Я собирался сказать «Что ты пробовал?», но в пятницу днем ​​я рано ушел с работы, поэтому воспользовался возможностью перевести свой старый код ObjC. Здесь он подходит для игровой площадки. Это должно быть тривиально, чтобы поместить его в ваш UIView.

Swift 2 См. Ниже для Swift 3 & amp; Обновления Swift 4 ...

import UIKit

func centreArcPerpendicularText(str: String, context: CGContextRef, radius r: CGFloat, angle theta: CGFloat, colour c: UIColor, font: UIFont, clockwise: Bool){
    // *******************************************************
    // This draws the String str around an arc of radius r,
    // with the text centred at polar angle theta
    // *******************************************************

    let l = str.characters.count
    let attributes = [NSFontAttributeName: font]

    var characters: [String] = [] // This will be an array of single character strings, each character in str
    var arcs: [CGFloat] = [] // This will be the arcs subtended by each character
    var totalArc: CGFloat = 0 // ... and the total arc subtended by the string

    // Calculate the arc subtended by each letter and their total
    for i in 0 ..< l {
        characters += [String(str[str.startIndex.advancedBy(i)])]
        arcs += [chordToArc(characters[i].sizeWithAttributes(attributes).width, radius: r)]
        totalArc += arcs[i]
    }

    // Are we writing clockwise (right way up at 12 o'clock, upside down at 6 o'clock)
    // or anti-clockwise (right way up at 6 o'clock)?
    let direction: CGFloat = clockwise ? -1 : 1
    let slantCorrection = clockwise ? -CGFloat(M_PI_2) : CGFloat(M_PI_2)

    // The centre of the first character will then be at
    // thetaI = theta - totalArc / 2 + arcs[0] / 2
    // But we add the last term inside the loop
    var thetaI = theta - direction * totalArc / 2

    for i in 0 ..< l {
        thetaI += direction * arcs[i] / 2
        // Call centerText with each character in turn.
        // Remember to add +/-90º to the slantAngle otherwise
        // the characters will "stack" round the arc rather than "text flow"
        centreText(characters[i], context: context, radius: r, angle: thetaI, colour: c, font: font, slantAngle: thetaI + slantCorrection)
        // The centre of the next character will then be at
        // thetaI = thetaI + arcs[i] / 2 + arcs[i + 1] / 2
        // but again we leave the last term to the start of the next loop...
        thetaI += direction * arcs[i] / 2
    }
}

func chordToArc(chord: CGFloat, radius: CGFloat) -> CGFloat {
    // *******************************************************
    // Simple geometry
    // *******************************************************
    return 2 * asin(chord / (2 * radius))
}

func centreText(str: String, context: CGContextRef, radius r:CGFloat, angle theta: CGFloat, colour c: UIColor, font: UIFont, slantAngle: CGFloat) {
    // *******************************************************
    // This draws the String str centred at the position
    // specified by the polar coordinates (r, theta)
    // i.e. the x= r * cos(theta) y= r * sin(theta)
    // and rotated by the angle slantAngle
    // *******************************************************

    // Set the text attributes
    let attributes = [NSForegroundColorAttributeName: c,
        NSFontAttributeName: font]
    // Save the context
    CGContextSaveGState(context)
    // Undo the inversion of the Y-axis (or the text goes backwards!)
    CGContextScaleCTM(context, 1, -1)
    // Move the origin to the centre of the text (negating the y-axis manually)
    CGContextTranslateCTM(context, r * cos(theta), -(r * sin(theta)))
    // Rotate the coordinate system
    CGContextRotateCTM(context, -slantAngle)
    // Calculate the width of the text
    let offset = str.sizeWithAttributes(attributes)
    // Move the origin by half the size of the text
    CGContextTranslateCTM (context, -offset.width / 2, -offset.height / 2) // Move the origin to the centre of the text (negating the y-axis manually)
    // Draw the text
    str.drawAtPoint(CGPointZero, withAttributes: attributes)
    // Restore the context
    CGContextRestoreGState(context)
}

// *******************************************************
// Playground code to test
// *******************************************************
let size = CGSize(width: 256, height: 256)

UIGraphicsBeginImageContextWithOptions(size, true, 0.0)
let context = UIGraphicsGetCurrentContext()!
// *******************************************************************
// Scale & translate the context to have 0,0
// at the centre of the screen maths convention
// Obviously change your origin to suit...
// *******************************************************************
CGContextTranslateCTM (context, size.width / 2, size.height / 2)
CGContextScaleCTM (context, 1, -1)

centreArcPerpendicularText("Hello round world", context: context, radius: 100, angle: 0, colour: UIColor.redColor(), font: UIFont.systemFontOfSize(16), clockwise: true)
centreArcPerpendicularText("Anticlockwise", context: context, radius: 100, angle: CGFloat(-M_PI_2), colour: UIColor.redColor(), font: UIFont.systemFontOfSize(16), clockwise: false)
centreText("Hello flat world", context: context, radius: 0, angle: 0 , colour: UIColor.yellowColor(), font: UIFont.systemFontOfSize(16), slantAngle: CGFloat(M_PI_4))


let image = UIGraphicsGetImageFromCurrentImageContext()
UIGraphicsEndImageContext()

Выход:

Обновление Добавлено по часовой стрелке / против часовой стрелки & amp; Прямой пример.

Обновить Swift 3

func centreArcPerpendicular(text str: String, context: CGContext, radius r: CGFloat, angle theta: CGFloat, colour c: UIColor, font: UIFont, clockwise: Bool){
    // *******************************************************
    // This draws the String str around an arc of radius r,
    // with the text centred at polar angle theta
    // *******************************************************

    let l = str.characters.count
    let attributes = [NSFontAttributeName: font]

    let characters: [String] = str.characters.map { String($0) } // An array of single character strings, each character in str
    var arcs: [CGFloat] = [] // This will be the arcs subtended by each character
    var totalArc: CGFloat = 0 // ... and the total arc subtended by the string

    // Calculate the arc subtended by each letter and their total
    for i in 0 ..< l {
        arcs += [chordToArc(characters[i].size(attributes: attributes).width, radius: r)]
        totalArc += arcs[i]
    }

    // Are we writing clockwise (right way up at 12 o'clock, upside down at 6 o'clock)
    // or anti-clockwise (right way up at 6 o'clock)?
    let direction: CGFloat = clockwise ? -1 : 1
    let slantCorrection = clockwise ? -CGFloat(M_PI_2) : CGFloat(M_PI_2)

    // The centre of the first character will then be at
    // thetaI = theta - totalArc / 2 + arcs[0] / 2
    // But we add the last term inside the loop
    var thetaI = theta - direction * totalArc / 2

    for i in 0 ..< l {
        thetaI += direction * arcs[i] / 2
        // Call centerText with each character in turn.
        // Remember to add +/-90º to the slantAngle otherwise
        // the characters will "stack" round the arc rather than "text flow"
        centre(text: characters[i], context: context, radius: r, angle: thetaI, colour: c, font: font, slantAngle: thetaI + slantCorrection)
        // The centre of the next character will then be at
        // thetaI = thetaI + arcs[i] / 2 + arcs[i + 1] / 2
        // but again we leave the last term to the start of the next loop...
        thetaI += direction * arcs[i] / 2
    }
}

func chordToArc(_ chord: CGFloat, radius: CGFloat) -> CGFloat {
    // *******************************************************
    // Simple geometry
    // *******************************************************
    return 2 * asin(chord / (2 * radius))
}

func centre(text str: String, context: CGContext, radius r:CGFloat, angle theta: CGFloat, colour c: UIColor, font: UIFont, slantAngle: CGFloat) {
    // *******************************************************
    // This draws the String str centred at the position
    // specified by the polar coordinates (r, theta)
    // i.e. the x= r * cos(theta) y= r * sin(theta)
    // and rotated by the angle slantAngle
    // *******************************************************

    // Set the text attributes
    let attributes = [NSForegroundColorAttributeName: c,
                      NSFontAttributeName: font]
    // Save the context
    context.saveGState()
    // Undo the inversion of the Y-axis (or the text goes backwards!)
    context.scaleBy(x: 1, y: -1)
    // Move the origin to the centre of the text (negating the y-axis manually)
    context.translateBy(x: r * cos(theta), y: -(r * sin(theta)))
    // Rotate the coordinate system
    context.rotate(by: -slantAngle)
    // Calculate the width of the text
    let offset = str.size(attributes: attributes)
    // Move the origin by half the size of the text
    context.translateBy (x: -offset.width / 2, y: -offset.height / 2) // Move the origin to the centre of the text (negating the y-axis manually)
    // Draw the text
    str.draw(at: CGPoint(x: 0, y: 0), withAttributes: attributes)
    // Restore the context
    context.restoreGState()
}

// *******************************************************
// Playground code to test
// *******************************************************
let size = CGSize(width: 256, height: 256)

UIGraphicsBeginImageContextWithOptions(size, true, 0.0)
let context = UIGraphicsGetCurrentContext()!
// *******************************************************************
// Scale & translate the context to have 0,0
// at the centre of the screen maths convention
// Obviously change your origin to suit...
// *******************************************************************
context.translateBy (x: size.width / 2, y: size.height / 2)
context.scaleBy (x: 1, y: -1)

centreArcPerpendicular(text: "Hello round world", context: context, radius: 100, angle: 0, colour: UIColor.red, font: UIFont.systemFont(ofSize: 16), clockwise: true)
centreArcPerpendicular(text: "Anticlockwise", context: context, radius: 100, angle: CGFloat(-M_PI_2), colour: UIColor.red, font: UIFont.systemFont(ofSize: 16), clockwise: false)
centre(text: "Hello flat world", context: context, radius: 0, angle: 0 , colour: UIColor.yellow, font: UIFont.systemFont(ofSize: 16), slantAngle: CGFloat(M_PI_4))


let image = UIGraphicsGetImageFromCurrentImageContext()
UIGraphicsEndImageContext()

Swift 4 Еще раз небольшие изменения, на этот раз фиксирующие устаревание из M_PI, String отказа от .characters, изменение метки параметра в .size(withAttributes... и изменение текстовых атрибутов в NSAttributedStringKey перечисление ...

import UIKit

func centreArcPerpendicular(text str: String, context: CGContext, radius r: CGFloat, angle theta: CGFloat, colour c: UIColor, font: UIFont, clockwise: Bool){
    // *******************************************************
    // This draws the String str around an arc of radius r,
    // with the text centred at polar angle theta
    // *******************************************************

    let characters: [String] = str.map { String($0) } // An array of single character strings, each character in str
    let l = characters.count
    let attributes = [NSAttributedStringKey.font: font]

    var arcs: [CGFloat] = [] // This will be the arcs subtended by each character
    var totalArc: CGFloat = 0 // ... and the total arc subtended by the string

    // Calculate the arc subtended by each letter and their total
    for i in 0 ..< l {
        arcs += [chordToArc(characters[i].size(withAttributes: attributes).width, radius: r)]
        totalArc += arcs[i]
    }

    // Are we writing clockwise (right way up at 12 o'clock, upside down at 6 o'clock)
    // or anti-clockwise (right way up at 6 o'clock)?
    let direction: CGFloat = clockwise ? -1 : 1
    let slantCorrection: CGFloat = clockwise ? -.pi / 2 : .pi / 2

    // The centre of the first character will then be at
    // thetaI = theta - totalArc / 2 + arcs[0] / 2
    // But we add the last term inside the loop
    var thetaI = theta - direction * totalArc / 2

    for i in 0 ..< l {
        thetaI += direction * arcs[i] / 2
        // Call centerText with each character in turn.
        // Remember to add +/-90º to the slantAngle otherwise
        // the characters will "stack" round the arc rather than "text flow"
        centre(text: characters[i], context: context, radius: r, angle: thetaI, colour: c, font: font, slantAngle: thetaI + slantCorrection)
        // The centre of the next character will then be at
        // thetaI = thetaI + arcs[i] / 2 + arcs[i + 1] / 2
        // but again we leave the last term to the start of the next loop...
        thetaI += direction * arcs[i] / 2
    }
}

func chordToArc(_ chord: CGFloat, radius: CGFloat) -> CGFloat {
    // *******************************************************
    // Simple geometry
    // *******************************************************
    return 2 * asin(chord / (2 * radius))
}

func centre(text str: String, context: CGContext, radius r: CGFloat, angle theta: CGFloat, colour c: UIColor, font: UIFont, slantAngle: CGFloat) {
    // *******************************************************
    // This draws the String str centred at the position
    // specified by the polar coordinates (r, theta)
    // i.e. the x= r * cos(theta) y= r * sin(theta)
    // and rotated by the angle slantAngle
    // *******************************************************

    // Set the text attributes
    let attributes = [NSAttributedStringKey.foregroundColor: c, NSAttributedStringKey.font: font]
    //let attributes = [NSForegroundColorAttributeName: c, NSFontAttributeName: font]
    // Save the context
    context.saveGState()
    // Undo the inversion of the Y-axis (or the text goes backwards!)
    context.scaleBy(x: 1, y: -1)
    // Move the origin to the centre of the text (negating the y-axis manually)
    context.translateBy(x: r * cos(theta), y: -(r * sin(theta)))
    // Rotate the coordinate system
    context.rotate(by: -slantAngle)
    // Calculate the width of the text
    let offset = str.size(withAttributes: attributes)
    // Move the origin by half the size of the text
    context.translateBy (x: -offset.width / 2, y: -offset.height / 2) // Move the origin to the centre of the text (negating the y-axis manually)
    // Draw the text
    str.draw(at: CGPoint(x: 0, y: 0), withAttributes: attributes)
    // Restore the context
    context.restoreGState()
}

// *******************************************************
// Playground code to test
// *******************************************************
let size = CGSize(width: 256, height: 256)

UIGraphicsBeginImageContextWithOptions(size, true, 0.0)
let context = UIGraphicsGetCurrentContext()!
// *******************************************************************
// Scale & translate the context to have 0,0
// at the centre of the screen maths convention
// Obviously change your origin to suit...
// *******************************************************************
context.translateBy (x: size.width / 2, y: size.height / 2)
context.scaleBy(x: 1, y: -1)

centreArcPerpendicular(text: "Hello round