【iOS】使用一组点画出平滑的曲线

今天在项目中需要人脸上的点来勾勒出人脸的轮廓，我的想法是将要画的点存入一个数组，使用了UIBezierPath来连接每一个点。但是这样画出来的图是折线，显得过于生硬。查了若干资料，后来终于在stackoverflow上找到了一个很好的解决办法。

这个做法的原理其实是在每两个点之间加入一些点，来使得两个点可以平滑的过度。这其实就是Centripetal Catmull–Rom spline的思想。

于是便照葫芦画瓢，写出了我的代码

#define POINT(_INDEX_) [(NSValue *)[points objectAtIndex:_INDEX_] CGPointValue]
- (void)smoothedPathWithPoints:(NSArray *) pointsArray andGranularity:(NSInteger)granularity {
    
    NSMutableArray *points = [pointsArray mutableCopy];
    
    CGContextRef context = UIGraphicsGetCurrentContext();
    CGContextSetAllowsAntialiasing(context, YES);
    CGContextSetStrokeColorWithColor(context, [UIColor greenColor].CGColor);
    CGContextSetLineWidth(context, 0.6);
    
    UIBezierPath *smoothedPath = [UIBezierPath bezierPath];
    
    // Add control points to make the math make sense
    [points insertObject:[points objectAtIndex:0] atIndex:0];
    [points addObject:[points lastObject]];
    [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)];
    
    CGContextAddPath(context, smoothedPath.CGPath);
    CGContextDrawPath(context, kCGPathStroke);
    
}