主要计算公式：

直线的一般方程      y = kx + b;

圆的一般方程        x^2 + y^2 + Dx + Ey + F = 0;

圆的基本系数关系     r = (根号(D^2 + E^2 - 4F))/2

一元二次方程求根公式    x = -b (+/-) (根号(b^2 - 4ac)) / 2a

/**

计算圆环上取色点，解任意点过圆心的直线与圆的交点取其一

@param pointOne 任意点

@param circleCenterPoint 圆心

*/

- (CGPoint)calculateColorPointWithPoint:(CGPoint)pointOne circleCenterPoint:(CGPoint)circleCenterPoint

{

//由于OC坐标系与数学坐标系的差异，y值取反,转成数学坐标系

CGPointtemp1 = pointOne;

CGPointtemp2 = circleCenterPoint;

pointOne =CGPointMake(temp1.x, -temp1.y);

circleCenterPoint =CGPointMake(temp2.x, -temp2.y);

//计算过圆心直线斜率和常数b

lineK= (CGFloat)(pointOne.y- circleCenterPoint.y) / (CGFloat)(pointOne.x- circleCenterPoint.x);

lineB= circleCenterPoint.y-lineK*circleCenterPoint.x;

//计算圆的方程常数  其圆心坐标(-D/2, -E/2)  半径公式 r = (根号(D^2 + E^2 - 4F))/2

CGFloatcircleR = circleCenterPoint.x-4;//圆的半径，取圆环的中间值

circleD= -2* circleCenterPoint.x;

circleE= -2* circleCenterPoint.y;

circleF= (powf(circleD,2) +powf(circleE,2) -4*powf(circleR,2))/4.0;

//一元二次方程求根公式    x = -b (+/-) (根号(b^2 - 4ac)) / 2a

CGFloata = (1+powf(lineK,2));

CGFloat b = (2*lineK*lineB + circleD + circleE*lineK);

CGFloat c = powf(lineB, 2) + circleE*lineB + circleF;

//直线与圆的两个交点

CGFloatx1 = ((-b) +sqrtf(powf(b,2) -4*a*c)) / (2*a);

CGFloaty1 =lineK*x1 +lineB;

CGFloatx2 = ((-b) -sqrtf(powf(b,2) -4*a*c)) / (2*a);

CGFloaty2 =lineK*x2 +lineB;

//当过圆心直线斜率不存在时

if(pointOne.x== circleCenterPoint.x) {

x1 = circleCenterPoint.x;

y1 = -4;

x2 = circleCenterPoint.x;

y2 = -(2*circleR +4);

}

//两个交点点到触发点的距离

CGFloatdistance1 =sqrtf(powf(x1 - pointOne.x,2) +powf(y1 - pointOne.y,2));

CGFloatdistance2 =sqrtf(powf(x2 - pointOne.x,2) +powf(y2 - pointOne.y,2));

//选择距离近的, 由于OC坐标系与数学坐标系的差异，y值取反转成OC坐标系

CGPointintersectPoint1 =CGPointMake(x1, -y1);

CGPointintersectPoint2 =CGPointMake(x2, -y2);

if(distance1 < distance2) {

returnintersectPoint1;

}

else{

returnintersectPoint2;

}

}