I want my node to travel in a sine curve wave, and I tried using that for CGPath. How do I create a CGPath that follows a sine curve? Is there any way other than to manually find the points on the curve, or could I just pass in a sine function?
let action = SKAction.followPath(<the sine path>, asOffset: true, orientToPath: true, duration: 5)
Could this be done through Bezier Paths and then converted into CGPaths? Thanks.
No, there isn't a built in method to build a path from a function, but you can easily write one of your own. In Swift 3:
/// Build path within rectangle
///
/// Given a `function` that converts values between zero and one to another values between zero and one, this method will create `UIBezierPath` within `rect` using that `function`.
///
/// - parameter rect: The `CGRect` of points on the screen.
///
/// - parameter count: How many points should be rendered. Defaults to `rect.size.width`.
///
/// - parameter function: A closure that will be passed an floating point number between zero and one and should return a return value between zero and one as well.
private func path(in rect: CGRect, count: Int? = nil, function: (CGFloat) -> (CGFloat)) -> UIBezierPath {
let numberOfPoints = count ?? Int(rect.size.width)
let path = UIBezierPath()
path.move(to: convert(point: CGPoint(x: 0, y: function(0)), in: rect))
for i in 1 ..< numberOfPoints {
let x = CGFloat(i) / CGFloat(numberOfPoints - 1)
path.addLine(to: convert(point: CGPoint(x: x, y: function(x)), in: rect))
}
return path
}
/// Convert point with x and y values between 0 and 1 within the `CGRect`.
///
/// - parameter point: A `CGPoint` value with x and y values between 0 and 1.
/// - parameter rect: The `CGRect` within which that point should be converted.
private func convert(point: CGPoint, in rect: CGRect) -> CGPoint {
return CGPoint(
x: rect.origin.x + point.x * rect.size.width,
y: rect.origin.y + rect.size.height - point.y * rect.size.height
)
}
So, let's pass a function that does one sine curve as it progresses across the width of the of the rect:
func sinePath(in rect: CGRect, count: Int? = nil) -> UIBezierPath {
// note, since sine returns values between -1 and 1, let's add 1 and divide by two to get it between 0 and 1
return path(in: rect, count: count) { (sin($0 * .pi * 2.0) + 1.0) / 2.0 }
}
Note, the above assumed that you wanted traverse from left to right, building the path defined by the function. You could also do more of a parametric rendition:
/// Build path within rectangle
///
/// Given a `function` that converts values between zero and one to another values between zero and one, this method will create `UIBezierPath` within `rect` using that `function`.
///
/// - parameter rect: The `CGRect` of points on the screen.
///
/// - parameter count: How many points should be rendered. Defaults to `rect.size.width` or `rect.size.width`, whichever is larger.
///
/// - parameter function: A closure that will be passed an floating point number between zero and one and should return a `CGPoint` with `x` and `y` values between 0 and 1.
private func parametricPath(in rect: CGRect, count: Int? = nil, function: (CGFloat) -> (CGPoint)) -> UIBezierPath {
let numberOfPoints = count ?? max(Int(rect.size.width), Int(rect.size.height))
let path = UIBezierPath()
let result = function(0)
path.move(to: convert(point: CGPoint(x: result.x, y: result.y), in: rect))
for i in 1 ..< numberOfPoints {
let t = CGFloat(i) / CGFloat(numberOfPoints - 1)
let result = function(t)
path.addLine(to: convert(point: CGPoint(x: result.x, y: result.y), in: rect))
}
return path
}
Then you can modify the x coordinate using sine curve, and just increment y:
func verticalSinePath(in rect: CGRect, count: Int? = nil) -> UIBezierPath {
// note, since sine returns values between -1 and 1, let's add 1 and divide by two to get it between 0 and 1
return parametricPath(in: rect, count: count) { CGPoint(
x: (sin($0 * .pi * 2.0) + 1.0) / 2.0,
y: $0
) }
}
The virtue of this is that you could also now define any sort of path you want, e.g. a spiral:
func spiralPath(in rect: CGRect, count: Int? = nil) -> UIBezierPath {
return parametricPath(in: rect, count: count) { t in
let r = 1.0 - sin(t * .pi / 2.0)
return CGPoint(
x: (r * sin(t * 10.0 * .pi * 2.0) + 1.0) / 2.0,
y: (r * cos(t * 10.0 * .pi * 2.0) + 1.0) / 2.0
)
}
}
Here are the Swift 2 renditions of the above:
/// Build path within rectangle
///
/// Given a `function` that converts values between zero and one to another values between zero and one, this method will create `UIBezierPath` within `rect` using that `function`.
///
/// - parameter rect: The `CGRect` of points on the screen.
///
/// - parameter count: How many points should be rendered. Defaults to `rect.size.width`.
///
/// - parameter function: A closure that will be passed an floating point number between zero and one and should return a return value between zero and one as well.
private func path(in rect: CGRect, count: Int? = nil, function: (CGFloat) -> (CGFloat)) -> UIBezierPath {
let numberOfPoints = count ?? Int(rect.size.width)
let path = UIBezierPath()
path.moveToPoint(convert(point: CGPoint(x: 0, y: function(0)), rect: rect))
for i in 1 ..< numberOfPoints {
let x = CGFloat(i) / CGFloat(numberOfPoints - 1)
path.addLineToPoint(convert(point: CGPoint(x: x, y: function(x)), rect: rect))
}
return path
}
/// Convert point with x and y values between 0 and 1 within the `CGRect`.
///
/// - parameter point: A `CGPoint` value with x and y values between 0 and 1.
/// - parameter rect: The `CGRect` within which that point should be converted.
private func convert(point point: CGPoint, rect: CGRect) -> CGPoint {
return CGPoint(
x: rect.origin.x + point.x * rect.size.width,
y: rect.origin.y + rect.size.height - point.y * rect.size.height
)
}
func sinePath(in rect: CGRect, count: Int? = nil) -> UIBezierPath {
// note, since sine returns values between -1 and 1, let's add 1 and divide by two to get it between 0 and 1
return path(in: rect, count: count) { (sin($0 * CGFloat(M_PI * 2.0)) + 1.0) / 2.0 }
}
/// Build path within rectangle
///
/// Given a `function` that converts values between zero and one to another values between zero and one, this method will create `UIBezierPath` within `rect` using that `function`.
///
/// - parameter rect: The `CGRect` of points on the screen.
///
/// - parameter count: How many points should be rendered. Defaults to `rect.size.width`.
///
/// - parameter function: A closure that will be passed an floating point number between zero and one and should return a `CGPoint` with `x` and `y` values between 0 and 1.
private func parametricPath(in rect: CGRect, count: Int? = nil, function: (CGFloat) -> (CGPoint)) -> UIBezierPath {
let numberOfPoints = count ?? max(Int(rect.size.width), Int(rect.size.height))
let path = UIBezierPath()
let result = function(0)
path.moveToPoint(convert(point: CGPoint(x: result.x, y: result.y), rect: rect))
for i in 1 ..< numberOfPoints {
let t = CGFloat(i) / CGFloat(numberOfPoints - 1)
let result = function(t)
path.addLineToPoint(convert(point: CGPoint(x: result.x, y: result.y), rect: rect))
}
return path
}
func verticalSinePath(in rect: CGRect, count: Int? = nil) -> UIBezierPath {
// note, since sine returns values between -1 and 1, let's add 1 and divide by two to get it between 0 and 1
return parametricPath(in: rect, count: count) { CGPoint(
x: (sin($0 * CGFloat(M_PI * 2.0)) + 1.0) / 2.0,
y: $0
) }
}
func spiralPath(in rect: CGRect, count: Int? = nil) -> UIBezierPath {
return parametricPath(in: rect, count: count) { t in
let r = 1.0 - sin(t * CGFloat(M_PI_2))
return CGPoint(
x: (r * sin(t * 10.0 * CGFloat(M_PI * 2.0)) + 1.0) / 2.0,
y: (r * cos(t * 10.0 * CGFloat(M_PI * 2.0)) + 1.0) / 2.0
)
}
}