I have a view that I draw using Core Graphics, which in this example is a segmented circle. The user can touch the circle to create a point along its circumference; this creates a subview on the UIView that contains the circle graphic.
Then I've implemented a pinch-zoom gesture which causes the circle to redraw to its new size. I've seen most implementations of pinch zoom use transform properties, but I've chosen to redraw because it's all vectors and gives a clean result.
My problem is repositioning the point views. I calculate the required position of those points based on the scale of the parent view: as it changes I update the x/y coords of the point views. However, it seems there are some precision issues: as the circle shape size increases, the points drift so they aren't right on the line anymore. Here's a couple examples:
This is where the circle is at 100% scale. Note the perfect positioning of that black point. But when you zoom in...
The point drifts off-line.
And here's some code. I derive the new size of the circle from the pinch gesture's scale (I modify if a bit to constrain and slow it down for UI purposes, so that's deltaScale) and then draw it like so:
let currentSize = self.shape!.bounds.size
let newSize = CGSize(width: self.originalSize.width * deltaScale, height: self.originalSize.height * deltaScale)
self.shape?.frame.size = newSize
self.shape?.center = self.originalCentre!
self.shape?.shapeSize = newSize
self.shape?.setNeedsDisplay()
As the pinch-zoom gesture completes, I calculate the factor:
let xScale = Double(newSize.width) / Double(currentSize.width)
let yScale = Double(newSize.height) / Double(currentSize.height)
self.points = self.points.map{(thisPoint) -> UIView in
thisPoint.center = CGPoint(x: Double(thisPoint.center.x) * xScale, y: Double(thisPoint.center.y) * yScale)
return thisPoint
}
(I was using CGFloats, but switched to Doubles in the hope that it would give me the precision I needed. Alas.)
You're accumulating roundoff errors. This is getting executed repeatedly:
thisPoint.center = CGPoint(x: Double(thisPoint.center.x) * xScale, y: Double(thisPoint.center.y) * yScale)
Repeating any calculation of the form 'x=f(x)' with anything less than unlimited precision will result in drift.
Trick is to not have 'thisPoint.center' on both sides of the equal sign. Best way to do that is to have thisPoint.center be a pure function of some other state. Commenter suggested storing desired angle, that would work well. Then you could do:
thisPoint.center = f(thisPoint.someRadians), where 'f' converts from polar to rectangular coordinates, factoring in the scale of the circle.
Related
I'm creating an audio waveform, which should look like this:
Notice how the corners of the lines are curved, according to the direction.
My waveform currently has only straight lines:
How can I achieve the desired results?
My current code for the waveform:
fileprivate func createPath(with points: [CGPoint], pointCount: Int, in rect: CGRect) -> CGPath {
let path = UIBezierPath()
guard pointCount > 0 else {
return path.cgPath
}
guard rect.height > 0, rect.width > 0 else {
return path.cgPath
}
path.move(to: CGPoint(x: 0, y: 0))
let minValue = 1 / (rect.height / 2)
for index in 0..<(pointCount / 2) {
var point = points[index * 2]
path.move(to: point)
point.y = max(point.y, minValue)
point.y = -point.y
path.addLine(to: point)
}
let scaleX = (rect.width - 1) / CGFloat(pointCount - 1)
let halfHeight = rect.height / 2
let scaleY = halfHeight
var transform = CGAffineTransform(scaleX: scaleX, y: scaleY)
transform.ty = halfHeight
path.apply(transform)
return path.cgPath
}
There are two ways to accomplish this:
Rather than treating each bar as a wide line, fill it as a shape, each with its own left, top, right, and bottom. And the top would then be a bézier.
Rather than adjust the top of each bar, you can make the bars all go from minimum to maximum values and then add a mask over the whole graph to render the smoothed shape.
E.g., this shows a few data points, overlays the Catmull Rom bézier, I then extend the bars (because sometimes the curve of the bézier goes above the existing bars, and then use the bézier as mask instead of an overlay.
Additional observations:
Please note, your first image with the curved tops of the bars has another feature that makes it look smooth: The data points, themselves, are smoothed. Your second image features far greater volatility than the first.
The source of this volatility (which is common in audio tracks, or pretty much any DSP dataset), or lack thereof, is not relevant here. What is relevant is that if the data samples are highly variable, an interpolation algorithm for curving the tops of the bars can actually exaggerate the volatility. Single point spikes will be unusually sharp. Double point spikes will actually appear higher than they really are.
E.g. consider this dataset:
With something this sort of variability, it could be argued that the “rounding” of the bars makes the results harder to read and/or is misleading:
While I have attempted to answer the question, one must ask whether this whole exercise is prudent. While there might be an aesthetic appeal to curves to the tops of the bars, it suggests a degree of continuity/precision that is greater than what the underlying data likely supports. The square bars more accurately represent the reality of ranges of values for which data was aggregated and, for this reason, are the common visual representation.
Before writing this question, I've
had experience with Affine transforms for views
read the Transforms documentation in the Quartz 2D Programming Guide
seen this detailed CALayer tutorial
downloaded and run the LayerPlayer project from Github
However, I'm still having trouble understanding how to do basic transforms on a layer. Finding explanations and simple examples for translate, rotate and scale has been difficult.
Today I finally decided to sit down, make a test project, and figure them out. My answer is below.
Notes:
I only do Swift, but if someone else wants to add the Objective-C code, be my guest.
At this point I am only concerned with understanding 2D transforms.
Basics
There are a number of different transforms you can do on a layer, but the basic ones are
translate (move)
scale
rotate
To do transforms on a CALayer, you set the layer's transform property to a CATransform3D type. For example, to translate a layer, you would do something like this:
myLayer.transform = CATransform3DMakeTranslation(20, 30, 0)
The word Make is used in the name for creating the initial transform: CATransform3DMakeTranslation. Subsequent transforms that are applied omit the Make. See, for example, this rotation followed by a translation:
let rotation = CATransform3DMakeRotation(CGFloat.pi * 30.0 / 180.0, 20, 20, 0)
myLayer.transform = CATransform3DTranslate(rotation, 20, 30, 0)
Now that we have the basis of how to make a transform, let's look at some examples of how to do each one. First, though, I'll show how I set up the project in case you want to play around with it, too.
Setup
For the following examples I set up a Single View Application and added a UIView with a light blue background to the storyboard. I hooked up the view to the view controller with the following code:
import UIKit
class ViewController: UIViewController {
var myLayer = CATextLayer()
#IBOutlet weak var myView: UIView!
override func viewDidLoad() {
super.viewDidLoad()
// setup the sublayer
addSubLayer()
// do the transform
transformExample()
}
func addSubLayer() {
myLayer.frame = CGRect(x: 0, y: 0, width: 100, height: 40)
myLayer.backgroundColor = UIColor.blue.cgColor
myLayer.string = "Hello"
myView.layer.addSublayer(myLayer)
}
//******** Replace this function with the examples below ********
func transformExample() {
// add transform code here ...
}
}
There are many different kinds of CALayer, but I chose to use CATextLayer so that the transforms will be more clear visually.
Translate
The translation transform moves the layer. The basic syntax is
CATransform3DMakeTranslation(_ tx: CGFloat, _ ty: CGFloat, _ tz: CGFloat)
where tx is the change in the x coordinates, ty is the change in y, and tz is the change in z.
Example
In iOS the origin of the coordinate system is in the top left, so if we wanted to move the layer 90 points to the right and 50 points down, we would do the following:
myLayer.transform = CATransform3DMakeTranslation(90, 50, 0)
Notes
Remember that you can paste this into the transformExample() method in the project code above.
Since we are just going to deal with two dimensions here, tz is set to 0.
The red line in the image above goes from the center of the original location to the center of the new location. That's because transforms are done in relation to the anchor point and the anchor point by default is in the center of the layer.
Scale
The scale transform stretches or squishes the layer. The basic syntax is
CATransform3DMakeScale(_ sx: CGFloat, _ sy: CGFloat, _ sz: CGFloat)
where sx, sy, and sz are the numbers by which to scale (multiply) the x, y, and z coordinates respectively.
Example
If we wanted to half the width and triple the height, we would do the following
myLayer.transform = CATransform3DMakeScale(0.5, 3.0, 1.0)
Notes
Since we are only working in two dimensions, we just multiply the z coordinates by 1.0 to leave them unaffected.
The red dot in the image above represents the anchor point. Notice how the scaling is done in relation to the anchor point. That is, everything is either stretched toward or away from the anchor point.
Rotate
The rotation transform rotates the layer around the anchor point (the center of the layer by default). The basic syntax is
CATransform3DMakeRotation(_ angle: CGFloat, _ x: CGFloat, _ y: CGFloat, _ z: CGFloat)
where angle is the angle in radians that the layer should be rotated and x, y, and z are the axes about which to rotate. Setting an axis to 0 cancels a rotation around that particular axis.
Example
If we wanted to rotate a layer clockwise 30 degrees, we would do the following:
let degrees = 30.0
let radians = CGFloat(degrees * Double.pi / 180)
myLayer.transform = CATransform3DMakeRotation(radians, 0.0, 0.0, 1.0)
Notes
Since we are working in two dimentions, we only want the xy plane to be rotated around the z axis. Thus we set x and y to 0.0 and set z to 1.0.
This rotated the layer in a clockwise direction. We could have rotated counterclockwise by setting z to -1.0.
The red dot shows where the anchor point is. The rotation is done around the anchor point.
Multiple transforms
In order to combine multiple transforms we could use concatination like this
CATransform3DConcat(_ a: CATransform3D, _ b: CATransform3D)
However, we will just do one after another. The first transform will use the Make in its name. The following transforms will not use Make, but they will take the previous transform as a parameter.
Example
This time we combine all three of the previous transforms.
let degrees = 30.0
let radians = CGFloat(degrees * Double.pi / 180)
// translate
var transform = CATransform3DMakeTranslation(90, 50, 0)
// rotate
transform = CATransform3DRotate(transform, radians, 0.0, 0.0, 1.0)
// scale
transform = CATransform3DScale(transform, 0.5, 3.0, 1.0)
// apply the transforms
myLayer.transform = transform
Notes
The order that the transforms are done in matters.
Everything was done in relation to the anchor point (red dot).
A Note about Anchor Point and Position
We did all our transforms above without changing the anchor point. Sometimes it is necessary to change it, though, like if you want to rotate around some other point besides the center. However, this can be a little tricky.
The anchor point and position are both at the same place. The anchor point is expressed as a unit of the layer's coordinate system (default is 0.5, 0.5) and the position is expressed in the superlayer's coordinate system. They can be set like this
myLayer.anchorPoint = CGPoint(x: 0.0, y: 1.0)
myLayer.position = CGPoint(x: 50, y: 50)
If you only set the anchor point without changing the position, then the frame changes so that the position will be in the right spot. Or more precisely, the frame is recalculated based on the new anchor point and old position. This usually gives unexpected results. The following two articles have an excellent discussion of this.
About the anchorPoint
Translate rotate translate?
See also
Border, rounded corners, and shadow on a CALayer
Using a border with a Bezier path for a layer
I'm trying to make Jigsaw puzzle game in SpriteKit. To make things easier I using 9x9 squared tiles board. On each tile is one childNode with piece of image from it area.
But here's starts my problem. Piece of jigsaw puzzle isn't perfect square, and when I apply SKTexture to node it just place from anchorPoint = {0,0}. And result isn't pretty, actually its terrible.
https://www.dropbox.com/s/2di30hk5evdd5fr/IMG_0086.jpg?dl=0
I managed to fix those tiles with right and top "hooks", but left and bottom side doesn't care about anything.
var sprite = SKSpriteNode()
let originSize = frame.size
let textureSize = texture.size()
sprite.size = originSize
sprite.texture = texture
sprite.size = texture.size()
let x = (textureSize.width - originSize.width)
let widthRate = x / textureSize.width
let y = (textureSize.height - originSize.height)
let heightRate = y / textureSize.height
sprite.anchorPoint = CGPoint(x: 0.5 - (widthRate * 0.5), y: 0.5 - (heightRate * 0.5))
sprite.position = CGPoint(x: frame.width * 0.5, y: frame.height * 0.5)
addChild(sprite)
Can you give me some advice?
I don't see a way you can get placement right without knowing more about the piece texture you are using because they will all be different. Like if the piece has a nob on any of the sides and the width width/height the nob will add to the texture. Hard to tell in the pic but even if it doesn't have a nob and instead has an inset it might add varying sizes.
Without knowing anything about how the texture is created I am not able to offer help on that. But I do believe the issue starts with that. If it were me I would create a square texture with additional alpha to center the piece correctly. So the center of that texture would always be placed in the center of a square on the grid.
With all that being said I do know that adding that texture to a node and then adding that node to a SKNode will make your placement go smoother with the way you currently have it. The trick will then only be placing that textured piece correctly within the empty SKNode.
For example...
let piece = SKSpriteNode()
let texturedPiece = SKSpriteNode(texture: texture)
//positioning
//offset x needs to be calculated with additional info about the texture
//for example it has just a nob on the right
let offsetX : CGFloat = -nobWidth/2
//offset y needs to be calculated with additional info about the texture
//for example it has a nob on the top and bottom
let offsetY : CGFloat = 0.0
texturedPiece.position = CGPointMake(offsetX, offsetY)
piece.addChild(texturedPiece)
let squareWidth = size.width/2
//Now that the textured piece is placed correctly within a parent
//placing the parent is super easy and consistent without messing
//with anchor points. This will also make rotations nice.
piece.position = CGPoint(x: squareWidth/2, y: squareWidth/2)
addChild(piece)
Hopefully that makes sense and didn't confuse things further.
I essentially want the "sprites" to collide when they stick together. However, I don't want the "joint" to be rigid; I essentially want the sprites to be able to move around as long as they are in contact with each other. Imagine two circles connected, and you can move one circle around the other, as long as it remains in contact.
I found this question: How to make one body stick to another moving object in SpriteKit and a lot of other resources that explain how to make sprites stick upon collision, but they all use SKJoints, which are rigid are not really flexible.
I guess another way to phrase it would be to say that I want the sprites to stick, but I want them to be able to "slide" on each other.
Well, I can think of one workaround, but this wouldn't work with non-normal polygons.
Sticking (pun unintended) with your circles example, what if you lock the position of the circle?
let circle1 = center circle
let circle2 = movable circle
Knowing the width of both circles, you can place in the update function that the position should be exactly the distance of:
((circle1.frame.width / 2) + (circle2.frame.width / 2))
If you're up to it, here's some code to help you on your way.
override func update(currentTime: CFTimeInterval) {
{
let distance = hypotf(Float(circle1.position.x - circle2.position.x), Float(circle1.position.y - circle2.position.y))
//calculate circle distances from each other
let radius = ((circle1.frame.width / 2) + (circle2.frame.width / 2))
//distance of circle positions
if distance != radius
{
//if distance is less or more than radius
let pointA = circle1.position
let pointB = circle2.position
let pointC = CGPointMake(pointB.x + 2, pointB.y)
let angle_ab = atan2(pointA.y - pointB.y, pointA.x - pointB.x)
let angle_cb = atan2(pointC.y - pointB.y, pointC.x - pointB.x)
let angle_abc = angle_ab - angle_cb
//get angle of circles from each other using atan2
let vectorx = cos(angle_abc)
let vectory = sin(angle_abc)
//convert angle into vectors
let x = circle1.position.x + radius * vectorx
let y = circle1.position.y + radius * vectory
//get new coordinates from vector, radius and center circle position
circle2.position = CGPointMake(x, y)
//set new position
}
}
Well you need to write code to make sure the movable circle, is well movable.
But, this should work.
I haven't tested this yet though, and I haven't even learned geometry let alone trig in school yet.
If I'm reading your question as you intended it, you can still use joints- just create actions with Inverse Kinematic constraints that allow rotation and translation around the contacting circles' joint.
https://developer.apple.com/library/prerelease/ios/documentation/SpriteKit/Reference/SKAction_Ref/index.html#//apple_ref/doc/uid/TP40013017-CH1-SW72
I am making a level based game with many different objects, all different. In each level, there will be different amounts of each type of object. Thus, I have been trying to make the drawing part as generic as possible so that all I have to do is pass in the coords and it will automatically draw. To do this, I have made a protocol that forces each object class to implement the method getBP(), which returns the UIBezierPath to draw for each. Then, the view class just has to say
Object.getBP().fill()
However, this has been leading to some strange problems. The object does not draw at the correct coordinates. The y coordinate is correct, but the x coordinate puts it always at the left of the screen. I think it may be the fact that the Bezier Path is not being created in the view class. Here is my code in Surface.swift (this is meant to draw a surface in the game):
func getBP() -> UIBezierPath {
var rect:CGRect
var length:Double = getSurfaceVector().getMagnitude()//length of the surface
var cx = points.1.x+(points.0.x-points.1.x)//center coords of the surface
var cy = points.1.y+(points.0.y-points.1.y)
var bp = UIBezierPath(roundedRect: CGRectMake(CGFloat(cx - length/2), CGFloat(cy-RECT_HEIGHT/2), CGFloat(length), CGFloat(RECT_HEIGHT)), cornerRadius: CGFloat(5))
let transform:CGAffineTransform = CGAffineTransformMakeRotation(CGFloat(Double(angle)*(Double(M_PI)/Double(180))))
bp.applyTransform(transform)
return bp
}
points is just a tuple with the start and end points of the surface. RECT_HEIGHT is the height of the rectangle that is drawn to represent the surface. angle is the angle from horizontal of the surface.
Creating the surface in View.swift, I do this:
Surface(fixed: true, points: (Vector(x: 50, y:100), Vector(x: Double(UIScreen.mainScreen().bounds.width), y: 100)))
I add that surface to the array of objects in the game. I draw it in the View.swift file by saying
surface.stroke()
The surface draws on the screen with a y value of 100, but it is centered at x = 0 so that it is half on and half off of the screen. Also, it doesn't draw at the angle - it is always horizontal. Is there some better way of doing this? What is happening?