Draw smooth curves - methods needed - drawing smooth curves - methods needed

problem ：

How do you smooth a set of points in an iOS drawing app WHILE MOVING? How to smooth when moving iOS A set of points in a drawing application ？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 tried UIBezierpaths But all I get is the jagged end where they intersect , When I just move a little 1,2,3,4 - 2,3,4,5 when .I have heard of spline curves and all the other types. I've heard of splines and all other types .I am quite new to iPhone programming and do not understand how to program it in my quartz drawing app. I am right. iPhone Programming is strange , I don't know how to program in my quartz drawing application .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. A reliable example would be appreciated , I spent weeks running in circles , I can never seem to find any of this task iOS Code .Most of the posts just link to a java simulation or pages on wikipedia about curve fitting which does nothing for me. Most posts just link to Java Simulation or Wikipedia page about curve fitting , It doesn't help me in any way .Also I do not want to switch to openGL ES. I don't want to switch to openGL ES.I hope someone can finally provide code to answer this circulating question. I hope someone will eventually provide code to answer this circular question .

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This was my code for the UIBezierPath which left edges at intersection/// This is my UIBezierPath Code , It leaves an edge at the intersection //

UPDATED TO AN ANSWER BELOW Update to the 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];}

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Solution ：

Reference resources ： https://stackoom.com/en/question/aVy4