UIBezierPath intersect

Question

I've been searching for an answer for hours but have trouble finding anything on the topic.

I have a question related to Objective-c. I'm making an application in which a UIView checks for touches from the user and if the user touches and moves his/her finger, a path using UIBezierPath is drawn. If the user draws so that the path intersects itself it should disappear from the screen. When the user is done drawing the pattern, a line from the last point in the path should connect with the first point in the path automatically (I'm using the method "closePath" for this), if this line intersects with another "line" in the path the path should also disappear from the screen.

I store every touch point in a CGPoint that I store in another class called Line as point A and point B. I'm then saving the "line" to an NSMutableArray called "lines". Every time a point is added to the path I check to see if the line between that point and the point drawn before it intersects with any of the "lines" in lines by using a method (-(BOOL)checkLineIntersection:(CGPoint)p1 :(CGPoint)p2 :(CGPoint)p3 :(CGPoint)p4) I got from this tutorial "http://www.iossourcecode.com/2012/08/02/how-to-make-a-game-like-cut-the-rope-part-2/".

The problem

The problem is that when I run the application it works sometimes but sometimes when I draw so the lines intersect the path doesn't disappear. I can't figure out why... It seems as it happens more often when I draw slowly.

The code:

MyView.h:

#import <UIKit/UIKit.h>
#import "Line.h"
@interface MyView : UIView {

NSMutableArray *pathArray;
UIBezierPath *myPath;
NSMutableArray *lines;
Line *line;
} 

@end

MyView.m:

#import "MyView.h"

@implementation MyView


- (id)initWithFrame:(CGRect)frame
{
self = [super initWithFrame:frame];
if (self) {
    // Initialization code
    pathArray=[[NSMutableArray alloc]init];

}
return self;
}

- (void)drawRect:(CGRect)rect
{
[[UIColor redColor] setStroke];
[[UIColor blueColor] setFill];

for (UIBezierPath *_path in pathArray) {
    //[_path fill];

    [_path strokeWithBlendMode:kCGBlendModeNormal alpha:1.0];
}
}

#pragma mark - Touch Methods
-(void)touchesBegan:(NSSet *)touches withEvent:(UIEvent *)event
{
myPath = [[UIBezierPath alloc]init];
lines = [[NSMutableArray alloc]init];
myPath.lineWidth=1;

UITouch *mytouch = [[event allTouches] anyObject];
[myPath moveToPoint:[mytouch locationInView:mytouch.view]];

[pathArray addObject:myPath];

}

-(void)touchesMoved:(NSSet *)touches withEvent:(UIEvent *)event
{

if(myPath.isEmpty) {

} else {

    UITouch *mytouch = [[event allTouches] anyObject];
    [myPath addLineToPoint:[mytouch locationInView:mytouch.view]];

    CGPoint pointA = [mytouch previousLocationInView:mytouch.view];
    CGPoint pointB = [mytouch locationInView:mytouch.view];

    line = [[Line alloc]init];
    [line setPointA:pointA];
    [line setPointB:pointB];

    [lines addObject:line];

    for(Line *l in lines) {

        CGPoint pa = l.pointA;
        CGPoint pb = l.pointB;

        //NSLog(@"Point A: %@", NSStringFromCGPoint(pa));
        //NSLog(@"Point B: %@", NSStringFromCGPoint(pb));

        if ([self checkLineIntersection:pointA :pointB :pa :pb])
        {
            [pathArray removeLastObject];
            [myPath removeAllPoints];
            [self setNeedsDisplay];
            NSLog(@"Removed path!");
            return;
        }
    }
}
[self setNeedsDisplay];
}

-(void)touchesEnded:(NSSet *)touches withEvent:(UIEvent *)event
{
if(myPath.isEmpty) {


} else if ([lines count] != 0){
    line = [[Line alloc]init];
    line = [lines lastObject];
    CGPoint pointA = line.pointA;
    line = [[Line alloc]init];
    line = [lines objectAtIndex:0];
    CGPoint pointB = line.pointA;

    [myPath closePath];
    for(Line *l in lines) {

        CGPoint pa = l.pointA;
        CGPoint pb = l.pointB;

        if ([self checkLineIntersection:pointA :pointB :pa :pb])
        {
            [pathArray removeLastObject];
            [myPath removeAllPoints];
            [self setNeedsDisplay];
            NSLog(@"Removed path!");
            return;
        }
    } 
}
[self setNeedsDisplay];
}

-(BOOL)checkLineIntersection:(CGPoint)p1 :(CGPoint)p2 :(CGPoint)p3 :(CGPoint)p4
{
CGFloat denominator = (p4.y - p3.y) * (p2.x - p1.x) - (p4.x - p3.x) * (p2.y - p1.y);

/*
// In this case the lines are parallel so you assume they don't intersect
if (denominator == 0.0f)
    return NO;
*/

CGFloat ua = ((p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x)) / denominator;
CGFloat ub = ((p2.x - p1.x) * (p1.y - p3.y) - (p2.y - p1.y) * (p1.x - p3.x)) / denominator;

if (ua > 0.0 && ua < 1.0 && ub > 0.0 && ub < 1.0)
{
    return YES;
}

return NO;
}


@end

Line.h:

#import <UIKit/UIKit.h>

@interface Line : UIView 

@property (nonatomic, assign) CGPoint pointA;
@property (nonatomic, assign) CGPoint pointB;

@end

Line.m:

#import "Line.h"

@implementation Line

@synthesize pointA;
@synthesize pointB;

- (id)initWithFrame:(CGRect)frame
{
self = [super initWithFrame:frame];
if (self) {
    // Initialization code
}
return self;
}

/*
// Only override drawRect: if you perform custom drawing.
// An empty implementation adversely affects performance during animation.
- (void)drawRect:(CGRect)rect
{
// Drawing code
}
*/

@end

I hope someone might be able to answer this. Sorry if it's something obvious. Thank you in advance!

Answer 1

The problem is in the checkLineIntersection method. With

if (ua > 0.0 && ua < 1.0 && ub > 0.0 && ub < 1.0) { return YES; }

you check only if the interior part of the lines segments intersect. But if the start or endpoint of the first line segment is equal to the start or endpoint of the second line segment, ua and ub will be 0.0 or 1.0.

The solution is to include one end of the interval in the condition:

if (ua > 0.0 && ua <= 1.0 && ub > 0.0 && ub <= 1.0) { return YES; }

This seemed to work as expected in my test program.

Some further remarks:

• I think you should activate the shortcut

  if (denominator == 0.0f) return NO;
  

  again to avoid division by zero.

• In touchesMoved, you could add the new line to the array after checking for intersections. Now the new line is inserted first, which means that it is checked against itself for intersections.

• You have declared Line as subclass of UIView, but this is not really a view class. You could just declare Line as subclass of NSObject.

---

ADDED: The following method might work even better, because it avoids the division and therefore possible overflow problems with small denominators:

-(BOOL)checkLineIntersection:(CGPoint)p1 :(CGPoint)p2 :(CGPoint)p3 :(CGPoint)p4
{
    CGFloat denominator = (p4.y - p3.y) * (p2.x - p1.x) - (p4.x - p3.x) * (p2.y - p1.y);
    CGFloat ua = (p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x);
    CGFloat ub = (p2.x - p1.x) * (p1.y - p3.y) - (p2.y - p1.y) * (p1.x - p3.x);
    if (denominator < 0) {
        ua = -ua; ub = -ub; denominator = -denominator;
    }
    return (ua > 0.0 && ua <= denominator && ub > 0.0 && ub <= denominator);
}

Answer 2

I've found another workaround to check if the line intersect it self. With SceneKit framework it possible to create shape from UIBezierPath. But if the path intersects then bounding box of the node will be zeroed.

   let path = UIBezierPath()

    //...

    let testGeometry = SCNShape(path:path, extrusionDepth: 0.5)
    let testNode = SCNNode(geometry: testGeometry)

    if (testNode.boundingBox.max - testNode.boundingBox.min).length() > 0 {
    // No intersection (or empty)
   }