的回答工作。

    UIBezierPath *path = [UIBezierPath bezierPath];
    [path setLineWidth:3.0];
    [path setLineCapStyle:kCGLineCapRound];
    [path setLineJoinStyle:kCGLineJoinRound];

    // actualPoints are my points array stored as NSValue

    NSValue *value = [actualPoints objectAtIndex:0];
    CGPoint p1 = [value CGPointValue];
    [path moveToPoint:p1];

    for (int k=1; k<[actualPoints count];k++) {

        NSValue *value = [actualPoints objectAtIndex:k];
        CGPoint p2 = [value CGPointValue];

        CGPoint centerPoint = CGPointMake((p1.x+p2.x)/2, (p1.y+p2.y)/2);

        // See if your curve is decreasing or increasing
        // You can optimize it further by finding point on normal of line passing through midpoint 

        if (p1.y<p2.y) {
             centerPoint = CGPointMake(centerPoint.x, centerPoint.y+(abs(p2.y-centerPoint.y)));
        }else if(p1.y>p2.y){
             centerPoint = CGPointMake(centerPoint.x, centerPoint.y-(abs(p2.y-centerPoint.y)));
        }

        [path addQuadCurveToPoint:p2 controlPoint:centerPoint];
        p1 = p2;
    }

    [path stroke];

Answer 5:

我已经做了一些工作在这，并从卡特莫尔-Rom样条不错的成果。 下面是采用CGPoints的阵列（存储为NSValues）和添加行给定的视图的方法。

- (void)addBezierPathBetweenPoints:(NSArray *)points
                        toView:(UIView *)view
                     withColor:(UIColor *)color
                andStrokeWidth:(NSUInteger)strokeWidth
{
    UIBezierPath *path = [UIBezierPath bezierPath];

    float granularity = 100;

    [path moveToPoint:[[points firstObject] CGPointValue]];

    for (int index = 1; index < points.count - 2 ; index++) {

        CGPoint point0 = [[points objectAtIndex:index - 1] CGPointValue];
        CGPoint point1 = [[points objectAtIndex:index] CGPointValue];
        CGPoint point2 = [[points objectAtIndex:index + 1] CGPointValue];
        CGPoint point3 = [[points objectAtIndex:index + 2] CGPointValue];

        for (int i = 1; i < granularity ; i++) {
            float t = (float) i * (1.0f / (float) granularity);
            float tt = t * t;
            float ttt = tt * t;

            CGPoint pi;
            pi.x = 0.5 * (2*point1.x+(point2.x-point0.x)*t + (2*point0.x-5*point1.x+4*point2.x-point3.x)*tt + (3*point1.x-point0.x-3*point2.x+point3.x)*ttt);
            pi.y = 0.5 * (2*point1.y+(point2.y-point0.y)*t + (2*point0.y-5*point1.y+4*point2.y-point3.y)*tt + (3*point1.y-point0.y-3*point2.y+point3.y)*ttt);

            if (pi.y > view.frame.size.height) {
                pi.y = view.frame.size.height;
            }
            else if (pi.y < 0){
                pi.y = 0;
            }

            if (pi.x > point0.x) {
                [path addLineToPoint:pi];
            }
        }

        [path addLineToPoint:point2];
    }

    [path addLineToPoint:[[points objectAtIndex:[points count] - 1] CGPointValue]];

    CAShapeLayer *shapeView = [[CAShapeLayer alloc] init];

    shapeView.path = [path CGPath];

    shapeView.strokeColor = color.CGColor;
    shapeView.fillColor = [UIColor clearColor].CGColor;
    shapeView.lineWidth = strokeWidth;
    [shapeView setLineCap:kCALineCapRound];

    [view.layer addSublayer:shapeView];
 }

我在这里使用它https://github.com/johnyorke/JYGraphViewController

Answer 6:

一个好的解决方案是创建一个直UIBezierPath通过您的积分，然后用样条曲线的线。 看看这个其他答案，给出了UIBezierPath一类是执行的Catmull-Rom样条。 绘制平滑的曲线-需要的方法

Answer 7:

这里的@转换为斯威夫特3 user1244109的回答

private func quadCurvedPath(with points:[CGPoint]) -> UIBezierPath {
   let path = UIBezierPath()
   var p1 = points[0]

   path.move(to: p1)

   if points.count == 2 {
     path.addLine(to: points[1])
     return path
   }

   for i in 1..<points.count {
    let mid = midPoint(for: (p1, points[i]))
     path.addQuadCurve(to: mid,
                     controlPoint: controlPoint(for: (mid, p1)))
     path.addQuadCurve(to: points[i],
                    controlPoint: controlPoint(for: (mid, points[i])))
     p1 = points[i]
   }
  return path
}


private func midPoint(for points: (CGPoint, CGPoint)) -> CGPoint {
   return CGPoint(x: (points.0.x + points.1.x) / 2 , y: (points.0.y + points.1.y) / 2)
}


private func controlPoint(for points: (CGPoint, CGPoint)) -> CGPoint {
   var controlPoint = midPoint(for: points)
   let diffY = abs(points.1.y - controlPoint.y)

   if points.0.y < points.1.y {
     controlPoint.y += diffY
   } else if points.0.y > points.1.y {
     controlPoint.y -= diffY
   }
   return controlPoint
}

Answer 8:

虽然分析来自@罗马菲利波夫的代码，我简化了一些代码。 下面是一个完整斯威夫特游乐场版本，再下面一个ObjC版本。

我发现，如果x增量都是不正规的，那么原来的算法产生了一些不幸的逆行线时，点靠近在x轴上在一起。 只要约束控制点不超过以下x值似乎解决这个问题，但我对这个没有数学证明，只是实验。 有标记为// ** added`它们实现这种变化两个部分。

import UIKit
import PlaygroundSupport

infix operator °
func °(x: CGFloat, y: CGFloat) -> CGPoint {
    return CGPoint(x: x, y: y)
}

extension UIBezierPath {
    func drawPoint(point: CGPoint, color: UIColor, radius: CGFloat) {
        let ovalPath = UIBezierPath(ovalIn: CGRect(x: point.x - radius, y: point.y - radius, width: radius * 2, height: radius * 2))
        color.setFill()
        ovalPath.fill()
    }

    func drawWithLine (point: CGPoint, color: UIColor) {
        let startP = self.currentPoint
        self.addLine(to: point)
        drawPoint(point: point, color: color, radius: 3)
        self.move(to: startP)
    }

}

class TestView : UIView {
    var step: CGFloat = 1.0;
    var yMaximum: CGFloat = 1.0
    var xMaximum: CGFloat = 1.0
    var data: [CGPoint] = [] {
        didSet {
            xMaximum = data.reduce(-CGFloat.greatestFiniteMagnitude, { max($0, $1.x) })
            yMaximum = data.reduce(-CGFloat.greatestFiniteMagnitude, { max($0, $1.y) })
            setNeedsDisplay()
        }
    }

    func scale(point: CGPoint) -> CGPoint {
        return  CGPoint(x: bounds.width * point.x / xMaximum ,
                        y: (bounds.height - bounds.height * point.y / yMaximum))
    }

    override func draw(_ rect: CGRect) {
        if data.count <= 1 {
            return
        }
        let path = cubicCurvedPath()

        UIColor.black.setStroke()
        path.lineWidth = 1
        path.stroke()
    }

    func cubicCurvedPath() -> UIBezierPath {
        let path = UIBezierPath()

        var p1 = scale(point: data[0])
        path.drawPoint(point: p1, color: UIColor.red, radius: 3)
        path.move(to: p1)
        var oldControlP = p1

        for i in 0..<data.count {
            let p2 = scale(point:data[i])
            path.drawPoint(point: p2, color: UIColor.red, radius: 3)
            var p3: CGPoint? = nil
            if i < data.count - 1 {
                p3 = scale(point:data [i+1])
            }

            let newControlP = controlPointForPoints(p1: p1, p2: p2, p3: p3)
            //uncomment the following four lines to graph control points
            //if let controlP = newControlP {
            //    path.drawWithLine(point:controlP, color: UIColor.blue)
            //}
            //path.drawWithLine(point:oldControlP, color: UIColor.gray)

            path.addCurve(to: p2, controlPoint1: oldControlP , controlPoint2: newControlP ?? p2)
            oldControlP = imaginFor(point1: newControlP, center: p2) ?? p1
            //***added to algorithm
            if let p3 = p3 {
                if oldControlP.x > p3.x { oldControlP.x = p3.x }
            }
            //***
            p1 = p2
        }
        return path;
    }

    func imaginFor(point1: CGPoint?, center: CGPoint?) -> CGPoint? {
        //returns "mirror image" of point: the point that is symmetrical through center.
        //aka opposite of midpoint; returns the point whose midpoint with point1 is center)
        guard let p1 = point1, let center = center else {
            return nil
        }
        let newX = center.x + center.x - p1.x
        let newY = center.y + center.y - p1.y

        return CGPoint(x: newX, y: newY)
    }

    func midPointForPoints(p1: CGPoint, p2: CGPoint) -> CGPoint {
        return CGPoint(x: (p1.x + p2.x) / 2, y: (p1.y + p2.y) / 2);
    }

    func clamp(num: CGFloat, bounds1: CGFloat, bounds2: CGFloat) -> CGFloat {
        //ensure num is between bounds.
        if (bounds1 < bounds2) {
            return min(max(bounds1,num),bounds2);
        } else {
            return min(max(bounds2,num),bounds1);
        }
    }

    func controlPointForPoints(p1: CGPoint, p2: CGPoint, p3: CGPoint?) -> CGPoint? {
        guard let p3 = p3 else {
            return nil
        }

        let leftMidPoint  = midPointForPoints(p1: p1, p2: p2)
        let rightMidPoint = midPointForPoints(p1: p2, p2: p3)
        let imaginPoint = imaginFor(point1: rightMidPoint, center: p2)

        var controlPoint = midPointForPoints(p1: leftMidPoint, p2: imaginPoint!)

        controlPoint.y = clamp(num: controlPoint.y, bounds1: p1.y, bounds2: p2.y)

        let flippedP3 = p2.y + (p2.y-p3.y)

        controlPoint.y = clamp(num: controlPoint.y, bounds1: p2.y, bounds2: flippedP3);
        //***added:
        controlPoint.x = clamp (num:controlPoint.x, bounds1: p1.x, bounds2: p2.x)
        //***
        // print ("p1: \(p1), p2: \(p2), p3: \(p3), LM:\(leftMidPoint), RM:\(rightMidPoint), IP:\(imaginPoint), fP3:\(flippedP3), CP:\(controlPoint)")
        return controlPoint
    }

}

let u = TestView(frame: CGRect(x: 0, y: 0, width: 700, height: 600));
u.backgroundColor = UIColor.white

PlaygroundPage.current.liveView = u
u.data = [0.5 ° 1, 1 ° 3, 2 ° 5, 4 ° 9, 8 ° 15, 9.4 ° 8, 9.5 ° 10, 12 ° 4, 13 ° 10, 15 ° 3, 16 ° 1]

而在ObjC相同的代码（更多或更少。这不包括绘图函数本身，以及它允许​​点阵列包括丢失数据

+ (UIBezierPath *)pathWithPoints:(NSArray <NSValue *> *)points open:(BOOL) open {
    //based on Roman Filippov code: http://stackoverflow.com/a/40203583/580850
    //open means allow gaps in path.
    UIBezierPath *path = [UIBezierPath bezierPath];
    CGPoint p1 = [points[0] CGPointValue];
    [path moveToPoint:p1];
    CGPoint oldControlPoint = p1;
    for (NSUInteger pointIndex = 1; pointIndex< points.count; pointIndex++) {
        CGPoint p2 = [points[pointIndex]  CGPointValue];  //note: mark missing data with CGFloatMax

        if (p1.y >= CGFloatMax || p2.y >= CGFloatMax) {
            if (open) {
                [path moveToPoint:p2];
            } else {
                [path addLineToPoint:p2];
            }
            oldControlPoint = p2;
        } else {
            CGPoint p3 = CGPointZero;
            if (pointIndex +1 < points.count) p3 = [points[pointIndex+1] CGPointValue] ;
            if (p3.y >= CGFloatMax) p3 = CGPointZero;
            CGPoint newControlPoint = controlPointForPoints2(p1, p2, p3);
            if (!CGPointEqualToPoint( newControlPoint, CGPointZero)) {
                [path addCurveToPoint: p2 controlPoint1:oldControlPoint controlPoint2: newControlPoint];
                oldControlPoint = imaginForPoints( newControlPoint,  p2);
                //**added to algorithm
                if (! CGPointEqualToPoint(p3,CGPointZero)) {
                   if (oldControlPoint.x > p3.x ) {
                       oldControlPoint.x = p3.x;
                   }
                //***
            } else {
                [path addCurveToPoint: p2 controlPoint1:oldControlPoint controlPoint2: p2];
                oldControlPoint = p2;
            }
        }
        p1 = p2;
    }
    return path;
}

static CGPoint imaginForPoints(CGPoint point, CGPoint center) {
    //returns "mirror image" of point: the point that is symmetrical through center.
    if (CGPointEqualToPoint(point, CGPointZero) || CGPointEqualToPoint(center, CGPointZero)) {
        return CGPointZero;
    }
    CGFloat newX = center.x + (center.x-point.x);
    CGFloat newY = center.y + (center.y-point.y);
    if (isinf(newY)) {
        newY = BEMNullGraphValue;
    }
    return CGPointMake(newX,newY);
}

static CGFloat clamp(CGFloat num, CGFloat bounds1, CGFloat bounds2) {
    //ensure num is between bounds.
    if (bounds1 < bounds2) {
        return MIN(MAX(bounds1,num),bounds2);
    } else {
        return MIN(MAX(bounds2,num),bounds1);
    }
}

static CGPoint controlPointForPoints2(CGPoint p1, CGPoint p2, CGPoint p3) {
    if (CGPointEqualToPoint(p3, CGPointZero)) return CGPointZero;
    CGPoint leftMidPoint = midPointForPoints(p1, p2);
    CGPoint rightMidPoint = midPointForPoints(p2, p3);
    CGPoint imaginPoint = imaginForPoints(rightMidPoint, p2);
    CGPoint controlPoint = midPointForPoints(leftMidPoint, imaginPoint);

    controlPoint.y = clamp(controlPoint.y, p1.y, p2.y);

    CGFloat flippedP3 = p2.y + (p2.y-p3.y);

    controlPoint.y = clamp(controlPoint.y, p2.y, flippedP3);
   //**added to algorithm
    controlPoint.x = clamp(controlPoint.x, p1.x, p2.x);
   //**
    return controlPoint;
}

Answer 9:

如果您需要靠近每一个点“水平”曲线：

let path = createCurve(from: points, withSmoothness: 0.5) // 0.5 smoothness

let path = createCurve(from: points, withSmoothness: 0) // 0 smoothness

    /// Create UIBezierPath
    ///
    /// - Parameters:
    ///   - points: the points
    ///   - smoothness: the smoothness: 0 - no smooth at all, 1 - maximum smoothness
    private func createCurve(from points: [CGPoint], withSmoothness smoothness: CGFloat, addZeros: Bool = false) -> UIBezierPath {

        let path = UIBezierPath()
        guard points.count > 0 else { return path }
        var prevPoint: CGPoint = points.first!
        let interval = getXLineInterval()
        if addZeros {
            path.move(to: CGPoint(x: interval.origin.x, y: interval.origin.y))
            path.addLine(to: points[0])
        }
        else {
            path.move(to: points[0])
        }
        for i in 1..<points.count {
            let cp = controlPoints(p1: prevPoint, p2: points[i], smoothness: smoothness)
            path.addCurve(to: points[i], controlPoint1: cp.0, controlPoint2: cp.1)
            prevPoint = points[i]
        }
        if addZeros {
            path.addLine(to: CGPoint(x: prevPoint.x, y: interval.origin.y))
        }
        return path
    }

    /// Create control points with given smoothness
    ///
    /// - Parameters:
    ///   - p1: the first point
    ///   - p2: the second point
    ///   - smoothness: the smoothness: 0 - no smooth at all, 1 - maximum smoothness
    /// - Returns: two control points
    private func controlPoints(p1: CGPoint, p2: CGPoint, smoothness: CGFloat) -> (CGPoint, CGPoint) {
        let cp1: CGPoint!
        let cp2: CGPoint!
        let percent = min(1, max(0, smoothness))
        do {
            var cp = p2
            // Apply smoothness
            let x0 = max(p1.x, p2.x)
            let x1 = min(p1.x, p2.x)
            let x = x0 + (x1 - x0) * percent
            cp.x = x
            cp2 = cp
        }
        do {
            var cp = p1
            // Apply smoothness
            let x0 = min(p1.x, p2.x)
            let x1 = max(p1.x, p2.x)
            let x = x0 + (x1 - x0) * percent
            cp.x = x
            cp1 = cp
        }
        return (cp1, cp2)
    }

文章来源: Draw Graph curves with UIBezierPath