使用贝塞尔曲线绘制螺旋
这是一个iPad应用程序，但它本质上是一个数学问题。
我需要绘制一条不同（单调递增）线宽的圆弧。 在曲线开始时，它会有一个起始厚度（比如说2pts），然后厚度会平滑增加，直到弧线达到最大厚度（比如12pts）。
我想通过创建一个UIBezierPath并填充形状来达到此目的的最佳方式。 我的第一个尝试是使用两个圆弧（有偏移中心），并且工作精度可达90°，但弧度通常在90°和180°之间，所以这种方法不会削减它。
我目前的做法是使用贝塞尔四边形或三次曲线稍作旋转（一个从圆弧稍微增长，一个稍微缩小）。 问题是我在哪里放置控制点，以便与圆弧的偏差（也就是形状“厚度”）是我想要的值。
约束：
我也接受其他解决方案。
我的方法是构造2个圆弧并填充其间的区域。 棘手的是找出这些弧的中心和半径。 看起来相当不错，只要厚度不太大。 （剪切并粘贴，如果它满足您的需求，请自行决定。）可以通过使用剪切路径来改进。
- (void)drawRect:(CGRect)rect
{
CGContextRef context = UIGraphicsGetCurrentContext();
CGMutablePathRef path = CGPathCreateMutable();
// As appropriate for iOS, the code below assumes a coordinate system with
// the x-axis pointing to the right and the y-axis pointing down (flipped from the standard Cartesian convention).
// Therefore, 0 degrees = East, 90 degrees = South, 180 degrees = West,
// -90 degrees = 270 degrees = North (once again, flipped from the standard Cartesian convention).
CGFloat startingAngle = 90.0; // South
CGFloat endingAngle = -45.0; // North-East
BOOL weGoFromTheStartingAngleToTheEndingAngleInACounterClockwiseDirection = YES; // change this to NO if necessary
CGFloat startingThickness = 2.0;
CGFloat endingThickness = 12.0;
CGPoint center = CGPointMake(CGRectGetMidX(self.bounds), CGRectGetMidY(self.bounds));
CGFloat meanRadius = 0.9 * fminf(self.bounds.size.width / 2.0, self.bounds.size.height / 2.0);
// the parameters above should be supplied by the user
// the parameters below are derived from the parameters supplied above
CGFloat deltaAngle = fabsf(endingAngle - startingAngle);
// projectedEndingThickness is the ending thickness we would have if the two arcs
// subtended an angle of 180 degrees at their respective centers instead of deltaAngle
CGFloat projectedEndingThickness = startingThickness + (endingThickness - startingThickness) * (180.0 / deltaAngle);
CGFloat centerOffset = (projectedEndingThickness - startingThickness) / 4.0;
CGPoint centerForInnerArc = CGPointMake(center.x + centerOffset * cos(startingAngle * M_PI / 180.0),
center.y + centerOffset * sin(startingAngle * M_PI / 180.0));
CGPoint centerForOuterArc = CGPointMake(center.x - centerOffset * cos(startingAngle * M_PI / 180.0),
center.y - centerOffset * sin(startingAngle * M_PI / 180.0));
CGFloat radiusForInnerArc = meanRadius - (startingThickness + projectedEndingThickness) / 4.0;
CGFloat radiusForOuterArc = meanRadius + (startingThickness + projectedEndingThickness) / 4.0;
CGPathAddArc(path,
NULL,
centerForInnerArc.x,
centerForInnerArc.y,
radiusForInnerArc,
endingAngle * (M_PI / 180.0),
startingAngle * (M_PI / 180.0),
!weGoFromTheStartingAngleToTheEndingAngleInACounterClockwiseDirection
);
CGPathAddArc(path,
NULL,
centerForOuterArc.x,
centerForOuterArc.y,
radiusForOuterArc,
startingAngle * (M_PI / 180.0),
endingAngle * (M_PI / 180.0),
weGoFromTheStartingAngleToTheEndingAngleInACounterClockwiseDirection
);
CGContextAddPath(context, path);
CGContextSetFillColorWithColor(context, [UIColor redColor].CGColor);
CGContextFillPath(context);
CGPathRelease(path);
}
一种解决方案可能是手动生成折线。 这很简单，但它的缺点是如果控件以高分辨率显示，则必须放大生成的点的数量。 我不太了解iOS给你iOS / ObjC示例代码，但这里有一些python-ish伪代码：
# lower: the starting angle
# upper: the ending angle
# radius: the radius of the circle
# we'll fill these with polar coordinates and transform later
innerSidePoints = []
outerSidePoints = []
widthStep = maxWidth / (upper - lower)
width = 0
# could use a finer step if needed
for angle in range(lower, upper):
innerSidePoints.append(angle, radius - (width / 2))
outerSidePoints.append(angle, radius + (width / 2))
width += widthStep
# now we have to flip one of the arrays and join them to make
# a continuous path. We could have built one of the arrays backwards
# from the beginning to avoid this.
outerSidePoints.reverse()
allPoints = innerSidePoints + outerSidePoints # array concatenation
xyPoints = polarToRectangular(allPoints) # if needed