I rotate my view with CGAffineTransform
[view setTransform:newTransform];
The frame values remain the same after transform is applied but how do I find "rotated" or transformed values of this frame?
(source: informit.com)
I want the exact coordinates of rotated frame edges, that is a, b, c, d points.
One thing to keep in mind is that the transform changes the coordinate system, so you will need to be able to convert between the parent 'view' and the child (transformed) view. Also, transforms preserve the center of the transformed object but not any of the other coordinates. So you need to calculate things in terms of the center. And there are several helpers you will need. (I got most of the following approach from Erica Sadun's book Core iOS Developer's Cookbook).
I usually add these as a category on UIView.
In order to transform the child's coordinates to those of the parent you need something like:
// helper to get pre transform frame
-(CGRect)originalFrame {
CGAffineTransform currentTransform = self.transform;
self.transform = CGAffineTransformIdentity;
CGRect originalFrame = self.frame;
self.transform = currentTransform;
return originalFrame;
}
// helper to get point offset from center
-(CGPoint)centerOffset:(CGPoint)thePoint {
return CGPointMake(thePoint.x - self.center.x, thePoint.y - self.center.y);
}
// helper to get point back relative to center
-(CGPoint)pointRelativeToCenter:(CGPoint)thePoint {
return CGPointMake(thePoint.x + self.center.x, thePoint.y + self.center.y);
}
// helper to get point relative to transformed coords
-(CGPoint)newPointInView:(CGPoint)thePoint {
// get offset from center
CGPoint offset = [self centerOffset:thePoint];
// get transformed point
CGPoint transformedPoint = CGPointApplyAffineTransform(offset, self.transform);
// make relative to center
return [self pointRelativeToCenter:transformedPoint];
}
// now get your corners
-(CGPoint)newTopLeft {
CGRect frame = [self originalFrame];
return [self newPointInView:frame.origin];
}
-(CGPoint)newTopRight {
CGRect frame = [self originalFrame];
CGPoint point = frame.origin;
point.x += frame.size.width;
return [self newPointInView:point];
}
-(CGPoint)newBottomLeft {
CGRect frame = [self originalFrame];
CGPoint point = frame.origin;
point.y += frame.size.height;
return [self newPointInView:point];
}
-(CGPoint)newBottomRight {
CGRect frame = [self originalFrame];
CGPoint point = frame.origin;
point.x += frame.size.width;
point.y += frame.size.height;
return [self newPointInView:point];
}
Swift 4
extension UIView {
/// Helper to get pre transform frame
var originalFrame: CGRect {
let currentTransform = transform
transform = .identity
let originalFrame = frame
transform = currentTransform
return originalFrame
}
/// Helper to get point offset from center
func centerOffset(_ point: CGPoint) -> CGPoint {
return CGPoint(x: point.x - center.x, y: point.y - center.y)
}
/// Helper to get point back relative to center
func pointRelativeToCenter(_ point: CGPoint) -> CGPoint {
return CGPoint(x: point.x + center.x, y: point.y + center.y)
}
/// Helper to get point relative to transformed coords
func newPointInView(_ point: CGPoint) -> CGPoint {
// get offset from center
let offset = centerOffset(point)
// get transformed point
let transformedPoint = offset.applying(transform)
// make relative to center
return pointRelativeToCenter(transformedPoint)
}
var newTopLeft: CGPoint {
return newPointInView(originalFrame.origin)
}
var newTopRight: CGPoint {
var point = originalFrame.origin
point.x += originalFrame.width
return newPointInView(point)
}
var newBottomLeft: CGPoint {
var point = originalFrame.origin
point.y += originalFrame.height
return newPointInView(point)
}
var newBottomRight: CGPoint {
var point = originalFrame.origin
point.x += originalFrame.width
point.y += originalFrame.height
return newPointInView(point)
}
}
You can find out the coordinates of the rotated view by using basic trigonometry. Here is how you can do it:
The first step is to know your view's width and height. Divide them by 2 and you get your triangle's adjacent and opposite sides (cyan and green respectively). In the example above width = 300 and height = 300. So adjacentSide = 150 and oppositeSice = 150.
Find the hypotenuse (red). For this you use the formula: h^2 = a^2 + b^2. After applying this formula we find the hypotenuse = 212.13
Find theta. This is the angle between the adjacentSide (cyan) and the hypotenuse (red). For this you use the formula cos(theta) = (h^2 + a^2 - o^2)/2*h*o. After applying this formula we find that theta = 0.785 (RADIANS). To convert this to degrees we apply the formula degrees = radians * 180 / PI = 45 (degrees). This is the initial (offset) angle of the hypotenuse. This is very important to realize. IF THE VIEW'S ROTATION OF YOUR VIEW IS ZERO THE HYPOTENUSE HAS AN OFFSET ANGLE OF 45(DEGREES). We're going to need theta shortly.
Now that we know the hypotenuse (red) we need the rotationAngle. In this example I used a UIRotationGestureRecognizer to rotate the square view. This class has a "rotation" property which tells us how much the view has rotated. This value is in RADIANS. In the example above the rotation is 0.3597 RADIANS. To convert it to degrees we use the formula degrees = radians * PI / 180. After applying the formula we find the rotation angle to be 20.61 degrees.
We can finally find the offset width (orange) and height (purple). For width we use the formula width = cos(rotationAngle - theta) * hypotenuse and for height we use the formula height = sen(rotationAngle - theta). WE HAVE TO SUBTRACT THETA (IN RADIANS!) FROM THE ROTATION ANGLE (IN RADIANS TOO!) BECAUSE THETA WAS THE INITIAL OFFSET. View it this way: the hypotenuse had an angle of 45(degrees) when the rotation angle was zero. After applying the formulas we find that width = 193.20 and height = -87.60
Finally, we can add those values (width and height) to the center of the square to find the coordinates of the blue point.
-Example-
// Get the center point
CGPoint squareCenter = self.squareView.center;
// Get the blue point coordinates
CGPoint bluePointCoordinates = CGPointMake(squareCenter.x + width, squareCenter.y + height);
The blue point coordinates are (963.20, 272.40)
To better understand the formulas please see the following links:
Trigonometry 1
Trigonometry 2
Also, if you want to play around with the test project I created (it's the one in the image) please feel free to download it from the following link.
UPDATE
Here is a condensed method that will calculate the offset top-right point (blue) you're looking for.
/* Params:
/ viewCenter: The center point (in superView coordinates) of your view
/ width: The total width of your view
/ height: The total height of your view
/ angleOfRotation: The rotation angle of your view. Can be either DEGREES or RADIANS
/ degrees: A boolean flag indicating whether 'angleOfRotation' is degrees
/ or radians. E.g.: If 'angleOfRotation' is expressed in degrees
/ this parameter must be 'YES'
*/
-(CGPoint)calculateTopRightCoordinatesFromViewCenter:(CGPoint)viewCenter viewWidth:(CGFloat)viewWidth viewHeight:(CGFloat)viewHeight angleOfRotation:(CGFloat)angleOfRotation degrees:(BOOL)degrees {
CGFloat adjacent = viewWidth/2.0;
CGFloat opposite = viewHeight/2.0;
CGFloat hipotenuse = sqrtf(powf(adjacent, 2.0) + pow(opposite, 2.0));
CGFloat thetaRad = acosf((powf(hipotenuse, 2.0) + powf(adjacent, 2.0) - pow(opposite, 2.0)) / (2 * hipotenuse * adjacent));
CGFloat angleRad = 0.0;
if (degrees) {
angleRad = angleOfRotation*M_PI/180.0;
} else {
angleRad = angleOfRotation;
}
CGFloat widthOffset = cosf(angleRad - thetaRad) * hipotenuse;
CGFloat heightOffset = sinf(angleRad - thetaRad) * hipotenuse;
CGPoint offsetPoint = CGPointMake(viewCenter.x + widthOffset, viewCenter.y + heightOffset);
return offsetPoint;
}
Hope this helps!
You should use:
CGPoint CGPointApplyAffineTransform (
CGPoint point,
CGAffineTransform t
);
To get a specific point, use the view's bounds and center, and then apply the view's transform to get a new point after transform. This is better than adding code specifically for rotation transform, as it can support any transform as well as chaining.
All of these answers are nuts, this is so simple...
CGPoint topLeft = [rotatedView convertPoint:CGPointMake(0, 0) toView:rotatedView.superview];
CGPoint topRight = [rotatedView convertPoint:CGPointMake(rotatedView.bounds.size.width, 0) toView:rotatedView.superview];
CGPoint bottomLeft = [rotatedView convertPoint:CGPointMake(0, rotatedView.bounds.size.height) toView:rotatedView.superview];
CGPoint bottomRight = [rotatedView convertPoint:CGPointMake(rotatedView.bounds.size.width, rotatedView.bounds.size.height) toView:rotatedView.superview];
Try this code
CGPoint localBeforeTransform = CGPointMake( view.bounds.size.width/2.0f, view.bounds.size.height/2.0f ); // lower left corner
CGPoint localAfterTransform = CGPointApplyAffineTransform(localBeforeTransform, transform);
CGPoint globalAfterTransform = CGPointMake(localAfterTransform.x + view.center.x, localAfterTransform.y + view.center.y);
Why the mess and fuss? Keep it simple? Where x was before the transform, it'll be q rads/degrees further just as every other point around the anchor is.
was going to explain it all, but this chap in this post explained it in even shorter context:
Get the current angle/rotation/radian for a UIview?
CGFloat radians = atan2f(yourView.transform.b, yourView.transform.a);
CGFloat degrees = radians * (180 / M_PI);
I wrote this class that can help us:
TransformedViewFrameCalculator.h
#import <Foundation/Foundation.h>
#interface TransformedViewFrameCalculator : NSObject
#property (nonatomic, strong) UIView *viewToProcess;
- (void)calculateTransformedCornersWithTranslation:(CGPoint)translation
scale:(CGFloat)scale
rotation:(CGFloat)rotation;
#property (nonatomic, readonly) CGPoint transformedTopLeftCorner;
#property (nonatomic, readonly) CGPoint transformedTopRightCorner;
#property (nonatomic, readonly) CGPoint transformedBottomLeftCorner;
#property (nonatomic, readonly) CGPoint transformedBottomRightCorner;
#end
TransformedViewFrameCalculator.m:
#import "TransformedViewFrameCalculator.h"
#interface TransformedViewFrameCalculator ()
#property (nonatomic, assign) CGRect viewToProcessNotTransformedFrame;
#property (nonatomic, assign) CGPoint viewToProcessNotTransformedCenter;
#end
#implementation TransformedViewFrameCalculator
- (void)setViewToProcess:(UIView *)viewToProcess {
_viewToProcess = viewToProcess;
CGAffineTransform t = _viewToProcess.transform;
_viewToProcess.transform = CGAffineTransformIdentity;
_viewToProcessNotTransformedFrame = _viewToProcess.frame;
_viewToProcessNotTransformedCenter = _viewToProcess.center;
_viewToProcess.transform = t;
}
- (void)calculateTransformedCornersWithTranslation:(CGPoint)translation
scale:(CGFloat)scale
rotation:(CGFloat)rotation {
double viewWidth = _viewToProcessNotTransformedFrame.size.width * scale;
double viewHeight = _viewToProcessNotTransformedFrame.size.height * scale;
CGPoint viewCenter = CGPointMake(_viewToProcessNotTransformedCenter.x + translation.x,
_viewToProcessNotTransformedCenter.y + translation.y);
_transformedTopLeftCorner = [self calculateCoordinatesForViewPoint:CGPointMake(0, 0)
fromViewCenter:viewCenter
viewWidth:viewWidth
viewHeight:viewHeight
angleOfRotation:rotation];
_transformedTopRightCorner = [self calculateCoordinatesForViewPoint:CGPointMake(0, viewHeight)
fromViewCenter:viewCenter
viewWidth:viewWidth
viewHeight:viewHeight
angleOfRotation:rotation];
_transformedBottomLeftCorner = [self calculateCoordinatesForViewPoint:CGPointMake(viewWidth, 0)
fromViewCenter:viewCenter
viewWidth:viewWidth
viewHeight:viewHeight
angleOfRotation:rotation];
_transformedBottomRightCorner = [self calculateCoordinatesForViewPoint:CGPointMake(viewWidth, viewHeight)
fromViewCenter:viewCenter
viewWidth:viewWidth
viewHeight:viewHeight
angleOfRotation:rotation];
}
- (CGPoint)calculateCoordinatesForViewPoint:(CGPoint)viewPoint
fromViewCenter:(CGPoint)viewCenter
viewWidth:(CGFloat)viewWidth
viewHeight:(CGFloat)viewHeight
angleOfRotation:(CGFloat)angleOfRotation {
CGPoint centeredViewPoint = CGPointMake(viewPoint.x - viewWidth/2.0, viewPoint.y - viewHeight/2.0);
CGPoint rotatedCenteredViewPoint = CGPointApplyAffineTransform(centeredViewPoint, CGAffineTransformMakeRotation(angleOfRotation));
CGPoint rotatedViewPoint = CGPointMake(rotatedCenteredViewPoint.x + viewCenter.x, rotatedCenteredViewPoint.y + viewCenter.y);
return rotatedViewPoint;
}
For example, I use it to restrict the move/scale/rotation of a sticker inside a container view in the following way:
#property (nonatomic, strong) TransformedViewFrameCalculator *transformedFrameCalculator;
...
self.transformedFrameCalculator = [TransformedViewFrameCalculator new];
self.transformedFrameCalculator.viewToProcess = someView;
...
- (BOOL)transformedView:(UIView *)view
withTranslation:(CGPoint)translation
scale:(double)scale
rotation:(double)rotation
isFullyInsideValidFrame:(CGRect)validFrame {
[self.transformedFrameCalculator calculateTransformedCornersWithTranslation:translation
scale:scale
BOOL topRightIsInsideValidFrame = CGRectContainsPoint(validFrame, self.transformedFrameCalculator.transformedTopRightCorner);
BOOL topLeftIsInsideValidFrame = CGRectContainsPoint(validFrame, self.transformedFrameCalculator.transformedTopLeftCorner);
BOOL bottomRightIsInsideValidFrame = CGRectContainsPoint(validFrame, self.transformedFrameCalculator.transformedBottomRightCorner);
BOOL bottomLeftIsInsideValidFrame = CGRectContainsPoint(validFrame, self.transformedFrameCalculator.transformedBottomLeftCorner);
return topRightIsInsideValidFrame && topLeftIsInsideValidFrame && bottomRightIsInsideValidFrame && bottomLeftIsInsideValidFrame;
}
I am still new to cocos2d and I have this problem that when I am using the ccp coordinates it stays at same position even when I move to the next screen. I came to the conclusion it must be that I am not using the tiles coordinates. So I need some help converting.
- (CGPoint)tileCoordForPosition:(CGPoint)position {
float x = floor(position.x / map.tileSize.width);
float levelHeightInPixels = map.mapSize.height * map.tileSize.height;
float y = floor((levelHeightInPixels - position.y) / map.tileSize.height);
return ccp(x, y);
}
-(CGRect)tileRectFromTileCoords:(CGPoint)tileCoords {
float levelHeightInPixels = map.mapSize.height * map.tileSize.height;
CGPoint origin = ccp(tileCoords.x * map.tileSize.width, levelHeightInPixels - ((tileCoords.y + 1) * map.tileSize.height));
return CGRectMake(origin.x, origin.y, map.tileSize.width, map.tileSize.height);
}
that is what i use to translate regular coordinates into tile map coordinates.
now I am trying to spawn an enemy at a certain position specifically (0,0)
-(void)addsaw{
CCSprite *saw = [CCSprite spriteWithFile:#"saw.png"];
// Determine where to spawn the target along the Y axis
CGSize winSize = [[CCDirector sharedDirector] winSize];
int minY =saw.contentSize.height/2;
int maxY = winSize.height - saw.contentSize.height/2;
int rangeY = maxY - minY;
int actualY = ( rangeY) + minY;
//THIS IS THE PROBLEM RIGHT HERE
saw.position = ccp(0,0);
[self addChild:saw];
// Create the actions
id actionMove = [CCMoveTo actionWithDuration:actualDuration
position:ccp(-saw.contentSize.width/2, actualY)];
id actionMoveDone = [CCCallFuncN actionWithTarget:self
selector:#selector(spriteMoveFinished2:)];
[saw runAction:[CCSequence actions:actionMove, actionMoveDone, nil]];
saw.tag = 1;
[_saws addObject:saw];
}
How do I change the ccp of my addsaw so I can have it spawn at the tile (0,0) rather than the cocos2d regular (0,0)
you should add your sprite to your cctmxtiledmap instead of the layer!
How do you smooth a set of points in an iOS drawing app WHILE MOVING? I have tried UIBezierpaths but all I get are jagged ends where they intersect, when I just shift the points 1,2,3,4 - 2,3,4,5. I have heard of spline curves and all the other types. I am quite new to iPhone programming and do not understand how to program it in my quartz drawing app. A solid example would be greatly appreciated, I have spent weeks running in circles and I can never seem to find any iOS code for this task. Most of the posts just link to a java simulation or pages on wikipedia about curve fitting which does nothing for me. Also I do not want to switch to openGL ES. I hope someone can finally provide code to answer this circulating question.
This was my code for the UIBezierPath which left edges at intersection///
UPDATED TO AN ANSWER BELOW
#define VALUE(_INDEX_) [NSValue valueWithCGPoint:points[_INDEX_]]
#define POINT(_INDEX_) [(NSValue *)[points objectAtIndex:_INDEX_] CGPointValue]
- (UIBezierPath*)smoothedPathWithGranularity:(NSInteger)granularity
{
NSMutableArray *points = [(NSMutableArray*)[self pointsOrdered] mutableCopy];
if (points.count < 4) return [self bezierPath];
// Add control points to make the math make sense
[points insertObject:[points objectAtIndex:0] atIndex:0];
[points addObject:[points lastObject]];
UIBezierPath *smoothedPath = [self bezierPath];
[smoothedPath removeAllPoints];
[smoothedPath moveToPoint:POINT(0)];
for (NSUInteger index = 1; index < points.count - 2; index++)
{
CGPoint p0 = POINT(index - 1);
CGPoint p1 = POINT(index);
CGPoint p2 = POINT(index + 1);
CGPoint p3 = POINT(index + 2);
// now add n points starting at p1 + dx/dy up until p2 using Catmull-Rom splines
for (int i = 1; i < granularity; i++)
{
float t = (float) i * (1.0f / (float) granularity);
float tt = t * t;
float ttt = tt * t;
CGPoint pi; // intermediate point
pi.x = 0.5 * (2*p1.x+(p2.x-p0.x)*t + (2*p0.x-5*p1.x+4*p2.x-p3.x)*tt + (3*p1.x-p0.x-3*p2.x+p3.x)*ttt);
pi.y = 0.5 * (2*p1.y+(p2.y-p0.y)*t + (2*p0.y-5*p1.y+4*p2.y-p3.y)*tt + (3*p1.y-p0.y-3*p2.y+p3.y)*ttt);
[smoothedPath addLineToPoint:pi];
}
// Now add p2
[smoothedPath addLineToPoint:p2];
}
// finish by adding the last point
[smoothedPath addLineToPoint:POINT(points.count - 1)];
return smoothedPath;
}
- (PVPoint *)pointAppendingCGPoint:(CGPoint)CGPoint
{
PVPoint *newPoint = [[PVPoint alloc] initInsertingIntoManagedObjectContext:[self managedObjectContext]];
[newPoint setCGPoint:CGPoint];
[newPoint setOrder:[NSNumber numberWithUnsignedInteger:[[self points] count]]];
[[self mutableSetValueForKey:#"points"] addObject:newPoint];
[(NSMutableArray *)[self pointsOrdered] addObject:newPoint];
[[self bezierPath] addLineToPoint:CGPoint];
return [newPoint autorelease];
if ([self bezierPath] && [pointsOrdered count] > 3)
{
PVPoint *control1 = [pointsOrdered objectAtIndex:[pointsOrdered count] - 2];
PVPoint *control2 = [pointsOrdered objectAtIndex:[pointsOrdered count] - 1];
[bezierPath moveToPoint:[[pointsOrdered objectAtIndex:[pointsOrdered count] - 3] CGPoint]];
[[self bezierPath] addCurveToPoint:CGPoint controlPoint1:[control1 CGPoint] controlPoint2:[control2 CGPoint]];
}
}
- (BOOL)isComplete { return [[self points] count] > 1; }
- (UIBezierPath *)bezierPath
{
if (!bezierPath)
{
bezierPath = [UIBezierPath bezierPath];
for (NSUInteger p = 0; p < [[self points] count]; p++)
{
if (!p) [bezierPath moveToPoint:[(PVPoint *)[[self pointsOrdered] objectAtIndex:p] CGPoint]];
else [bezierPath addLineToPoint:[(PVPoint *)[[self pointsOrdered] objectAtIndex:p] CGPoint]];
}
[bezierPath retain];
}
return bezierPath;
}
- (CGPathRef)CGPath
{
return [[self bezierPath] CGPath];
}
I just implemented something similar in a project I am working on. My solution was to use a Catmull-Rom spline instead of using Bezier splines. These provide a very smooth curve THROUGH a set a points rather then a bezier spline 'around' points.
// Based on code from Erica Sadun
#import "UIBezierPath+Smoothing.h"
void getPointsFromBezier(void *info, const CGPathElement *element);
NSArray *pointsFromBezierPath(UIBezierPath *bpath);
#define VALUE(_INDEX_) [NSValue valueWithCGPoint:points[_INDEX_]]
#define POINT(_INDEX_) [(NSValue *)[points objectAtIndex:_INDEX_] CGPointValue]
#implementation UIBezierPath (Smoothing)
// Get points from Bezier Curve
void getPointsFromBezier(void *info, const CGPathElement *element)
{
NSMutableArray *bezierPoints = (__bridge NSMutableArray *)info;
// Retrieve the path element type and its points
CGPathElementType type = element->type;
CGPoint *points = element->points;
// Add the points if they're available (per type)
if (type != kCGPathElementCloseSubpath)
{
[bezierPoints addObject:VALUE(0)];
if ((type != kCGPathElementAddLineToPoint) &&
(type != kCGPathElementMoveToPoint))
[bezierPoints addObject:VALUE(1)];
}
if (type == kCGPathElementAddCurveToPoint)
[bezierPoints addObject:VALUE(2)];
}
NSArray *pointsFromBezierPath(UIBezierPath *bpath)
{
NSMutableArray *points = [NSMutableArray array];
CGPathApply(bpath.CGPath, (__bridge void *)points, getPointsFromBezier);
return points;
}
- (UIBezierPath*)smoothedPathWithGranularity:(NSInteger)granularity;
{
NSMutableArray *points = [pointsFromBezierPath(self) mutableCopy];
if (points.count < 4) return [self copy];
// Add control points to make the math make sense
[points insertObject:[points objectAtIndex:0] atIndex:0];
[points addObject:[points lastObject]];
UIBezierPath *smoothedPath = [self copy];
[smoothedPath removeAllPoints];
[smoothedPath moveToPoint:POINT(0)];
for (NSUInteger index = 1; index < points.count - 2; index++)
{
CGPoint p0 = POINT(index - 1);
CGPoint p1 = POINT(index);
CGPoint p2 = POINT(index + 1);
CGPoint p3 = POINT(index + 2);
// now add n points starting at p1 + dx/dy up until p2 using Catmull-Rom splines
for (int i = 1; i < granularity; i++)
{
float t = (float) i * (1.0f / (float) granularity);
float tt = t * t;
float ttt = tt * t;
CGPoint pi; // intermediate point
pi.x = 0.5 * (2*p1.x+(p2.x-p0.x)*t + (2*p0.x-5*p1.x+4*p2.x-p3.x)*tt + (3*p1.x-p0.x-3*p2.x+p3.x)*ttt);
pi.y = 0.5 * (2*p1.y+(p2.y-p0.y)*t + (2*p0.y-5*p1.y+4*p2.y-p3.y)*tt + (3*p1.y-p0.y-3*p2.y+p3.y)*ttt);
[smoothedPath addLineToPoint:pi];
}
// Now add p2
[smoothedPath addLineToPoint:p2];
}
// finish by adding the last point
[smoothedPath addLineToPoint:POINT(points.count - 1)];
return smoothedPath;
}
#end
The original Catmull-Rom implementation is based on some code from Erica Sadun in one of her books, I modified it slightly to allow for a full smoothed curve. This is implemented as a category on UIBezierPath and worked out very well for me.
Some good answers here, though I think they are either way off (user1244109's answer only supports horizontal tangents, not useful for generic curves), or overly complicated (sorry Catmull-Rom fans).
I implemented this in a much simpler way, using Quad bezier curves. These need a start point, an end point, and a control point. The natural thing to do might be to use the touch points as the start & end points. Don't do this! There are no appropriate control points to use. Instead, try this idea: use the touch points as control points, and the midpoints as the start/end points. You're guaranteed to have proper tangents this way, and the code is stupid simple. Here's the algorithm:
The "touch down" point is the start of the path, and store location in prevPoint.
For every dragged location, calculate midPoint, the point between currentPoint and prevPoint.
If this is the first dragged location, add currentPoint as a line segment.
For all points in the future, add a quad curve that terminates at the midPoint, and use the prevPoint as the control point. This will create a segment that gently curves from the previous point to the current point.
Store currentPoint in prevPoint, and repeat #2 until dragging ends.
Add the final point as another straight segment, to finish up the path.
This results in very good looking curves, because using the midPoints guarantees that the curve is a smooth tangent at the end points (see attached photo).
Swift code looks like this:
var bezierPath = UIBezierPath()
var prevPoint: CGPoint?
var isFirst = true
override func touchesBegan(touchesSet: Set<UITouch>, withEvent event: UIEvent?) {
let location = touchesSet.first!.locationInView(self)
bezierPath.removeAllPoints()
bezierPath.moveToPoint(location)
prevPoint = location
}
override func touchesMoved(touchesSet: Set<UITouch>, withEvent event: UIEvent?) {
let location = touchesSet.first!.locationInView(self)
if let prevPoint = prevPoint {
let midPoint = CGPoint(
x: (location.x + prevPoint.x) / 2,
y: (location.y + prevPoint.y) / 2,
)
if isFirst {
bezierPath.addLineToPoint(midPoint)
else {
bezierPath.addQuadCurveToPoint(midPoint, controlPoint: prevPoint)
}
isFirst = false
}
prevPoint = location
}
override func touchesEnded(touchesSet: Set<UITouch>, withEvent event: UIEvent?) {
let location = touchesSet.first!.locationInView(self)
bezierPath.addLineToPoint(location)
}
Or, if you have an array of points and want to construct the UIBezierPath in one shot:
var points: [CGPoint] = [...]
var bezierPath = UIBezierPath()
var prevPoint: CGPoint?
var isFirst = true
// obv, there are lots of ways of doing this. let's
// please refrain from yak shaving in the comments
for point in points {
if let prevPoint = prevPoint {
let midPoint = CGPoint(
x: (point.x + prevPoint.x) / 2,
y: (point.y + prevPoint.y) / 2,
)
if isFirst {
bezierPath.addLineToPoint(midPoint)
}
else {
bezierPath.addQuadCurveToPoint(midPoint, controlPoint: prevPoint)
}
isFirst = false
}
else {
bezierPath.moveToPoint(point)
}
prevPoint = point
}
if let prevPoint = prevPoint {
bezierPath.addLineToPoint(prevPoint)
}
Here are my notes:
#Rakesh is absolutely right - you dont need to use Catmull-Rom algorithm if you just want a curved line. And the link he suggested does exacly that. So here's an addition to his answer.
The code bellow does NOT use Catmull-Rom algorithm & granularity, but draws a quad-curved line (control points are calculated for you). This is essentially what's done in the ios freehand drawing tutorial suggested by Rakesh, but in a standalone method that you can drop anywhere (or in a UIBezierPath category) and get a quad-curved spline out of the box.
You do need to have an array of CGPoint's wrapped in NSValue's
+ (UIBezierPath *)quadCurvedPathWithPoints:(NSArray *)points
{
UIBezierPath *path = [UIBezierPath bezierPath];
NSValue *value = points[0];
CGPoint p1 = [value CGPointValue];
[path moveToPoint:p1];
if (points.count == 2) {
value = points[1];
CGPoint p2 = [value CGPointValue];
[path addLineToPoint:p2];
return path;
}
for (NSUInteger i = 1; i < points.count; i++) {
value = points[i];
CGPoint p2 = [value CGPointValue];
CGPoint midPoint = midPointForPoints(p1, p2);
[path addQuadCurveToPoint:midPoint controlPoint:controlPointForPoints(midPoint, p1)];
[path addQuadCurveToPoint:p2 controlPoint:controlPointForPoints(midPoint, p2)];
p1 = p2;
}
return path;
}
static CGPoint midPointForPoints(CGPoint p1, CGPoint p2) {
return CGPointMake((p1.x + p2.x) / 2, (p1.y + p2.y) / 2);
}
static CGPoint controlPointForPoints(CGPoint p1, CGPoint p2) {
CGPoint controlPoint = midPointForPoints(p1, p2);
CGFloat diffY = abs(p2.y - controlPoint.y);
if (p1.y < p2.y)
controlPoint.y += diffY;
else if (p1.y > p2.y)
controlPoint.y -= diffY;
return controlPoint;
}
Here's the result:
The key to getting two bezier curves to join smoothly is that the relevant control points and the start/end points on the curves must be collinear. Think of the control point and the endpoint as forming a line that's tangent to the curve at the endpoint. If one curve starts at the same point where another ends, and if they both have the same tangent line at that point, the curve will be smooth. Here's a bit of code to illustrate:
- (void)drawRect:(CGRect)rect
{
#define commonY 117
CGPoint point1 = CGPointMake(20, 20);
CGPoint point2 = CGPointMake(100, commonY);
CGPoint point3 = CGPointMake(200, 50);
CGPoint controlPoint1 = CGPointMake(50, 60);
CGPoint controlPoint2 = CGPointMake(20, commonY);
CGPoint controlPoint3 = CGPointMake(200, commonY);
CGPoint controlPoint4 = CGPointMake(250, 75);
UIBezierPath *path1 = [UIBezierPath bezierPath];
UIBezierPath *path2 = [UIBezierPath bezierPath];
[path1 setLineWidth:3.0];
[path1 moveToPoint:point1];
[path1 addCurveToPoint:point2 controlPoint1:controlPoint1 controlPoint2:controlPoint2];
[[UIColor blueColor] set];
[path1 stroke];
[path2 setLineWidth:3.0];
[path2 moveToPoint:point2];
[path2 addCurveToPoint:point3 controlPoint1:controlPoint3 controlPoint2:controlPoint4];
[[UIColor orangeColor] set];
[path2 stroke];
}
Notice that path1 ends at point2, path2 starts at point2, and control points 2 and 3 share the same Y-value, commonY, with point2. You can change any of the values in the code as you like; as long as those three points all fall on the same line, the two paths will join smoothly. (In the code above, the line is y = commonY. The line doesn't have to be parallel to the X axis; it's just easier to see that the points are collinear that way.)
Here's the image that the code above draws:
After looking at your code, the reason that your curve is jagged is that you're thinking of control points as points on the curve. In a bezier curve, the control points are usually not on the curve. Since you're taking the control points from the curve, the control points and the point of intersection are not collinear, and the paths therefore don't join smoothly.
We need to observe some thing before applying any algorithm on captured points.
Generally UIKit does not give the points at equal distance.
We need to calculate the intermediate points in between two CGPoints[ Which has captured with Touch moved method]
Now to get smooth line, there are so many ways.
Some times we can achieve the by applying second degree polynomial or third degree polynomial or catmullRomSpline algorithms
- (float)findDistance:(CGPoint)point lineA:(CGPoint)lineA lineB:(CGPoint)lineB
{
CGPoint v1 = CGPointMake(lineB.x - lineA.x, lineB.y - lineA.y);
CGPoint v2 = CGPointMake(point.x - lineA.x, point.y - lineA.y);
float lenV1 = sqrt(v1.x * v1.x + v1.y * v1.y);
float lenV2 = sqrt(v2.x * v2.x + v2.y * v2.y);
float angle = acos((v1.x * v2.x + v1.y * v2.y) / (lenV1 * lenV2));
return sin(angle) * lenV2;
}
- (NSArray *)douglasPeucker:(NSArray *)points epsilon:(float)epsilon
{
int count = [points count];
if(count < 3) {
return points;
}
//Find the point with the maximum distance
float dmax = 0;
int index = 0;
for(int i = 1; i < count - 1; i++) {
CGPoint point = [[points objectAtIndex:i] CGPointValue];
CGPoint lineA = [[points objectAtIndex:0] CGPointValue];
CGPoint lineB = [[points objectAtIndex:count - 1] CGPointValue];
float d = [self findDistance:point lineA:lineA lineB:lineB];
if(d > dmax) {
index = i;
dmax = d;
}
}
//If max distance is greater than epsilon, recursively simplify
NSArray *resultList;
if(dmax > epsilon) {
NSArray *recResults1 = [self douglasPeucker:[points subarrayWithRange:NSMakeRange(0, index + 1)] epsilon:epsilon];
NSArray *recResults2 = [self douglasPeucker:[points subarrayWithRange:NSMakeRange(index, count - index)] epsilon:epsilon];
NSMutableArray *tmpList = [NSMutableArray arrayWithArray:recResults1];
[tmpList removeLastObject];
[tmpList addObjectsFromArray:recResults2];
resultList = tmpList;
} else {
resultList = [NSArray arrayWithObjects:[points objectAtIndex:0], [points objectAtIndex:count - 1],nil];
}
return resultList;
}
- (NSArray *)catmullRomSplineAlgorithmOnPoints:(NSArray *)points segments:(int)segments
{
int count = [points count];
if(count < 4) {
return points;
}
float b[segments][4];
{
// precompute interpolation parameters
float t = 0.0f;
float dt = 1.0f/(float)segments;
for (int i = 0; i < segments; i++, t+=dt) {
float tt = t*t;
float ttt = tt * t;
b[i][0] = 0.5f * (-ttt + 2.0f*tt - t);
b[i][1] = 0.5f * (3.0f*ttt -5.0f*tt +2.0f);
b[i][2] = 0.5f * (-3.0f*ttt + 4.0f*tt + t);
b[i][3] = 0.5f * (ttt - tt);
}
}
NSMutableArray *resultArray = [NSMutableArray array];
{
int i = 0; // first control point
[resultArray addObject:[points objectAtIndex:0]];
for (int j = 1; j < segments; j++) {
CGPoint pointI = [[points objectAtIndex:i] CGPointValue];
CGPoint pointIp1 = [[points objectAtIndex:(i + 1)] CGPointValue];
CGPoint pointIp2 = [[points objectAtIndex:(i + 2)] CGPointValue];
float px = (b[j][0]+b[j][1])*pointI.x + b[j][2]*pointIp1.x + b[j][3]*pointIp2.x;
float py = (b[j][0]+b[j][1])*pointI.y + b[j][2]*pointIp1.y + b[j][3]*pointIp2.y;
[resultArray addObject:[NSValue valueWithCGPoint:CGPointMake(px, py)]];
}
}
for (int i = 1; i < count-2; i++) {
// the first interpolated point is always the original control point
[resultArray addObject:[points objectAtIndex:i]];
for (int j = 1; j < segments; j++) {
CGPoint pointIm1 = [[points objectAtIndex:(i - 1)] CGPointValue];
CGPoint pointI = [[points objectAtIndex:i] CGPointValue];
CGPoint pointIp1 = [[points objectAtIndex:(i + 1)] CGPointValue];
CGPoint pointIp2 = [[points objectAtIndex:(i + 2)] CGPointValue];
float px = b[j][0]*pointIm1.x + b[j][1]*pointI.x + b[j][2]*pointIp1.x + b[j][3]*pointIp2.x;
float py = b[j][0]*pointIm1.y + b[j][1]*pointI.y + b[j][2]*pointIp1.y + b[j][3]*pointIp2.y;
[resultArray addObject:[NSValue valueWithCGPoint:CGPointMake(px, py)]];
}
}
{
int i = count-2; // second to last control point
[resultArray addObject:[points objectAtIndex:i]];
for (int j = 1; j < segments; j++) {
CGPoint pointIm1 = [[points objectAtIndex:(i - 1)] CGPointValue];
CGPoint pointI = [[points objectAtIndex:i] CGPointValue];
CGPoint pointIp1 = [[points objectAtIndex:(i + 1)] CGPointValue];
float px = b[j][0]*pointIm1.x + b[j][1]*pointI.x + (b[j][2]+b[j][3])*pointIp1.x;
float py = b[j][0]*pointIm1.y + b[j][1]*pointI.y + (b[j][2]+b[j][3])*pointIp1.y;
[resultArray addObject:[NSValue valueWithCGPoint:CGPointMake(px, py)]];
}
}
// the very last interpolated point is the last control point
[resultArray addObject:[points objectAtIndex:(count - 1)]];
return resultArray;
}
For achieving this we need to use this method.
BezierSpline
the code is in C# to generate arrays of control points for a bezier spline. I converted this code to Objective C and it works brilliantly for me.
To convert the code from C# to Objective C.
understand the C# code line by line, even if you dont know C#, u must be knowing C++/Java ?
While converting:
Replace Point struct used here with CGPoint.
Replace Point array with NSMutableArray and store NSvalues wrapping CGPoints in it.
Replace all double arrays with NSMutableArrays and store NSNumber wrapping double in it.
use objectAtIndex: method in case of subscript for accessing array elements.
use replaceObjectAtIndex:withObject: to store objects at specific index.
Remember that NSMutableArray is a linkedList and what C# uses are dynamic arrays so they already have existing indices.
In your case, in a NSMutableArray if it is empty, you cant store objects at random indices as the C# code does.
they at times in this C# code, populate index 1 before index 0 and they can do so as index 1 exists.
in NSMutabelArrays here, index 1 should be there if u want to call replaceObject on it.
so before storing anything make a method that will add n NSNull objects in the NSMutableArray.
ALSO :
well this logic has a static method that will accept an array of points and give you two arrays:-
array of first control points.
array of second control points.
These arrays will hold first and second control point for each curve between two points you pass in the first array.
In my case, I already had all the points and I could draw curve through them.
In you case while drawing, you will need to some how supply a set of points through which you want a smooth curve to pass.
and refresh by calling setNeedsDisplay and draw the spline which is nothing but UIBezierPath between two adjacent points in the first array.
and taking control points from both the control point arrays index wise.
Problem in your case is that, its difficult to understand while moving what all critical points to take.
What you can do is:
Simply while moving the finger keep drawing straight lines between previous and current point.
Lines will be so small that it wont be visible to naked eye that they are small small straight lines unless you zoom in.
UPDATE
Anyone interested in an Objective C implementation of the link above can refer to
this GitHub repo.
I wrote it sometime back and it doesn't support ARC, but you can easily edit it and remove few release and autorelease calls and get it working with ARC.
This one just generates two arrays of control points for a set of points which one wants to join using bezier spline.
Dont need to write this much of code.
Just refer to the ios freehand drawing tutorial; it really smoothen the drawing, also cache mechanism is there so that performance does not go down even when you keep drawing continuously.
Swift:
let point1 = CGPoint(x: 50, y: 100)
let point2 = CGPoint(x: 50 + 1 * CGFloat(60) * UIScreen.main.bounds.width / 375, y: 200)
let point3 = CGPoint(x: 50 + 2 * CGFloat(60) * UIScreen.main.bounds.width / 375, y: 250)
let point4 = CGPoint(x: 50 + 3 * CGFloat(60) * UIScreen.main.bounds.width / 375, y: 50)
let point5 = CGPoint(x: 50 + 4 * CGFloat(60) * UIScreen.main.bounds.width / 375, y: 100)
let points = [point1, point2, point3, point4, point5]
let bezier = UIBezierPath()
let count = points.count
var prevDx = CGFloat(0)
var prevDy = CGFloat(0)
var prevX = CGFloat(0)
var prevY = CGFloat(0)
let div = CGFloat(7)
for i in 0..<count {
let x = points[i].x
let y = points[i].y
var dx = CGFloat(0)
var dy = CGFloat(0)
if (i == 0) {
bezier.move(to: points[0])
let nextX = points[i + 1].x
let nextY = points[i + 1].y
prevDx = (nextX - x) / div
prevDy = (nextY - y) / div
prevX = x
prevY = y
} else if (i == count - 1) {
dx = (x - prevX) / div
dy = (y - prevY) / div
} else {
let nextX = points[i + 1].x
let nextY = points[i + 1].y
dx = (nextX - prevX) / div;
dy = (nextY - prevY) / div;
}
bezier.addCurve(to: CGPoint(x: x, y: y), controlPoint1: CGPoint(x: prevX + prevDx, y: prevY + prevDy), controlPoint2: CGPoint(x: x - dx, y: y - dy))
prevDx = dx;
prevDy = dy;
prevX = x;
prevY = y;
}
Here is the code in Swift 4/5
func quadCurvedPathWithPoint(points: [CGPoint] ) -> UIBezierPath {
let path = UIBezierPath()
if points.count > 1 {
var prevPoint:CGPoint?
for (index, point) in points.enumerated() {
if index == 0 {
path.move(to: point)
} else {
if index == 1 {
path.addLine(to: point)
}
if prevPoint != nil {
let midPoint = self.midPointForPoints(from: prevPoint!, to: point)
path.addQuadCurve(to: midPoint, controlPoint: controlPointForPoints(from: midPoint, to: prevPoint!))
path.addQuadCurve(to: point, controlPoint: controlPointForPoints(from: midPoint, to: point))
}
}
prevPoint = point
}
}
return path
}
func midPointForPoints(from p1:CGPoint, to p2: CGPoint) -> CGPoint {
return CGPoint(x: (p1.x + p2.x) / 2, y: (p1.y + p2.y) / 2)
}
func controlPointForPoints(from p1:CGPoint,to p2:CGPoint) -> CGPoint {
var controlPoint = midPointForPoints(from:p1, to: p2)
let diffY = abs(p2.y - controlPoint.y)
if p1.y < p2.y {
controlPoint.y = controlPoint.y + diffY
} else if ( p1.y > p2.y ) {
controlPoint.y = controlPoint.y - diffY
}
return controlPoint
}
I found a pretty nice tutorial that describes a slight modification to Bezier curve drawing that does tend to smooth out the edges pretty nicely. It's essentially what Caleb is referring to above about putting the joining end points on the same line as the control points. It's one of the best tutorials (on anything) that I've read in a while. And it comes with a fully working Xcode project.
I tried all of the above, but can't make it work. One of the answer yield a broken result for me even. Upon searching more I found this: https://github.com/sam-keene/uiBezierPath-hermite-curve. I did not write this code, but I implemented it and it works really really well. Just copy the UIBezierPath+Interpolation.m/h and CGPointExtension.m/h. Then you use it like this:
UIBezierPath *path = [UIBezierPath interpolateCGPointsWithHermite:arrayPoints closed:YES];
It is really a robust and neat solution overall.
I was inspired by the answer of u/User1244109 ... but it only works if the points are constantly fluctuating up and then down each time, so that every point should be joined by an S curve.
I built off of his answer to include custom logic to check if the point is going to be a local minima or not, and then use the S-curve if so, otherwise determine if it should curve up or down based on the points before and after it or if it should curve tangentially and if so I use the intersection of tangents as the control point.
#define AVG(__a, __b) (((__a)+(__b))/2.0)
-(UIBezierPath *)quadCurvedPathWithPoints:(NSArray *)points {
if (points.count < 2) {
return [UIBezierPath new];
}
UIBezierPath *path = [UIBezierPath bezierPath];
CGPoint p0 = [points[0] CGPointValue];
CGPoint p1 = [points[1] CGPointValue];
[path moveToPoint:p0];
if (points.count == 2) {
[path addLineToPoint:p1];
return path;
}
for (int i = 1; i <= points.count-1; i++) {
CGPoint p1 = [points[i-1] CGPointValue];
CGPoint p2 = [points[i] CGPointValue];//current point
CGPoint p0 = p1;
CGPoint p3 = p2;
if (i-2 >= 0) {
p0 = [points[i-2] CGPointValue];
}
if (i+1 <= points.count-1) {
p3 = [points[i+1] CGPointValue];
}
if (p2.y == p1.y) {
[path addLineToPoint:p2];
continue;
}
float previousSlope = p1.y-p0.y;
float currentSlope = p2.y-p1.y;
float nextSlope = p3.y-p2.y;
BOOL shouldCurveUp = NO;
BOOL shouldCurveDown = NO;
BOOL shouldCurveS = NO;
BOOL shouldCurveTangental = NO;
if (previousSlope < 0) {//up hill
if (currentSlope < 0) {//up hill
if (nextSlope < 0) {//up hill
shouldCurveTangental = YES;
} else {//down hill
shouldCurveUp = YES;
}
} else {//down hill
if (nextSlope > 0) {//down hill
shouldCurveUp = YES;
} else {//up hill
shouldCurveS = YES;
}
}
} else {//down hill
if (currentSlope > 0) {//down hill
if (nextSlope > 0) {//down hill
shouldCurveTangental = YES;
} else {//up hill
shouldCurveDown = YES;
}
} else {//up hill
if (nextSlope < 0) {//up hill
shouldCurveDown = YES;
} else {//down hill
shouldCurveS = YES;
}
}
}
if (shouldCurveUp) {
[path addQuadCurveToPoint:p2 controlPoint:CGPointMake(AVG(p1.x, p2.x), MIN(p1.y, p2.y))];
}
if (shouldCurveDown) {
[path addQuadCurveToPoint:p2 controlPoint:CGPointMake(AVG(p1.x, p2.x), MAX(p1.y, p2.y))];
}
if (shouldCurveS) {
CGPoint midPoint = midPointForPoints(p1, p2);
[path addQuadCurveToPoint:midPoint controlPoint:controlPointForPoints(midPoint, p1)];
[path addQuadCurveToPoint:p2 controlPoint:controlPointForPoints(midPoint, p2)];
}
if (shouldCurveTangental) {
float nextTangent_dy = p3.y-p2.y;
float nextTangent_dx = p3.x-p2.x;
float previousTangent_dy = p1.y-p0.y;
float previousTangent_dx = p1.x-p0.x;
float nextTangent_m = 0;
if (nextTangent_dx != 0) {
nextTangent_m = nextTangent_dy/nextTangent_dx;
}
float previousTangent_m = 0;
if (nextTangent_dx != 0) {
previousTangent_m = previousTangent_dy/previousTangent_dx;
}
if (isnan(previousTangent_m) ||
isnan(nextTangent_m) ||
nextTangent_dx == 0 ||
previousTangent_dx == 0) {//division by zero would have occured, etc
[path addLineToPoint:p2];
} else {
CGPoint nextTangent_start = CGPointMake(p1.x, (nextTangent_m*p1.x) - (nextTangent_m*p2.x) + p2.y);
CGPoint nextTangent_end = CGPointMake(p2.x, (nextTangent_m*p2.x) - (nextTangent_m*p2.x) + p2.y);
CGPoint previousTangent_start = CGPointMake(p1.x, (previousTangent_m*p1.x) - (previousTangent_m*p1.x) + p1.y);
CGPoint previousTangent_end = CGPointMake(p2.x, (previousTangent_m*p2.x) - (previousTangent_m*p1.x) + p1.y);
NSValue *tangentIntersection_pointValue = [self intersectionOfLineFrom:nextTangent_start to:nextTangent_end withLineFrom:previousTangent_start to:previousTangent_end];
if (tangentIntersection_pointValue) {
[path addQuadCurveToPoint:p2 controlPoint:[tangentIntersection_pointValue CGPointValue]];
} else {
[path addLineToPoint:p2];
}
}
}
}
return path;
}
-(NSValue *)intersectionOfLineFrom:(CGPoint)p1 to:(CGPoint)p2 withLineFrom:(CGPoint)p3 to:(CGPoint)p4 {//from https://stackoverflow.com/a/15692290/2057171
CGFloat d = (p2.x - p1.x)*(p4.y - p3.y) - (p2.y - p1.y)*(p4.x - p3.x);
if (d == 0)
return nil; // parallel lines
CGFloat u = ((p3.x - p1.x)*(p4.y - p3.y) - (p3.y - p1.y)*(p4.x - p3.x))/d;
CGFloat v = ((p3.x - p1.x)*(p2.y - p1.y) - (p3.y - p1.y)*(p2.x - p1.x))/d;
if (u < 0.0 || u > 1.0)
return nil; // intersection point not between p1 and p2
if (v < 0.0 || v > 1.0)
return nil; // intersection point not between p3 and p4
CGPoint intersection;
intersection.x = p1.x + u * (p2.x - p1.x);
intersection.y = p1.y + u * (p2.y - p1.y);
return [NSValue valueWithCGPoint:intersection];
}
static CGPoint midPointForPoints(CGPoint p1, CGPoint p2) {
return CGPointMake((p1.x + p2.x) / 2, (p1.y + p2.y) / 2);
}
static CGPoint controlPointForPoints(CGPoint p1, CGPoint p2) {
CGPoint controlPoint = midPointForPoints(p1, p2);
CGFloat diffY = fabs(p2.y - controlPoint.y);
if (p1.y < p2.y)
controlPoint.y += diffY;
else if (p1.y > p2.y)
controlPoint.y -= diffY;
return controlPoint;
}