objective-c - NSBezierPath:创建一个 "curved"正方形

Question

我想创建一个 NSBezierPath 来表示“弯曲”或“臃肿”的正方形，如下所示:

我正在努力想出正确的数学方法来使这个形状完全正确。我查遍了互联网，但谷歌搜索这个主题主要是“这就是如何绘制圆角”，这不是我需要的。

任何人都可以向我指出一个可以用来放置这些曲线的控制点的公式吗？谢谢!

Answer 1

好的；经过多次尝试和错误，我得到了一些有用的东西。下面的代码将绘制一个像这样的形状。 (此图像对代码中的 #define 语句使用以下值):

#define SIDE_DEFLECTION 18.0f
#define CORNER_RAD 18.0f
#define KAPPA 0.55238f
#define CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION .10
#define SIDE_CENTER_CP_OFFSET 0.60

给定 500x500 像素 View ，这些值将绘制此形状:

绘图代码

就我而言，我在 NSButtonCell 子类中绘制此形状。因为我知道这个单元格的框架永远不会在我的应用程序中调整大小，所以我可以做一些优化。具体来说，我将 NSBezierPath 存储为 iVar，因此我不必每次通过 -drawImage 重新创建它...此外，我将 NSShadow 和 NSColor 存储为 iVar，因此也不必重新创建它们。

如果您要在可调整大小的 View 中绘制此形状，则需要稍微调整代码。如果正方形的大小发生剧烈变化，则需要立即手动调整 #define 语句的值(否则，角看起来不太正确。侧曲线过渡到圆角曲线时几乎没有缩进，等等)

下面的代码配置为在 52x52 像素的正方形中绘制相同的形状。一般的方法是设置你想要的“侧面偏转”和“拐角半径”，然后调整两个“偏移”定义语句(它们是百分比)，直到拐角看起来完美。 “kappa”的值绝不能改变——这个值取 self 发现的一篇数学论文。

这是优化的绘图代码:

    #import "LPProjectIconButtonCell.h"


#define SIDE_DEFLECTION 1.0f
#define CORNER_RAD 4.0f

// Distance (%) control points should be from curve start/end to form perfectly circular rounded corners
#define KAPPA 0.55238f

// Percentage offset (from perfectly circular rounded corner location) that the corner control points use to
// compensate for the fact that our sides are rounded. Without this, we get a rough transition between the
// curve of the side and the start of the corner curve
#define CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION .85

// As the curve approaches each side-center point, this is the percentage of the distance between the side endpoints
// and the side centerpoint where the control point for approaching the centerpoint is located. You are not expected
// to understand the preceeding sentence.
#define SIDE_CENTER_CP_OFFSET 0.60



@implementation LPProjectIconButtonCell

- (void) awakeFromNib
{
    _shadow = [[NSShadow alloc] init];
    [_shadow setShadowBlurRadius:1.0f];
    [_shadow setShadowColor:[NSColor colorWithCalibratedWhite:1.0f alpha:0.2f]];
    [_shadow setShadowOffset:NSMakeSize(0.0f, -1.0f)];

    _borderColor = [[NSColor colorWithCalibratedWhite:0.13 alpha:1.0f] retain];
}

- (void) dealloc
{
    [_path release];
    _path = nil;

    [_shadow release];
    _shadow = nil;

    [_borderColor release];
    _borderColor = nil;

    [super dealloc];
}


- (void) drawImage:(NSImage *)image withFrame:(NSRect)frame inView:(NSView *)controlView
{
    NSGraphicsContext *currentContext = [NSGraphicsContext currentContext];

    // The path never changes because this view never resizes. So we'll save it to be efficient
    if (!_path)
    {
        NSRect rect = NSInsetRect(frame, 2.0f, 2.0f);

        // Create the primary points -- 3 per side
        NSPoint TCenter = NSMakePoint(rect.size.width/2.0f, rect.origin.y);
        NSPoint TLeft = NSMakePoint(rect.origin.x + CORNER_RAD + SIDE_DEFLECTION, rect.origin.y + SIDE_DEFLECTION);
        NSPoint TRight = NSMakePoint(rect.origin.x + rect.size.width - (CORNER_RAD + SIDE_DEFLECTION), rect.origin.y + SIDE_DEFLECTION);

        NSPoint LTop = NSMakePoint(rect.origin.x + SIDE_DEFLECTION, rect.origin.y + CORNER_RAD + SIDE_DEFLECTION);
        NSPoint LCenter = NSMakePoint(rect.origin.x, rect.size.height/2.0f);
        NSPoint LBottom = NSMakePoint(rect.origin.x + SIDE_DEFLECTION, rect.origin.y + rect.size.height - CORNER_RAD - SIDE_DEFLECTION);

        NSPoint BLeft = NSMakePoint(TLeft.x, rect.origin.y + rect.size.height - SIDE_DEFLECTION);
        NSPoint BCenter = NSMakePoint(TCenter.x, rect.origin.y + rect.size.height);
        NSPoint BRight = NSMakePoint(TRight.x, BLeft.y);

        NSPoint RTop = NSMakePoint(rect.origin.x + rect.size.width - SIDE_DEFLECTION, LTop.y);
        NSPoint RCenter = NSMakePoint(rect.origin.x + rect.size.width, LCenter.y);
        NSPoint RBottom = NSMakePoint(RTop.x, LBottom.y);


        // Create corner control points for rounded corners
        // We don't want them to be perfectly circular, because our sides are curved. So we adjust them slightly to compensate for that.
        NSPoint CP_TLeft = NSMakePoint(TLeft.x - (TLeft.x - LTop.x) * KAPPA, TLeft.y + SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION);
        NSPoint CP_LTop = NSMakePoint(LTop.x + SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION, LTop.y - (LTop.y - TLeft.y) * KAPPA);

        NSPoint CP_LBottom = NSMakePoint(LBottom.x + SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION, LBottom.y + (BLeft.y - LBottom.y) * KAPPA);
        NSPoint CP_BLeft = NSMakePoint(BLeft.x - (BLeft.x - LBottom.x) * KAPPA, BLeft.y - SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION);

        NSPoint CP_BRight = NSMakePoint(BRight.x + (RBottom.x - BRight.x) * KAPPA, BRight.y - SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION);
        NSPoint CP_RBottom = NSMakePoint(RBottom.x - SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION, RBottom.y + (BRight.y - RBottom.y) * KAPPA);

        NSPoint CP_RTop = NSMakePoint(RTop.x - SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION, RTop.y - (RTop.y - TRight.y) * KAPPA);
        NSPoint CP_TRight = NSMakePoint(TRight.x + (RTop.x - TRight.x) * KAPPA, TRight.y + SIDE_DEFLECTION * CORNER_CP_OFFSET_FOR_SIDE_DEFLECTION);


        // Create control points for the rounded sides. (The "duplicate" control points are here in case I ever tweak this in the future.)
        NSPoint CP_DepartingTCenterForTLeft = NSMakePoint(TCenter.x - (TCenter.x - TLeft.x) * SIDE_CENTER_CP_OFFSET, TCenter.y);
        NSPoint CP_ApproachingTLeft = TLeft;

        NSPoint CP_DepartingLTopForLCenter = LTop;
        NSPoint CP_ApproachingLCenterFromLTop = NSMakePoint(LCenter.x, LCenter.y - (LCenter.y - LTop.y) * SIDE_CENTER_CP_OFFSET);

        NSPoint CP_DepartingLCenterForLBottom = NSMakePoint(LCenter.x, LCenter.y + (LBottom.y - LCenter.y) * SIDE_CENTER_CP_OFFSET);
        NSPoint CP_ApproachingLBottom = LBottom;

        NSPoint CP_DepartingBLeftForBCenter = BLeft;
        NSPoint CP_ApproachingBCenter = NSMakePoint(BCenter.x - (BCenter.x - BLeft.x) * SIDE_CENTER_CP_OFFSET, BCenter.y);

        NSPoint CP_DepartingBCenterForBRight = NSMakePoint(BCenter.x + (BRight.x - BCenter.x) * SIDE_CENTER_CP_OFFSET, BCenter.y);
        NSPoint CP_ApproachingBRight = BRight;

        NSPoint CP_DepartingRBottomForRCenter = RBottom;
        NSPoint CP_ApproachingRCenterFromRBottom = NSMakePoint(RCenter.x, RCenter.y + (RBottom.y - RCenter.y) * SIDE_CENTER_CP_OFFSET);

        NSPoint CP_DepartingRCenterForRTop = NSMakePoint(RCenter.x, RCenter.y - (RCenter.y - RTop.y) * SIDE_CENTER_CP_OFFSET);
        NSPoint CP_ApproachingRTopFromRCenter = RTop;

        NSPoint CP_DepartingTRightForTCenter = TRight;
        NSPoint CP_ApproachingTCenterFromTRight = NSMakePoint(TCenter.x + (TRight.x - TCenter.x) * SIDE_CENTER_CP_OFFSET, TCenter.y);


        // Draw the bloody square
        NSBezierPath *p = [[NSBezierPath alloc] init];

        [p moveToPoint:TCenter];
        [p curveToPoint:TLeft controlPoint1:CP_DepartingTCenterForTLeft controlPoint2:CP_ApproachingTLeft];
        [p curveToPoint:LTop controlPoint1:CP_TLeft controlPoint2:CP_LTop];
        [p curveToPoint:LCenter controlPoint1:CP_DepartingLTopForLCenter controlPoint2:CP_ApproachingLCenterFromLTop];
        [p curveToPoint:LBottom controlPoint1:CP_DepartingLCenterForLBottom controlPoint2:CP_ApproachingLBottom];
        [p curveToPoint:BLeft controlPoint1:CP_LBottom controlPoint2:CP_BLeft];
        [p curveToPoint:BCenter controlPoint1:CP_DepartingBLeftForBCenter controlPoint2:CP_ApproachingBCenter];
        [p curveToPoint:BRight controlPoint1:CP_DepartingBCenterForBRight controlPoint2:CP_ApproachingBRight];
        [p curveToPoint:RBottom controlPoint1:CP_BRight controlPoint2:CP_RBottom];
        [p curveToPoint:RCenter controlPoint1:CP_DepartingRBottomForRCenter controlPoint2:CP_ApproachingRCenterFromRBottom];
        [p curveToPoint:RTop controlPoint1:CP_DepartingRCenterForRTop controlPoint2:CP_ApproachingRTopFromRCenter];
        [p curveToPoint:TRight controlPoint1:CP_RTop controlPoint2:CP_TRight];
        [p curveToPoint:TCenter controlPoint1:CP_DepartingTRightForTCenter controlPoint2:CP_ApproachingTCenterFromTRight];

        [p closePath];

        _path = p;
    }

    //  We want a slightly white drop shadow on the stroke and fill, giving our square some sense of depth.
    [_shadow set];

    [[NSColor blackColor] set];
    [_path fill];


    // Clip to the bezier path and draw a fill image inside of it.
    [currentContext saveGraphicsState];

        [_path addClip];
        [image drawInRect:frame fromRect:NSZeroRect operation:NSCompositeCopy fraction:1.0f respectFlipped:YES hints:nil];

        if (self.isHighlighted)
        {
            // If we're clicked, draw a 50% black overlay to show that
            NSColor *overColor = [NSColor colorWithCalibratedWhite:0.0 alpha:0.5];
            [overColor set];
            [_path fill];
        }

    [currentContext restoreGraphicsState];


    // Stroke the square to create a nice border with a drop shadow at top and bottom.
    [_borderColor set];
    [_path stroke];
}

@end