获得CGPath总长度

Question

我有许多UIBezierPath,我用CALyerAnimation @"StrokeStart"和@"strokeEnd"进行动画制作.

我希望动画对所有路径都具有相同的速度,所以我想我可以使用路径的长度:

距离/时间=速度

有没有办法计算路径"长度"？

谢谢

沙尼

Answer 1

虽然您可以通过数值积分来计算Bezier路径的长度,但通过将路径划分为线性段可以更轻松地完成.如果片段足够小,则可以忽略近似误差,尤其是您只是想要对其进行动画处理.

我将向您展示四条曲线的功能,但您也可以轻松地将立方曲线的解决方案合并到:

- (float) bezierCurveLengthFromStartPoint: (CGPoint) start toEndPoint: (CGPoint) end withControlPoint: (CGPoint) control
{
    const int kSubdivisions = 50;
    const float step = 1.0f/(float)kSubdivisions;

    float totalLength = 0.0f;
    CGPoint prevPoint = start;

    // starting from i = 1, since for i = 0 calulated point is equal to start point
    for (int i = 1; i <= kSubdivisions; i++)
    {
        float t = i*step;

        float x = (1.0 - t)*(1.0 - t)*start.x + 2.0*(1.0 - t)*t*control.x + t*t*end.x;
        float y = (1.0 - t)*(1.0 - t)*start.y + 2.0*(1.0 - t)*t*control.y + t*t*end.y;

        CGPoint diff = CGPointMake(x - prevPoint.x, y - prevPoint.y);

        totalLength += sqrtf(diff.x*diff.x + diff.y*diff.y); // Pythagorean

        prevPoint = CGPointMake(x, y);
    }

    return totalLength;
}

编辑

如果您无法访问路径控制点(例如,您使用弧创建路径),则始终可以使用CGPathApply函数访问基础贝塞尔曲线:

- (void) testPath
{
    UIBezierPath *path = [UIBezierPath bezierPath];
    [path moveToPoint:CGPointZero];
    [path addQuadCurveToPoint:CGPointMake(1, 1) controlPoint:CGPointMake(-2, 2)];

    CGPathRef p = path.CGPath;

    CGPathApply(p, nil, pathFunction);
}

void pathFunction(void *info, const CGPathElement *element)
{
    if (element->type == kCGPathElementAddQuadCurveToPoint)
    {
        CGPoint p;
        p = element->points[0]; // control point
        NSLog(@"%lg %lg", p.x, p.y);

        p = element->points[1]; // end point
        NSLog(@"%lg %lg", p.x, p.y);
    }
    // check other cases as well!
}

请注意,它不提供路径的起点,但您可以轻松地自行跟踪它.