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This chapter is from the book

Recipe: Smoothing Drawings

Depending on the device in use and the amount of simultaneous processing involved, capturing user gestures may produce results that are rougher than desired. Touch events are often limited by CPU demands as well as by shaking hands. A smoothing algorithm can offset those limitations by interpolating between points. Figure 1-4 demonstrates the kind of angularity that derives from granular input and the smoothing that can be applied instead.

Figure 1-4

Figure 1-4 Catmull-Rom smoothing can be applied in real time to improve arcs between touch events. The images shown here are based on identical gesture input, with (right) and without (left) smoothing applied.

Catmull-Rom splines create continuous curves between key points. This algorithm ensures that each initial point you provide remains part of the final curve. The resulting path retains the original path’s shape. You choose the number of interpolation points between each pair of reference points. The trade-off is between processing power and greater smoothing. The more points you add, the more CPU resources you’ll consume. As you can see when using the sample code that accompanies this chapter, a little smoothing goes a long way, even on newer devices. The latest iPad is so responsive that it’s hard to draw a particularly jaggy line in the first place.

Recipe 1-8 demonstrates how to extract points from an existing Bezier path and then apply splining to create a smoothed result. Catmull-Rom uses four points at a time to calculate intermediate values between the second and third points, using a granularity you specify between those points.

Recipe 1-8 provides an example of just one kind of real-time geometric processing you might add to your applications. Many other algorithms out there in the world of computational geometry can be applied in a similar manner.

Recipe 1-8 Creating Smoothed Bezier Paths Using Catmull-Rom Splining

#define VALUE(_INDEX_) [NSValue valueWithCGPoint:points[_INDEX_]]

@implementation UIBezierPath (Points)
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 *)points
    NSMutableArray *points = [NSMutableArray array];
        (__bridge void *)points, getPointsFromBezier);
    return points;

#define POINT(_INDEX_)     [(NSValue *)[points objectAtIndex:_INDEX_] CGPointValue]

@implementation UIBezierPath (Smoothing)
- (UIBezierPath *)smoothedPath:(int)granularity
    NSMutableArray *points = [self.points mutableCopy];
    if (points.count < 4) return [self copy];

    // Add control points to make the math make sense
    // Via Josh Weinberg
    [points insertObject:[points objectAtIndex:0] atIndex:0];
    [points addObject:[points lastObject]];

    UIBezierPath *smoothedPath = [UIBezierPath bezierPath];

    // Copy traits
    smoothedPath.lineWidth = self.lineWidth;

    // Draw out the first 3 points (0..2)
    [smoothedPath moveToPoint:POINT(0)];

    for (int index = 1; index < 3; index++)
        [smoothedPath addLineToPoint:POINT(index)];

    for (int index = 4; index < points.count; index++)
        CGPoint p0 = POINT(index - 3);
        CGPoint p1 = POINT(index - 2);
        CGPoint p2 = POINT(index - 1);
        CGPoint p3 = POINT(index);

        // 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 +
            pi.y = 0.5 * (2*p1.y+(p2.y-p0.y)*t +
                (2*p0.y-5*p1.y+4*p2.y-p3.y)*tt +
            [smoothedPath addLineToPoint:pi];

        // Now add p2
        [smoothedPath addLineToPoint:p2];

    // finish by adding the last point
    [smoothedPath addLineToPoint:POINT(points.count - 1)];

    return smoothedPath;

// Example usage:
// Replace the path with a smoothed version after drawing completes
- (void)touchesEnded:(NSSet *)touches withEvent:(UIEvent *)event
    UITouch *touch = [touches anyObject];
    [path addLineToPoint:[touch locationInView:self]];
    path = [path smoothedPath:4];
    [self setNeedsDisplay];
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