UIBezierPath+forEachElement.h

#import <UIKit/UIKit.h>

@interface UIBezierPath (forEachElement)

- (void)forEachElement:(void (^)(CGPathElement const *element))block;

@end

UIBezierPath+forEachElement.m

#import "UIBezierPath+forEachElement.h"

typedef void (^UIBezierPath_forEachElement_Block)(CGPathElement const *element);

@implementation UIBezierPath (forEachElement)

static void applyBlockToPathElement(void *info, CGPathElement const *element) {
    __unsafe_unretained UIBezierPath_forEachElement_Block block =(__bridge  UIBezierPath_forEachElement_Block)info;
    block(element);
}

- (void)forEachElement:(void (^)(const CGPathElement *))block {
    CGPathApply(self.CGPath, (__bridge void *)block, applyBlockToPathElement);
}

@end

ViewController.m

// This code is described here:
// http://stackoverflow.com/questions/13664615/drag-uiview-around-oval-shape-comprised-of-cgmutablepaths

#import "ViewController.h"
#import "UIBezierPath+forEachElement.h"

@interface ViewController ()

@end

@implementation ViewController {
    UIBezierPath *path_;
    CAShapeLayer *pathLayer_;
    NSMutableData *pathPointsData_;
    CGPoint const *pathPoints_;
    NSInteger pathPointsCount_;
    UIView *handleView_;
    NSInteger handlePathPointIndex_;
    CGPoint desiredHandleCenter_;
}

- (void)viewDidLoad {
    [super viewDidLoad];
    [self initPathLayer];
    [self initHandleView];
    [self initHandlePanGestureRecognizer];
}

- (void)initPathLayer {
    pathLayer_ = [CAShapeLayer layer];
    pathLayer_.lineWidth = 1;
    pathLayer_.fillColor = nil;
    pathLayer_.strokeColor = [UIColor blackColor].CGColor;
    pathLayer_.lineCap = kCALineCapButt;
    pathLayer_.lineJoin = kCALineJoinRound;
    [self.view.layer addSublayer:pathLayer_];
}

- (void)initHandleView {
    handlePathPointIndex_ = 0;
    
    CGRect rect = CGRectMake(0, 0, 30, 30);
    CAShapeLayer *circleLayer = [CAShapeLayer layer];
    circleLayer.fillColor = nil;
    circleLayer.strokeColor = [UIColor redColor].CGColor;
    circleLayer.lineWidth = 2;
    circleLayer.path = [UIBezierPath bezierPathWithOvalInRect:CGRectInset(rect, circleLayer.lineWidth, circleLayer.lineWidth)].CGPath;
    circleLayer.frame = rect;

    handleView_ = [[UIView alloc] initWithFrame:rect];
    [handleView_.layer addSublayer:circleLayer];
    [self.view addSubview:handleView_];
}

- (void)initHandlePanGestureRecognizer {
    UIPanGestureRecognizer *recognizer = [[UIPanGestureRecognizer alloc] initWithTarget:self action:@selector(handleWasPanned:)];
    [handleView_ addGestureRecognizer:recognizer];
}

- (void)viewDidLayoutSubviews {
    [super viewDidLayoutSubviews];
    [self createPath];
    [self createPathPoints];
    [self layoutPathLayer];
    [self layoutHandleView];
}

- (void)layoutHandleView {
    // Make sure the index is in bounds.
    handlePathPointIndex_ = [self handlePathPointIndexWithOffset:0];
    
    handleView_.center = [pathLayer_ convertPoint:pathPoints_[handlePathPointIndex_] toLayer:self.view.layer];
}

- (void)createPath {
    CGRect bounds = self.view.bounds;
    CGFloat const radius = bounds.size.height / 6;
    CGFloat const offset = 2 * radius * M_SQRT1_2;
    CGPoint const topCenter = CGPointMake(CGRectGetMidX(bounds), CGRectGetMidY(bounds) - offset);
    CGPoint const bottomCenter = { topCenter.x, CGRectGetMidY(bounds) + offset };
    path_ = [UIBezierPath bezierPath];
    [path_ addArcWithCenter:topCenter radius:radius startAngle:M_PI_4 endAngle:-M_PI - M_PI_4 clockwise:NO];
    [path_ addArcWithCenter:bottomCenter radius:radius startAngle:-M_PI_4 endAngle:M_PI + M_PI_4 clockwise:YES];
    [path_ closePath];
}

static CGPoint *lastPointOfPathElement(CGPathElement const *element) {
    int index;
    switch (element->type) {
        case kCGPathElementMoveToPoint: index = 0; break;
        case kCGPathElementAddCurveToPoint: index = 2; break;
        case kCGPathElementAddLineToPoint: index = 0; break;
        case kCGPathElementAddQuadCurveToPoint: index = 1; break;
        case kCGPathElementCloseSubpath: index = NSNotFound; break;
    }
    return index == NSNotFound ? 0 : &element->points[index];
}

- (void)createPathPoints {
    CGPathRef cgDashedPath = CGPathCreateCopyByDashingPath(path_.CGPath, NULL, 0, (CGFloat[]){ 1.0f, 1.0f }, 2);
    UIBezierPath *dashedPath = [UIBezierPath bezierPathWithCGPath:cgDashedPath];
    CGPathRelease(cgDashedPath);

    static CGFloat const kMinimumDistance = 0.1f;

    __block CGPoint priorPoint = { HUGE_VALF, HUGE_VALF };

    pathPointsData_ = [[NSMutableData alloc] init];

    [dashedPath forEachElement:^(const CGPathElement *element) {
        CGPoint *p = lastPointOfPathElement(element);
        if (!p)
            return;
        if (hypotf(p->x - priorPoint.x, p->y - priorPoint.y) < kMinimumDistance)
            return;
        [pathPointsData_ appendBytes:p length:sizeof *p];
        priorPoint = *p;
    }];

    pathPoints_ = (CGPoint const *)pathPointsData_.bytes;
    pathPointsCount_ = pathPointsData_.length / sizeof *pathPoints_;

    if (pathPointsCount_ > 1 && hypotf(pathPoints_[0].x - priorPoint.x, pathPoints_[0].y - priorPoint.y) < kMinimumDistance) {
        pathPointsCount_ -= 1;
    }
}

- (void)layoutPathLayer {
    pathLayer_.path = path_.CGPath;
    pathLayer_.frame = self.view.bounds;
}

- (void)handleWasPanned:(UIPanGestureRecognizer *)recognizer {
    switch (recognizer.state) {
        case UIGestureRecognizerStateBegan: {
            desiredHandleCenter_ = handleView_.center;
            break;
        }

        case UIGestureRecognizerStateChanged:
        case UIGestureRecognizerStateEnded:
        case UIGestureRecognizerStateCancelled: {
            CGPoint translation = [recognizer translationInView:self.view];
            desiredHandleCenter_.x += translation.x;
            desiredHandleCenter_.y += translation.y;
            [self moveHandleTowardPoint:desiredHandleCenter_];
            break;
        }

        default:
            break;
    }

    [recognizer setTranslation:CGPointZero inView:self.view];
}

- (void)moveHandleTowardPoint:(CGPoint)point {
    CGFloat earlierDistance = [self distanceToPoint:point ifHandleMovesByOffset:-1];
    CGFloat currentDistance = [self distanceToPoint:point ifHandleMovesByOffset:0];
    CGFloat laterDistance = [self distanceToPoint:point ifHandleMovesByOffset:1];
    if (currentDistance <= earlierDistance && currentDistance <= laterDistance)
        return;

    NSInteger direction;
    CGFloat distance;
    if (earlierDistance < laterDistance) {
        direction = -1;
        distance = earlierDistance;
    } else {
        direction = 1;
        distance = laterDistance;
    }

    NSInteger offset = direction;
    while (true) {
        NSInteger nextOffset = offset + direction;
        CGFloat nextDistance = [self distanceToPoint:point ifHandleMovesByOffset:nextOffset];
        if (nextDistance >= distance)
            break;
        distance = nextDistance;
        offset = nextOffset;
    }

    handlePathPointIndex_ += offset;
    [self layoutHandleView];
}

- (CGFloat)distanceToPoint:(CGPoint)point ifHandleMovesByOffset:(NSInteger)offset {
    int index = [self handlePathPointIndexWithOffset:offset];
    CGPoint proposedHandlePoint = pathPoints_[index];
    return hypotf(point.x - proposedHandlePoint.x, point.y - proposedHandlePoint.y);
}

- (NSInteger)handlePathPointIndexWithOffset:(NSInteger)offset {
    NSInteger index = handlePathPointIndex_ + offset;
    while (index < 0) {
        index += pathPointsCount_;
    }
    while (index >= pathPointsCount_) {
        index -= pathPointsCount_;
    }
    return index;
}

@end