I am trying to break CGAffineTransform into rotate, scale, and translate components as follows:
public extension CGAffineTransform {
func rotationRadians() -> CGFloat {
return atan2(b, a)
}
func translation() -> CGPoint {
return CGPoint(x: tx, y: ty)
}
func scaleXY() -> CGPoint {
let scalex = sqrt(a * a + c * c)
let scaley = sqrt(d * d + b * b)
return CGPoint(x: scalex, y: scaley)
}
}
Now I try this code on random transform by breaking it and then constructing it back from the same components, but the answer never comes out to be same, no matter what order I use in concatenation. Not sure what I am doing wrong.
let randomTransform = __CGAffineTransformMake(2.078, 3.459, 1.676, 0, 591, 397)
let rotationRadians = randomTransform.rotationRadians()
let scaleXY = randomTransform.scaleXY()
let translation = randomTransform.translation()
let translationTransform = CGAffineTransform(translationX: translation.x, y: translation.y)
let scalingTransform = CGAffineTransform(scaleX: scaleXY.x, y: scaleXY.y)
let rotationTransform = CGAffineTransform(rotationAngle: rotationRadians)
var newTransform = rotationTransform.concatenating(scalingTransform).concatenating(translationTransform)
NSLog("New transform \(newTransform), original \(randomTransform)")
Here is the output from console:
New transform CGAffineTransform(a: 1.374790977280978, b: 2.965084308709465, c: -2.2884513909600113, d: 1.7812793274062642, tx: 591.0, ty: 397.0), original CGAffineTransform(a: 2.078, b: 3.459, c: 1.676, d: 0.0, tx: 591.0, ty: 397.0)
What you're trying to do is basically impossible, although it might be approachable in some instances using some sophisticated mathematical techniques. See http://callumhay.blogspot.com/2010/10/decomposing-affine-transforms.html for an example.
Related
I would like to project ARPlaneAnchor point to captured image coordinate system.
At this moment i am able to get plane point and project it to view coordinate system by method
func translateTransform(_ x: Float, _ y: Float, _ z: Float) -> float4x4 {
var tf = float4x4(diagonal: SIMD4<Float>(repeating: 1))
tf.columns.3 = SIMD4<Float>(x: x, y: y, z: z, w: 1)
return tf
}
extension ARPlaneAnchor {
func worldPoints() -> (SCNVector3, SCNVector3, SCNVector3, SCNVector3) {
let worldTransform = transform * translateTransform(center.x, 0, center.z)
let width = extent.x
let height = extent.z
let topLeft = worldTransform * translateTransform(-width / 2.0, 0, -height / 2.0)
let topRight = worldTransform * translateTransform(width / 2.0, 0, -height / 2.0)
let bottomLeft = worldTransform * translateTransform(-width / 2.0, 0, height / 2.0)
let bottomRight = worldTransform * translateTransform(width / 2.0, 0, height / 2.0)
let pointTopLeft = SCNVector3(
x: topLeft.columns.3.x,
y: topLeft.columns.3.y,
z: topLeft.columns.3.z
)
let pointTopRight = SCNVector3(
x: topRight.columns.3.x,
y: topRight.columns.3.y,
z: topRight.columns.3.z
)
let pointBottomLeft = SCNVector3(
x: bottomLeft.columns.3.x,
y: bottomLeft.columns.3.y,
z: bottomLeft.columns.3.z
)
let pointBottomRight = SCNVector3(
x: bottomRight.columns.3.x,
y: bottomRight.columns.3.y,
z: bottomRight.columns.3.z
)
return (
pointTopLeft,
pointTopRight,
pointBottomLeft,
pointBottomRight
)
}
And then by projectPoint convert 3D point to 2D like in example
guard let point = arPlane?.worldPoints().0 else { return }
let pp = self.sceneView.session.currentFrame?.camera.projectPoint(SIMD3.init(point), orientation: .landscapeRight, viewportSize: self.view.bounds.size)
But how to convert this point to capturedImage coordinate system?
I am using the below to modify UICollectionViewLayoutAttributes. Method 1 works but not Method 2, anyone can help explain the difference?
guard let newAttrs = attributes?.copy() as? UICollectionViewLayoutAttributes,
let imageViewInfo = imageViewInfo else { return nil }
let center = imageViewInfo.center
//Method 1
newAttrs.transform = CGAffineTransform(scaleX: scale, y: scale)
let x = (newAttrs.center.x-center.x) * scale + igCenter.x
let y = (newAttrs.center.y-center.y) * scale + igCenter.y
newAttrs.center = CGPoint(x: x, y: y)
//Method 2
newAttrs.transform = CGAffineTransform(translationX: -center.x, y: -center.y)
.scaledBy(x: scale, y: scale)
.translatedBy(x: igCenter.x, y: igCenter.y)
https://developer.apple.com/documentation/uikit/uiview/1622459-transform
to change position of the view/cell, modify 'center' instead.
I have an animation like this:
bubble.frame.origin = CGPoint(x: 75, y: -120)
UIView.animate(
withDuration: 2.5,
animations: {
self.bubble.transform = CGAffineTransform(translationX: 0, y: self.view.frame.height * -1.3)
}
)
However, the animation goes in a straight line. I want the animation to do a little back and forth action on its way to its destination. Like a bubble. Any ideas?
If you want to animate along a path you can use CAKeyframeAnimation. The only question is what sort of path do you want. A dampened sine curve might be sufficient:
func animate() {
let box = UIView(frame: CGRect(x: 0, y: 0, width: 100, height: 100))
box.backgroundColor = .blue
box.center = bubblePoint(1)
view.addSubview(box)
let animation = CAKeyframeAnimation(keyPath: "position")
animation.path = bubblePath().cgPath
animation.duration = 5
box.layer.add(animation, forKey: nil)
}
where
private func bubblePath() -> UIBezierPath {
let path = UIBezierPath()
path.move(to: bubblePoint(0))
for value in 1...100 {
path.addLine(to: bubblePoint(CGFloat(value) / 100))
}
return path
}
/// Point on curve at moment in time.
///
/// - Parameter time: A value between 0 and 1.
/// - Returns: The corresponding `CGPoint`.
private func bubblePoint(_ time: CGFloat) -> CGPoint {
let startY = view.bounds.maxY - 100
let endY = view.bounds.minY + 100
let rangeX = min(30, view.bounds.width * 0.4)
let midX = view.bounds.midX
let y = startY + (endY - startY) * time
let x = sin(time * 4 * .pi) * rangeX * (0.1 + time * 0.9) + midX
let point = CGPoint(x: x, y: y)
return point
}
Yielding:
I'm trying to create a curly bracket in Swift, from two points. The idea works fine, with a straight line, because it's currently not dynamic in anyway. My issue lies in finding the dynamic control points and center depending on the location of p1 and p2 points.
This is my current code:
override func viewDidLoad() {
super.viewDidLoad()
let path = UIBezierPath()
let p1 = CGPointMake(100, 100)
let p2 = CGPointMake(300, 100)
let c1 = CGPointMake(150, 80)
let c2 = CGPointMake(250, 80)
var midPoint = midPointForPoints(p1, p2: p2)
var midP1 = midPoint
midP1.x -= 10
var midP2 = midPoint
midP2.x += 10
midPoint.y -= 20
path.moveToPoint(p1)
path.addQuadCurveToPoint(midP1, controlPoint: c1)
path.addLineToPoint(midPoint)
path.addLineToPoint(midP2)
path.addQuadCurveToPoint(p2, controlPoint: c2)
let shape = CAShapeLayer()
shape.lineWidth = 5
shape.strokeColor = UIColor.redColor().CGColor
shape.fillColor = UIColor.clearColor().CGColor
shape.path = path.CGPath
self.view.layer.addSublayer(shape)
}
func midPointForPoints(p1: CGPoint, p2: CGPoint)->CGPoint{
let deltaX = (p1.x + p2.x)/2
let deltaY = (p1.y + p2.y)/2
let midPoint = CGPointMake(deltaX, deltaY)
return midPoint
}
This doesen't take the degrees of the points into account, so if I were to create the two points as:
let p1 = CGPointMake(100, 100)
let p2 = CGPointMake(300, 300)
It would not find the proper control points and midpoint.
Hope someone can help me in the right direction. The idea is of course in the end to just know the two points (p1, p2) and dynamically create every other points, I just typed in values for the moment, to make it easier for myself. I've added images of the issue to better show you.
First create a path for a brace that starts at (0, 0) and ends at (1, 0). Then apply an affine transformation that moves, scales, and rotates the path to span your designed endpoints. It needs to transform (0, 0) to your start point and (1, 0) to your end point. Creating the transformation efficiently requires some trigonometry, but I've done the homework for you:
extension UIBezierPath {
class func brace(from start: CGPoint, to end: CGPoint) -> UIBezierPath {
let path = self.init()
path.move(to: .zero)
path.addCurve(to: CGPoint(x: 0.5, y: -0.1), controlPoint1: CGPoint(x: 0, y: -0.2), controlPoint2: CGPoint(x: 0.5, y: 0.1))
path.addCurve(to: CGPoint(x: 1, y: 0), controlPoint1: CGPoint(x: 0.5, y: 0.1), controlPoint2: CGPoint(x: 1, y: -0.2))
let scaledCosine = end.x - start.x
let scaledSine = end.y - start.y
let transform = CGAffineTransform(a: scaledCosine, b: scaledSine, c: -scaledSine, d: scaledCosine, tx: start.x, ty: start.y)
path.apply(transform)
return path
}
}
Result:
Here's the entire Swift playground I used to make the demo:
import UIKit
import PlaygroundSupport
extension UIBezierPath {
class func brace(from start: CGPoint, to end: CGPoint) -> UIBezierPath {
let path = self.init()
path.move(to: .zero)
path.addCurve(to: CGPoint(x: 0.5, y: -0.1), controlPoint1: CGPoint(x: 0, y: -0.2), controlPoint2: CGPoint(x: 0.5, y: 0.1))
path.addCurve(to: CGPoint(x: 1, y: 0), controlPoint1: CGPoint(x: 0.5, y: 0.1), controlPoint2: CGPoint(x: 1, y: -0.2))
let scaledCosine = end.x - start.x
let scaledSine = end.y - start.y
let transform = CGAffineTransform(a: scaledCosine, b: scaledSine, c: -scaledSine, d: scaledCosine, tx: start.x, ty: start.y)
path.apply(transform)
return path
}
}
class ShapeView: UIView {
override class var layerClass: Swift.AnyClass { return CAShapeLayer.self }
lazy var shapeLayer: CAShapeLayer = { self.layer as! CAShapeLayer }()
}
class ViewController: UIViewController {
override func loadView() {
let view = UIView(frame: CGRect(x: 0, y: 0, width: 600, height: 200))
view.backgroundColor = .white
for (i, handle) in handles.enumerated() {
handle.autoresizingMask = [ .flexibleTopMargin, .flexibleTopMargin, .flexibleBottomMargin, .flexibleRightMargin ]
let frame = CGRect(x: view.bounds.width * 0.1 + CGFloat(i) * view.bounds.width * 0.8 - 22, y: view.bounds.height / 2 - 22, width: 44, height: 44)
handle.frame = frame
handle.shapeLayer.path = CGPath(ellipseIn: handle.bounds, transform: nil)
handle.shapeLayer.lineWidth = 2
handle.shapeLayer.lineDashPattern = [2, 6]
handle.shapeLayer.lineCap = kCALineCapRound
handle.shapeLayer.strokeColor = UIColor.blue.cgColor
handle.shapeLayer.fillColor = nil
view.addSubview(handle)
let panner = UIPanGestureRecognizer(target: self, action: #selector(pannerDidFire(panner:)))
handle.addGestureRecognizer(panner)
}
brace.shapeLayer.lineWidth = 2
brace.shapeLayer.lineCap = kCALineCapRound
brace.shapeLayer.strokeColor = UIColor.black.cgColor
brace.shapeLayer.fillColor = nil
view.addSubview(brace)
setBracePath()
self.view = view
}
override func viewDidLayoutSubviews() {
super.viewDidLayoutSubviews()
setBracePath()
}
private let handles: [ShapeView] = [
ShapeView(),
ShapeView()
]
private let brace = ShapeView()
private func setBracePath() {
brace.shapeLayer.path = UIBezierPath.brace(from: handles[0].center, to: handles[1].center).cgPath
}
#objc private func pannerDidFire(panner: UIPanGestureRecognizer) {
let view = panner.view!
let offset = panner.translation(in: view)
panner.setTranslation(.zero, in: view)
var center = view.center
center.x += offset.x
center.y += offset.y
view.center = center
setBracePath()
}
}
let vc = ViewController()
PlaygroundPage.current.liveView = vc.view
The key to the problem is when the figure is rotated your base vectors will rotate. When your figure is axis-aligned your base vectors are u (1, 0) and v (0, 1).
So when you are performing midPoint.y -= 20 you can see it as the same as midPoint.x -= v.x * 20; midPoint.y -= v.y * 20 where v is (0, 1). The results are the same, check for yourself.
This implementation will do what your code does, only axis independent.
let path = UIBezierPath()
let p1 = CGPointMake(100, 100)
let p2 = CGPointMake(300, 100)
let o = p1.plus(p2).divide(2.0) // origo
let u = p2.minus(o) // base vector 1
let v = u.turn90() // base vector 2
let c1 = o.minus(u.times(0.5)).minus(v.times(0.2)) // CGPointMake(150, 80)
let c2 = o.plus(u.times(0.5)).minus(v.times(0.2)) // CGPointMake(250, 80)
var midPoint = o.minus(v.times(0.2))
var midP1 = o.minus(u.times(0.2))
var midP2 = o.plus(u.times(0.2))
Note: I set the factors to match the initial values in your implementation.
Also added this CGPoint extension for convenience. Hope it helps.
extension CGPoint {
public func plus(p: CGPoint) -> (CGPoint)
{
return CGPoint(x: self.x + p.x, y: self.y + p.y)
}
public func minus(p: CGPoint) -> (CGPoint)
{
return CGPoint(x: self.x - p.x, y: self.y - p.y)
}
public func times(f: CGFloat) -> (CGPoint)
{
return CGPoint(x: self.x * f, y: self.y * f)
}
public func divide(f: CGFloat) -> (CGPoint)
{
return self.times(1.0/f)
}
public func turn90() -> (CGPoint)
{
return CGPoint(x: -self.y, y: x)
}
}
I use the following CAGradientLayer:
let layer = CAGradientLayer()
layer.colors = [
UIColor.redColor().CGColor,
UIColor.greenColor().CGColor,
UIColor.blueColor().CGColor
]
layer.startPoint = CGPointMake(0, 1)
layer.endPoint = CGPointMake(1, 0)
layer.locations = [0.0, 0.6, 1.0]
But when I set bounds property for the layer, it just stretches a square gradient. I need a result like in Sketch 3 app image (see above).
How can I achieve this?
Update: Use context.drawLinearGradient() instead of CAGradientLayer in a manner similar to the following. It will draw gradients that are consistent with Sketch/Photoshop.
If you absolutely must use CAGradientLayer, then here is the math you'll need to use...
It took some time to figure out, but from careful observation, I found out that Apple's implementation of gradients in CAGradientLayer is pretty odd:
First it converts the view to a square.
Then it applies the gradient using start/end points.
The middle gradient will indeed form a 90 degree angle in this resolution.
Finally, it squishes the view down to the original size.
This means that the middle gradient will no longer form a 90 degree angle in the new size. This contradicts the behavior of virtually every other paint application: Sketch, Photoshop, etc.
If you want to implement start/end points as it works in Sketch, you'll need to translate the start/end points to account for the fact that Apple is going to squish the view.
Steps to perform (Diagrams)
Code
import UIKit
/// Last updated 4/3/17.
/// See https://stackoverflow.com/a/43176174 for more information.
public enum LinearGradientFixer {
public static func fixPoints(start: CGPoint, end: CGPoint, bounds: CGSize) -> (CGPoint, CGPoint) {
// Naming convention:
// - a: point a
// - ab: line segment from a to b
// - abLine: line that passes through a and b
// - lineAB: line that passes through A and B
// - lineSegmentAB: line segment that passes from A to B
if start.x == end.x || start.y == end.y {
// Apple's implementation of horizontal and vertical gradients works just fine
return (start, end)
}
// 1. Convert to absolute coordinates
let startEnd = LineSegment(start, end)
let ab = startEnd.multiplied(multipliers: (x: bounds.width, y: bounds.height))
let a = ab.p1
let b = ab.p2
// 2. Calculate perpendicular bisector
let cd = ab.perpendicularBisector
// 3. Scale to square coordinates
let multipliers = calculateMultipliers(bounds: bounds)
let lineSegmentCD = cd.multiplied(multipliers: multipliers)
// 4. Create scaled perpendicular bisector
let lineSegmentEF = lineSegmentCD.perpendicularBisector
// 5. Unscale back to rectangle
let ef = lineSegmentEF.divided(divisors: multipliers)
// 6. Extend line
let efLine = ef.line
// 7. Extend two lines from a and b parallel to cd
let aParallelLine = Line(m: cd.slope, p: a)
let bParallelLine = Line(m: cd.slope, p: b)
// 8. Find the intersection of these lines
let g = efLine.intersection(with: aParallelLine)
let h = efLine.intersection(with: bParallelLine)
if let g = g, let h = h {
// 9. Convert to relative coordinates
let gh = LineSegment(g, h)
let result = gh.divided(divisors: (x: bounds.width, y: bounds.height))
return (result.p1, result.p2)
}
return (start, end)
}
private static func unitTest() {
let w = 320.0
let h = 60.0
let bounds = CGSize(width: w, height: h)
let a = CGPoint(x: 138.5, y: 11.5)
let b = CGPoint(x: 151.5, y: 53.5)
let ab = LineSegment(a, b)
let startEnd = ab.divided(divisors: (x: bounds.width, y: bounds.height))
let start = startEnd.p1
let end = startEnd.p2
let points = fixPoints(start: start, end: end, bounds: bounds)
let pointsSegment = LineSegment(points.0, points.1)
let result = pointsSegment.multiplied(multipliers: (x: bounds.width, y: bounds.height))
print(result.p1) // expected: (90.6119039567129, 26.3225059181603)
print(result.p2) // expected: (199.388096043287, 38.6774940818397)
}
}
private func calculateMultipliers(bounds: CGSize) -> (x: CGFloat, y: CGFloat) {
if bounds.height <= bounds.width {
return (x: 1, y: bounds.width/bounds.height)
} else {
return (x: bounds.height/bounds.width, y: 1)
}
}
private struct LineSegment {
let p1: CGPoint
let p2: CGPoint
init(_ p1: CGPoint, _ p2: CGPoint) {
self.p1 = p1
self.p2 = p2
}
init(p1: CGPoint, m: CGFloat, distance: CGFloat) {
self.p1 = p1
let line = Line(m: m, p: p1)
let measuringPoint = line.point(x: p1.x + 1)
let measuringDeltaH = LineSegment(p1, measuringPoint).distance
let deltaX = distance/measuringDeltaH
self.p2 = line.point(x: p1.x + deltaX)
}
var length: CGFloat {
let dx = p2.x - p1.x
let dy = p2.y - p1.y
return sqrt(dx * dx + dy * dy)
}
var distance: CGFloat {
return p1.x <= p2.x ? length : -length
}
var midpoint: CGPoint {
return CGPoint(x: (p1.x + p2.x)/2, y: (p1.y + p2.y)/2)
}
var slope: CGFloat {
return (p2.y-p1.y)/(p2.x-p1.x)
}
var perpendicularSlope: CGFloat {
return -1/slope
}
var line: Line {
return Line(p1, p2)
}
var perpendicularBisector: LineSegment {
let p1 = LineSegment(p1: midpoint, m: perpendicularSlope, distance: -distance/2).p2
let p2 = LineSegment(p1: midpoint, m: perpendicularSlope, distance: distance/2).p2
return LineSegment(p1, p2)
}
func multiplied(multipliers: (x: CGFloat, y: CGFloat)) -> LineSegment {
return LineSegment(
CGPoint(x: p1.x * multipliers.x, y: p1.y * multipliers.y),
CGPoint(x: p2.x * multipliers.x, y: p2.y * multipliers.y))
}
func divided(divisors: (x: CGFloat, y: CGFloat)) -> LineSegment {
return multiplied(multipliers: (x: 1/divisors.x, y: 1/divisors.y))
}
}
private struct Line {
let m: CGFloat
let b: CGFloat
/// y = mx+b
init(m: CGFloat, b: CGFloat) {
self.m = m
self.b = b
}
/// y-y1 = m(x-x1)
init(m: CGFloat, p: CGPoint) {
// y = m(x-x1) + y1
// y = mx-mx1 + y1
// y = mx + (y1 - mx1)
// b = y1 - mx1
self.m = m
self.b = p.y - m*p.x
}
init(_ p1: CGPoint, _ p2: CGPoint) {
self.init(m: LineSegment(p1, p2).slope, p: p1)
}
func y(x: CGFloat) -> CGFloat {
return m*x + b
}
func point(x: CGFloat) -> CGPoint {
return CGPoint(x: x, y: y(x: x))
}
func intersection(with line: Line) -> CGPoint? {
// Line 1: y = mx + b
// Line 2: y = nx + c
// mx+b = nx+c
// mx-nx = c-b
// x(m-n) = c-b
// x = (c-b)/(m-n)
let n = line.m
let c = line.b
if m-n == 0 {
// lines are parallel
return nil
}
let x = (c-b)/(m-n)
return point(x: x)
}
}
Proof it works regardless of rectangle size
I tried this with a view size=320x60, gradient=[red#0,green#0.5,blue#1], startPoint = (0,1), and endPoint = (1,0).
Sketch 3:
Actual generated iOS screenshot using the code above:
Note that the angle of the green line looks 100% accurate. The difference lies in how the red and blue are blended. I can't tell if that's because I'm calculating the start/end points incorrectly, or if it's just a difference in how Apple blends gradients vs. how Sketch blends gradients.
Here's the math to fix the endPoint
let width = bounds.width
let height = bounds.height
let dx = endPoint.x - startPoint.x
let dy = endPoint.y - startPoint.y
if width == 0 || height == 0 || width == height || dx == 0 || dy == 0 {
return
}
let ux = dx * width / height
let uy = dy * height / width
let coef = (dx * ux + dy * uy) / (ux * ux + uy * uy)
endPoint = CGPoint(x: startPoint.x + coef * ux, y: startPoint.y + coef * uy)
Full code of layoutSubviews method is
override func layoutSubviews() {
super.layoutSubviews()
let gradientOffset = self.bounds.height / self.bounds.width / 2
self.gradientLayer.startPoint = CGPointMake(0, 0.5 + gradientOffset)
self.gradientLayer.endPoint = CGPointMake(1, 0.5 - gradientOffset)
self.gradientLayer.frame = self.bounds
}