How to convert points to radians in Objective-C? - ios

In my app I'm using UIBezierPath to draw an arc into a circle. I'm trying to correlate a number to radians. So let's say a user has a certain number of points, and the points are capped at 100 points. I want 100 points to be 360 degrees. I want the first 33% of the circle to be green, and then from 34% to the next 66% of the circle to be stroked in orange, and then from 67% to 100% in red.
The issue I'm having here is converting percents of a circle to radians. When creating a UIBezier path, I need to provide a startAngle and endAngle, and I'm having a bit of trouble converting these points to radian values.
How would I go about solving this?
Thanks

CGFloat radians = percent * 0.01 * 2 * M_PI;
Simple algebra.
Swift version
Making it more general purpose, you can write a conversion function:
func radiansFromPercent(_ percent: CGFloat) -> CGFloat {
return percent * 0.01 * 2 * CGFloat.pi
}

I think what you want is the unit circle. Remember back to trigonometry when you used the unit circle? Same thing will apply here. If you need to get π - in Swift just say let π = CGFloat.pi (hold alt+p for the special character). In Objective-C - I think it's CGFloat π = M_PI;.
You could go from zero to 2π/3 for the first 1/3, then from 2π/3 to 4π/3, then from 4π/3 to 2π (full circle).
I should not that I didn't make this graphic - it's from a tutorial on RayWenderlich.com - but it's oriented perfectly for the iOS coordinate system.

Objective-C
CGFloat fullCircle = 2 * M_PI ; // M_PI Pi number which is half of the circle in radian
CGFloat startPoint = 0.0 ;
CGFloat endPoint = fullCircle * 0.33 ;
// Assuming circling clockwise
// .... Draw first step UIBezierPath
startPoint = endPoint ;
endPoint = startPoint + fullCircle * 0.33 ;
// .... Draw second step UIBezierPath
startPoint = endPoint ;
endPoint = fullCircle - startPoint ; // This to make sure the whole circle will be covered
// .... Draw the last step UIBezierPath
Swift
let fullCircle = 2 * M_PI // M_PI Pi number which is half of the circle in radian
var startPoint: Float = 0.0
var endPoint: Float = fullCircle * 0.33
// Assuming circling clockwise
// .... Draw first step UIBezierPath
startPoint = endPoint
endPoint = startPoint + fullCircle * 0.33
// .... Draw second step UIBezierPath
startPoint = endPoint
endPoint = fullCircle - startPoint // This to make sure the whole circle will be covered
// .... Draw the last step UIBezierPath

Related

Choosing a random point within a circular image in a UIImageView

I have an app with a color wheel and I'm trying to pick a random color within the color wheel. However, I'm having problems verifying that the random point falls within the color wheel.
Here's the code as it currently is:
CGPoint randomPoint = CGPointMake(arc4random() % (int)colorWheel.bounds.size.width, arc4random() % (int)colorWheel.bounds.size.height);
UIColor *randomColor = [self colorOfPoint:randomPoint];
CGPoint pointInView = [colorWheel convertPoint:randomPoint fromView:colorWheel.window];
if (CGRectContainsPoint(colorWheel.bounds, pointInView)) {
NSLog(#"%#", randomColor);
}
else {
NSLog(#"out of bounds");
}
A couple of other methods of verifying the point that I've tried with no luck:
if (CGRectContainsPoint(colorWheel.frame, randomPoint)) {
NSLog(#"%#", randomColor);
}
if ([colorWheel pointInside:[self.view convertPoint:randomPoint toView: colorWheel] withEvent: nil]) {
NSLog(#"%#", randomColor);
}
Sometimes it'll output "out of bounds", and sometimes it'll just output that the color is white (the background around the color wheel is currently white but there's no white in the color wheel image).
The color wheel image is a circle, so I'm not sure if that's throwing off the test, although it seems like white pops up way too frequently for it to just be a transparent square outline around the image giving a white color.
If you want to generate a random point in a circle, you would do better to pick your point in polar coordinates and then convert it to Cartesian.
The polar coordinate space uses two dimesions, radius and angle. Radius is just the distance from the center, and angle usually starts at "due east" for 0, and goes around counter-clockwise up to 2π (that's in radians, 360˚ of course in degrees).
Presumably your wheel is divided into simple wedges, so the radius actually doesn't matter; you just need to pick a random angle.
uint32_t angle = arc4random_uniform(360);
// Radius will just be halfway from the center to the edge.
// This assumes the circle is exactly enclosed, i.e., diameter == width
CGFloat radius = colorWheel.bounds.size.width / 4;
This function will give you a Cartesian point from your polar coordinates. Wikipedia explains the simple math if you're interested.
/** Convert the polar point (radius, theta) to a Cartesian (x,y). */
CGPoint poltocar(CGFloat radius, CGFloat theta)
{
return (CGPoint){radius * cos(theta), radius * sin(theta)};
}
The function uses radians for theta, because sin() and cos() do, so change the angle to radians, and then you can convert:
CGFloat theta = (angle * M_PI) / 180.0
CGPoint randomPoint = poltocar(radius, theta);
One last step: this circle has its origin at the same place as the view, that is, in the corner, so you need to translate the point to use the center as the origin.
CGPoint addPoints(CGPoint lhs, CGPoint rhs)
{
return (CGPoint){lhs.x + rhs.x, lhs.y, rhs.y};
}
CGPoint offset = (CGPoint){colorWheel.bounds.size.width / 2,
colorWheel.bounds.size.height / 2};
randomPoint = addPoints(randomPoint, offset);
And your new randomPoint will always be within the circle.
I agree with #JoshCaswell's approach, but FYI, the reason the OP code is not working is that the test for inside a circle is incorrect.
The coordinate conversion is unnecessary, and the test against a rectangle is sure to be wrong. Instead, work out how far the random point is from the center and compare that with the radius.
CGFloat centerX = colorWheel.bounds.size.width / 2.0;
CGFloat centerY = colorWheel.bounds.size.height / 2.0;
CGFloat distanceX = centerX - randomPoint.x;
CGFloat distanceY = centerY - randomPoint.y;
CGFloat distance = distanceX*distanceX + distanceY*distanceY;
CGFloat radius = colorWheel.bounds.size.width / 2.0; // just a guess
CGFloat r2 = radius*radius;
// this compares the square of the distance with r^2, to save a sqrt operation
BOOL isInCircle = distance < r2;

How to create graph pies with different sizes using bézier paths in swift?

I want to make a nice graphic pie with 8 equal slices, that can be individually scaled or resized depending on an Int or something like this. This would look something like below just that all the slices should be equally cut:
I have tried this in Objective-C but it makes just one slice:
-(CAShapeLayer *)createPieSlice {
CAShapeLayer *slice = [CAShapeLayer layer];
slice.fillColor = [UIColor redColor].CGColor;
slice.strokeColor = [UIColor blackColor].CGColor;
slice.lineWidth = 3.0;
CGFloat angle = DEG2RAD(-60.0);
CGPoint center = CGPointMake(100.0, 100.0);
CGFloat radius = 100.0;
UIBezierPath *piePath = [UIBezierPath bezierPath];
[piePath moveToPoint:center];
[piePath addLineToPoint:CGPointMake(center.x + radius * cosf(angle), center.y + radius * sinf(angle))];
[piePath addArcWithCenter:center radius:radius startAngle:angle endAngle:DEG2RAD(60.0) clockwise:YES];
// [piePath addLineToPoint:center];
[piePath closePath]; // this will automatically add a straight line to the center
slice.path = piePath.CGPath;
return slice;
}
How can I achieve that graph in swift?
Break the problem into logical pieces.
You have wedges of different arc widths. All those radii need to add up to a full circle. I assume they represent fractions of something that adds up to 100%. Do you want a specific order? If so, map your fractions in the order you want, such that they all add up to 100%.
Then write code that starts at an angle of zero, and creates arcs that are the specified fraction of 2π. Each one would start at the end of the previous one. Assign a radius that's appropriate based on the data you need.
Now write code that creates closed path segments in a UIBezierPath.
EDIT
You've clarified, and told us that you always want 8 slices of the same width but with different radii.
So you need to write code that takes 8 input values and plots it as 8 arcs with different radius values.
Let's say your input value is an array of floats ranging from 0 to 1. At zero, the wedge is zero-sized. At 1.0, it's the largest circle size that will fit in your view (half the width of a square view.
So you would create an array of 8 floats:
var fractions = [0.5, 0.7, 0.3, 0.1, 1.0 .6, .2, .9]
The code to create a bezier curve with 8 arcs might look something like this:
let pi = 3.1415826
let largestRadius = myView.width/2
let piePath = UIBezierPath()
for (index, afloat) in fractions
{
let startAngle = Double(index) / fractions.count * 2 * pi
let endAngle = Double(index+1) / fractions.count * 2 * pi
let thisRadius = largestRadius * afloat
let center = CGPointMake( myView.width/2, myView.height/2)
piePath.moveToPoint(center)
piePath.addArcWithCenter(center,
radius: thisRadius,
startAngle: startAngle,
endAngle: endAngle,
clockwise: true)
piePath.lineToPoint(center)
piePath.closePath()
}
I think the code above would create 8 closed pie-slice paths, but I'm not positive. It might be necessary to add a lineToPoint call between the first moveToPoint call and the arc call.
Edit #2:
Since I am learning Swift, I decided to take this as an exercise and wrote a sample project that generates pie charts using a shape layer and a a custom path created from a UIBezierPath, as outlined above. You can find the sample project on github: PieCharts project on Github
I have managed to solve my problem using Core Graphics! Thanks #duncan-c for your interest.
EDIT:
I have dropped my first solution in the favour of #duncan-c's solution, that works better for my needs!
import UIKit
class Pie: UIView {
// In range of 0.0 to 1.0
var endArc:CGFloat = 0.0 {
didSet {
setNeedsDisplay()
}
}
var arcWidth:CGFloat = 5.0
var arcColor = UIColor()
var arcBackgroundColor = UIColor.clearColor()
var arcStrokeColor = UIColor()
var startFloat:CGFloat = 0.0
var radius:CGFloat = 0.0
var radiusSize: CGFloat = 0.0
override func drawRect(rect: CGRect) {
// Important constants for circle
let fullCircle = 2.0 * CGFloat(M_PI)
let start:CGFloat = startFloat * fullCircle
let end:CGFloat = endArc * fullCircle + start
// Find the centerpoint of the rect
var centerPoint = CGPointMake(CGRectGetMidX(rect), CGRectGetMidY(rect))
// Set the radius
radius = (radiusSize - arcWidth) / 2.0
// Starting point for all drawing code is getting the context.
let context = UIGraphicsGetCurrentContext()
// Set colorspace
let colorspace = CGColorSpaceCreateDeviceRGB()
// Set line attributes
CGContextSetLineWidth(context, arcWidth)
// Draw the pie
CGContextSetStrokeColorWithColor(context, arcStrokeColor.CGColor)
CGContextSetFillColorWithColor(context, arcColor.CGColor)
CGContextMoveToPoint(context, centerPoint.x, centerPoint.y)
CGContextAddArc(context, centerPoint.x, centerPoint.y, radius, start, end, 0)
CGContextFillPath(context)
}
}
And then subclassd the UIView where I needed using:
#IBOutlet weak var graph: Pie!
override func awakeFromNib() {
super.awakeFromNib()
let backgroundTrackColor = UIColor.clearColor()
let strokeColor = UIColor(white: 0.15, alpha: 1.0)
graph.radiusSize = 50.0
graph.arcBackgroundColor = backgroundTrackColor
graph.arcStrokeColor = strokeColor
graph.arcColor = UIColor.redColor()
graph.startFloat = 0.750
graph.arcWidth = 5.0
graph.endArc = 0.125
}

Finding an angle with 3 CGPoints

In my application, a user taps 3 times and an angle will be created by the 3 points that were tapped. It draws the angle perfectly. I am trying to calculate the angle at the second tap, but I think I am doing it wrong (probably a math error). I haven't covered this in my calculus class yet, so I am going off of a formula on wikipedia.
http://en.wikipedia.org/wiki/Law_of_cosines
Here is what I am trying:
Note: First, Second, and Third are CGPoints created at the user's tap.
CGFloat xDistA = (second.x - third.x);
CGFloat yDistA = (second.y - third.y);
CGFloat a = sqrt((xDistA * xDistA) + (yDistA * yDistA));
CGFloat xDistB = (first.x - third.x);
CGFloat yDistB = (first.y - third.y);
CGFloat b = sqrt((xDistB * xDistB) + (yDistB * yDistB));
CGFloat xDistC = (second.x - first.x);
CGFloat yDistC = (second.y - first.y);
CGFloat c = sqrt((xDistC * xDistC) + (yDistC * yDistC));
CGFloat angle = acos(((a*a)+(b*b)-(c*c))/((2*(a)*(b))));
NSLog(#"FULL ANGLE IS: %f, ANGLE IS: %.2f",angle, angle);
Sometimes, it gives the angle as 1 which doesn't make sense to me. Can anyone explain why this is, or how to fix it please?
Not sure if this is the main problem but it is a problem
Your answer gives the angle at the wrong point:
To get the angle in green (which is probably angle you want based on your variable names "first", "second" and "third), use:
CGFloat angle = acos(((a*a)+(c*c)-(b*b))/((2*(a)*(c))));
Here's a way that circumvents the law of cosines and instead calculates the angles of the two vectors. The difference between the angles is the searched value:
CGVector vec1 = { first.x - second.x, first.y - second.y };
CGVector vec2 = { third.x - second.x, third.y - second.y };
CGFloat theta1 = atan2f(vec1.dy, vec1.dx);
CGFloat theta2 = atan2f(vec2.dy, vec2.dx);
CGFloat angle = theta1 - theta2;
NSLog(#"angle: %.1f°, ", angle / M_PI * 180);
Note the atan2 function that takes the x and y components as separate arguments and thus avoids the 0/90/180/270° ambiguity.
The cosine formula implementation looks right; did you take into account that acos() returns the angle in radians, not in degrees? In order to convert into degrees, multiply the angle by 180 and divide by Pi (3.14159...).
The way I have done it is to calculate the two angles separately using atan2(y,x) then using this function.
static inline double
AngleDiff(const double Angle1, const double Angle2)
{
double diff = 0;
diff = fabs(Angle1 - Angle2);
if (diff > <Pi>) {
diff = (<2Pi>) - diff;
}
return diff;
}
The function deals in radians, but you can change <Pi> to 180 and <2Pi> to 360
Using this answer to compute angle of the vector:
CGFloat angleForVector(CGFloat dx, CGFloat dy) {
return atan2(dx, -dy) * 180.0/M_PI;
}
// Compute angle at point Corner, that is between AC and BC:
CGFloat angle = angleForVector(A.x - Corner.x, A.y - Corner.y)
- angleForVector(B.x - Corner.x, B.y - Corner.y);
NSLog(#"FULL ANGLE IS: %f, ANGLE IS: %.2f",angle, angle);

Using a Bezier Curve to draw a spiral

This is for an iPad application, but it is essentially a math question.
I need to draw a circular arc of varying (monotonically increasing) line width. At the beginning of the curve, it would have a starting thickness (let's say 2pts) and then the thickness would smoothly increase until the end of the arc where it would be at its greatest thickness (let's say 12pts).
I figure the best way to make this is by creating a UIBezierPath and filling the shape. My first attempt was to use two circular arcs (with offset centers), and that worked fine up to 90°, but the arc will often be between 90° and 180°, so that approach won't cut it.
My current approach is to make a slight spiral (one slightly growing from the circular arc and one slightly shrinking) using bezier quad or cubic curves. The question is where do I put the control points so that the deviation from the circular arc (aka the shape "thickness") is the value I want.
Constraints:
The shape must be able to start and end at an arbitrary angle (within 180° of each other)
The "thickness" of the shape (deviation from the circle) must start and end with the given values
The "thickness" must increase monotonically (it can't get bigger and then smaller again)
It has to look smooth to the eye, there can't be any sharp bends
I am open to other solutions as well.
My approach just constructs 2 circular arcs and fills the region in between. The tricky bit is figuring out the centers and radii of these arcs. Looks quite good provided the thicknesses are not too large. (Cut and paste and decide for yourself if it meet your needs.) Could possibly be improved by use of a clipping path.
- (void)drawRect:(CGRect)rect
{
CGContextRef context = UIGraphicsGetCurrentContext();
CGMutablePathRef path = CGPathCreateMutable();
// As appropriate for iOS, the code below assumes a coordinate system with
// the x-axis pointing to the right and the y-axis pointing down (flipped from the standard Cartesian convention).
// Therefore, 0 degrees = East, 90 degrees = South, 180 degrees = West,
// -90 degrees = 270 degrees = North (once again, flipped from the standard Cartesian convention).
CGFloat startingAngle = 90.0; // South
CGFloat endingAngle = -45.0; // North-East
BOOL weGoFromTheStartingAngleToTheEndingAngleInACounterClockwiseDirection = YES; // change this to NO if necessary
CGFloat startingThickness = 2.0;
CGFloat endingThickness = 12.0;
CGPoint center = CGPointMake(CGRectGetMidX(self.bounds), CGRectGetMidY(self.bounds));
CGFloat meanRadius = 0.9 * fminf(self.bounds.size.width / 2.0, self.bounds.size.height / 2.0);
// the parameters above should be supplied by the user
// the parameters below are derived from the parameters supplied above
CGFloat deltaAngle = fabsf(endingAngle - startingAngle);
// projectedEndingThickness is the ending thickness we would have if the two arcs
// subtended an angle of 180 degrees at their respective centers instead of deltaAngle
CGFloat projectedEndingThickness = startingThickness + (endingThickness - startingThickness) * (180.0 / deltaAngle);
CGFloat centerOffset = (projectedEndingThickness - startingThickness) / 4.0;
CGPoint centerForInnerArc = CGPointMake(center.x + centerOffset * cos(startingAngle * M_PI / 180.0),
center.y + centerOffset * sin(startingAngle * M_PI / 180.0));
CGPoint centerForOuterArc = CGPointMake(center.x - centerOffset * cos(startingAngle * M_PI / 180.0),
center.y - centerOffset * sin(startingAngle * M_PI / 180.0));
CGFloat radiusForInnerArc = meanRadius - (startingThickness + projectedEndingThickness) / 4.0;
CGFloat radiusForOuterArc = meanRadius + (startingThickness + projectedEndingThickness) / 4.0;
CGPathAddArc(path,
NULL,
centerForInnerArc.x,
centerForInnerArc.y,
radiusForInnerArc,
endingAngle * (M_PI / 180.0),
startingAngle * (M_PI / 180.0),
!weGoFromTheStartingAngleToTheEndingAngleInACounterClockwiseDirection
);
CGPathAddArc(path,
NULL,
centerForOuterArc.x,
centerForOuterArc.y,
radiusForOuterArc,
startingAngle * (M_PI / 180.0),
endingAngle * (M_PI / 180.0),
weGoFromTheStartingAngleToTheEndingAngleInACounterClockwiseDirection
);
CGContextAddPath(context, path);
CGContextSetFillColorWithColor(context, [UIColor redColor].CGColor);
CGContextFillPath(context);
CGPathRelease(path);
}
One solution could be to generate a polyline manually. This is simple but it has the disadvantage that you'd have to scale up the amount of points you generate if the control is displayed at high resolution. I don't know enough about iOS to give you iOS/ObjC sample code, but here's some python-ish pseudocode:
# lower: the starting angle
# upper: the ending angle
# radius: the radius of the circle
# we'll fill these with polar coordinates and transform later
innerSidePoints = []
outerSidePoints = []
widthStep = maxWidth / (upper - lower)
width = 0
# could use a finer step if needed
for angle in range(lower, upper):
innerSidePoints.append(angle, radius - (width / 2))
outerSidePoints.append(angle, radius + (width / 2))
width += widthStep
# now we have to flip one of the arrays and join them to make
# a continuous path. We could have built one of the arrays backwards
# from the beginning to avoid this.
outerSidePoints.reverse()
allPoints = innerSidePoints + outerSidePoints # array concatenation
xyPoints = polarToRectangular(allPoints) # if needed
A view with a spiral .. 2023
It's very easy to draw a spiral mathematically and there are plenty of examples around.
https://github.com/mabdulsubhan/UIBezierPath-Spiral/blob/master/UIBezierPath%2BSpiral.swift
Put it in a view in the obvious way:
class Example: UIView {
private lazy var spiral: CAShapeLayer = {
let s = CAShapeLayer()
s.strokeColor = UIColor.systemPurple.cgColor
s.fillColor = UIColor.clear.cgColor
s.lineWidth = 12.0
s.lineCap = .round
layer.addSublayer(s)
return s
}()
private lazy var sp: CGPath = {
let s = UIBezierPath.getSpiralPath(
center: bounds.centerOfCGRect(),
startRadius: 0,
spacePerLoop: 4,
startTheta: 0,
endTheta: CGFloat.pi * 2 * 5,
thetaStep: 10.radians)
return s.cgPath
}()
override func layoutSubviews() {
super.layoutSubviews()
clipsToBounds = true
spiral.path = sp
}
}

How can I rotate an UIImageView by 20 degrees?

What do I have to do, if I need to rotate a UIImageView? I have a UIImage which I want to rotate by 20 degrees.
The Apple docs talk about a transformation matrix, but that sounds difficult. Are there any helpful methods or functions to achieve that?
If you want to turn right, the value must be greater than 0 if you want to rotate to the left indicates the value with the sign "-". For example -20.
CGFloat degrees = 20.0f; //the value in degrees
CGFloat radians = degrees * M_PI/180;
imageView.transform = CGAffineTransformMakeRotation(radians);
Swift 4:
let degrees: CGFloat = 20.0 //the value in degrees
let radians: CGFloat = degrees * (.pi / 180)
imageView.transform = CGAffineTransform(rotationAngle: radians)
A transformation matrix is not incredibly difficult. It's quite simple, if you use the supplied functions:
imgView.transform = CGAffineTransformMakeRotation(.34906585);
(.34906585 is 20 degrees in radians)
Swift 5:
imgView.transform = CGAffineTransform(rotationAngle: .34906585)
Swift version:
let degrees:CGFloat = 20
myImageView.transform = CGAffineTransformMakeRotation(degrees * CGFloat(M_PI/180) )
Swift 4.0
imageView.transform = CGAffineTransform(rotationAngle: CGFloat(20.0 * Double.pi / 180))
Here's an extension for Swift 3.
extension UIImageView {
func rotate(degrees:CGFloat){
self.transform = CGAffineTransform(rotationAngle: degrees * CGFloat(M_PI/180))
}
}
Usage:
myImageView.rotate(degrees: 20)
_YourImageView.transform = CGAffineTransformMakeRotation(1.57);
where 1.57 is the radian value for 90 degree
This is an easier formatting example (for 20 degrees):
CGAffineTransform(rotationAngle: ((20.0 * CGFloat(M_PI)) / 180.0))
As far as I know, using the matrix in UIAffineTransform is the only way to achieve a rotation without the help of a third-party framework.

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