ios 和 javascript 的三次贝塞尔曲线不同

Question

背景：

在我的应用程序中，我必须沿着用户点击屏幕的点绘制一条曲线。我发现下面的博客解释了如何根据贝塞尔曲线的路径点计算控制点。

Spline Interpolation - Scaled Innovation

示例在 javascript 中，我将其改编为 iOS。下面是我在我的应用程序中使用的代码

void (^calculateAndAddControlPoints)(CGPoint firstPoint, CGPoint secondPoint, CGPoint thirdPoint) = ^void (CGPoint firstPoint, CGPoint secondPoint, CGPoint thirdPoint)
{
    CGPoint controlPoint1;
    CGPoint controlPoint2;

    CGFloat distance12 = sqrt(pow(firstPoint.x-secondPoint.x, 2) + pow(firstPoint.y-secondPoint.y, 2));
    CGFloat distance23 = sqrt(pow(secondPoint.x-thirdPoint.x, 2) + pow(secondPoint.y-thirdPoint.y, 2));
    CGFloat scallingFactor12 = (tension * distance12) / (distance12 + distance23);
    CGFloat scallingFactor23 = tension - scallingFactor12;

    controlPoint1.x = secondPoint.x - (scallingFactor12 * (thirdPoint.x - firstPoint.x));
    controlPoint1.y = secondPoint.y - (scallingFactor12 * (thirdPoint.y - firstPoint.y));
    controlPoint2.x = secondPoint.x + (scallingFactor23 * (thirdPoint.x - firstPoint.x));
    controlPoint2.y = secondPoint.y + (scallingFactor23 * (thirdPoint.y - firstPoint.y));

    CGContextRef context = UIGraphicsGetCurrentContext();
    CGContextSetStrokeColorWithColor(context, [UIColor yellowColor].CGColor);
    UIBezierPath *path = [UIBezierPath bezierPath];
    [path moveToPoint:controlPoint1];
    [path addLineToPoint:controlPoint2];
    [path stroke];

    [controlPoints addObject:[NSValue valueWithCGPoint:controlPoint1]];
    [controlPoints addObject:[NSValue valueWithCGPoint:controlPoint2]];
};
NSUInteger curvePointsCount = [curvePoints count];
if (_closed) {
    NSValue *lastPoint = [curvePoints lastObject];
    [curvePoints addObject:curvePoints[0]];
    [curvePoints addObject:curvePoints[1]];
    [curvePoints insertObject:lastPoint atIndex:0];
    for (NSInteger i=0; i < curvePointsCount; ++i) {
        calculateAndAddControlPoints([curvePoints[i + 0] CGPointValue],
                                     [curvePoints[i + 1] CGPointValue],
                                     [curvePoints[i + 2] CGPointValue]);
    }
    [controlPoints addObject:controlPoints[0]];
    [controlPoints addObject:controlPoints[1]];

    CGContextRef context = UIGraphicsGetCurrentContext();
    CGContextSetStrokeColorWithColor(context, [UIColor whiteColor].CGColor);
    UIBezierPath *path = [UIBezierPath bezierPath];
    [path moveToPoint:[curvePoints[1] CGPointValue]];
    for (NSInteger i=1; i < curvePointsCount + 1; ++i) {
        [path addCurveToPoint:[curvePoints[i + 1] CGPointValue]
                controlPoint1:[controlPoints[2 * i + 0] CGPointValue]
                controlPoint2:[controlPoints[2 * i + 1] CGPointValue]];
    }
    [path stroke];
} else {
    for (NSInteger i=0; i < curvePointsCount - 2; ++i) {
        calculateAndAddControlPoints([curvePoints[i + 0] CGPointValue],
                                     [curvePoints[i + 1] CGPointValue],
                                     [curvePoints[i + 2] CGPointValue]);
    }

    CGContextRef context = UIGraphicsGetCurrentContext();
    CGContextSetStrokeColorWithColor(context, [UIColor whiteColor].CGColor);
    UIBezierPath *path = [UIBezierPath bezierPath];
    [path moveToPoint:[curvePoints[0] CGPointValue]];
    [path addQuadCurveToPoint:[curvePoints[1] CGPointValue]
                 controlPoint:[controlPoints[0] CGPointValue]];

    for (NSInteger i=1; i < curvePointsCount - 2; ++i) {
        [path addCurveToPoint:[curvePoints[i + 1] CGPointValue]
                controlPoint1:[controlPoints[2 * i + 0] CGPointValue]
                controlPoint2:[controlPoints[2 * i + 1] CGPointValue]];
    }

    [path moveToPoint:[curvePoints[curvePointsCount - 2] CGPointValue]];
    [path addQuadCurveToPoint:[curvePoints[curvePointsCount - 1] CGPointValue]
                 controlPoint:[controlPoints[[controlPoints count] - 1] CGPointValue]];
    [path stroke];
}

问题：

iOS 中的输出与 javascript 中的输出不同，如下图所示，曲线在路径点附近并不平滑。白线是实际曲线，黄线是连接控制点的线，红点是曲线点。

这是相同曲线在 javascript 中的样子。

使用的曲线点数：(100, 100), (300, 100), (300, 300), (100, 300)

生成的控制点：(50, 150), (150, 50), (250, 50), (350, 150), (350, 250), (250, 350), (150, 350 ), (50, 250)

为什么我在 iOS 中没有得到一个圆圈，如何解决这个问题？

解决方案：

事实证明我正确计算了控制点，但错误地将它们映射到曲线点。感谢@gabbler，我现在修复了它，下面是绘制曲线的正确循环

for (NSInteger i=1; i < curvePointsCount + 1; ++i) {
    [_bezierPath moveToPoint:[curvePoints[i] CGPointValue]];
    [_bezierPath addCurveToPoint:[curvePoints[i + 1] CGPointValue]
            controlPoint1:[controlPoints[2 * i - 1] CGPointValue]
            controlPoint2:[controlPoints[2 * i + 0] CGPointValue]];
}

Answer 1

当你添加一条从(100,100)到(300,100)的曲线时，控制点应该是(150,50)和(250,50)，在你的代码中，控制点是(350,150)和(250) ,50), 指定正确的控制点应该使它工作。

ios 和 javascript 的三次贝塞尔曲线不同

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bezier

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