两圆的外切线与内切线的切点算法

最近想画两球水滴效果所有在网上找两圆外切点和内切点的算法，找了很久没有找到所以自己写了一个工具类来计算两圆的公切线点。具体效果如下图：

根据CircleUtils类的getCircleTangentPointOut方法返回外切点坐标[r1p1, r1p2, r2p1, r2p2],依次为左边圆的两个切点坐标和右边两个切点坐标。

根据CircleUtils类的getCircleTangentPointIn方法返回外切点坐标[r1p1, r1p2, r2p1, r2p2],依次为左边圆的两个切点坐标和右边两个切点坐标。

根据获取坐标绘制线段和点，如下代码

@Overrideprotected void onDraw(Canvas canvas) {super.onDraw(canvas);mPaint.setColor(0XFF00FF00);mPaint.setStyle(Paint.Style.FILL);float r1 = 300;float r2 = 200;canvas.drawCircle(mDownX, mDownY, r1, mPaint);canvas.drawCircle(mCurrentX, mCurrentY, r2, mPaint);PointF[] points2 = CircleUtils.getCircleTangentPointOut(new PointF(mDownX, mDownY), r1, new PointF(mCurrentX, mCurrentY), r2);if (points2 != null) {mPaint.setColor(0XFF0000FF);mPaint.setStyle(Paint.Style.STROKE);canvas.drawLine(points2[0].x, points2[0].y, points2[2].x, points2[2].y, mPaint);canvas.drawLine(points2[1].x, points2[1].y, points2[3].x, points2[3].y, mPaint);}PointF[] points1 = CircleUtils.getCircleTangentPointIn(new PointF(mDownX, mDownY), r1, new PointF(mCurrentX, mCurrentY), r2);if (points1 != null) {mPaint.setColor(0XFF0000FF);mPaint.setStyle(Paint.Style.STROKE);canvas.drawLine(points1[0].x, points1[0].y, points1[3].x, points1[3].y, mPaint);canvas.drawLine(points1[1].x, points1[1].y, points1[2].x, points1[2].y, mPaint);}if (points2 != null) {mPaint.setColor(0XFFFF0000);mPaint.setStyle(Paint.Style.FILL);for (PointF p : points2) {canvas.drawCircle(p.x, p.y, 5, mPaint);}}if (points1 != null) {mPaint.setColor(0XFFFF0000);mPaint.setStyle(Paint.Style.FILL);for (PointF p : points1) {canvas.drawCircle(p.x, p.y, 5, mPaint);}}}

CircleUtils工具类如下代码


public class CircleUtils {//返回两圆外切点坐标public static PointF[] getCircleTangentPointOut(PointF c1, float r1, PointF c2, float r2){float centerLine = getPointDistance(c1, c2);if(centerLine > Math.abs(r1-r2)){//计算外切PointF[] points = new PointF[8];//圆心连线与圆1的交点PointF r1Point = ratioPoint(c1, c2, r1/centerLine);points[6] = r1Point;//圆心连线与圆2的交点PointF r2Point = ratioPoint(c1, c2, (centerLine-r2)/centerLine);points[7] = r2Point;//两元交点连线和两圆焦点在左边圆的角度float angleR1 = getAngle(r1, centerLine, r2);//两元交点连线和两圆焦点在右边圆的角度float angleR2 = getAngle(r2, centerLine, r1);//外切线与圆心连线的角度(0~90度之间的角度)float angle = (float) Math.acos(Math.abs(r1-r2)/centerLine);//两圆的交点points[4] = rotatePoint(r1Point, c1, angleR1);points[5] = rotatePoint(r2Point, c2, angleR2);if(r1>=r2){//切线与第一个圆的交点points[0] = rotatePoint(r1Point, c1, angle);points[1] = rotatePoint(r1Point, c1, -angle);//切线与第二个圆的交点points[2] = rotatePoint(r2Point, c2, -(float) (Math.PI-angle));points[3] = rotatePoint(r2Point, c2, (float) (Math.PI-angle));}else{//切线与第一个圆的交点points[0] = rotatePoint(r1Point, c1, (float) (Math.PI-angle));points[1] = rotatePoint(r1Point, c1, -(float) (Math.PI-angle));//切线与第二个圆的交点points[2] = rotatePoint(r2Point, c2, -angle);points[3] = rotatePoint(r2Point, c2, angle);}return points;}return null;}//返回两圆内切点坐标public static PointF[] getCircleTangentPointIn(PointF c1, float r1, PointF c2, float r2){float centerLine = getPointDistance(c1, c2);if(centerLine > r1+r2){//计算内切PointF[] points = new PointF[7];//内切线焦点points[4] = new PointF((c1.x*r2+c2.x*r1)/(r1+r2), (c1.y*r2+c2.y*r1)/(r1+r2));float l1 = centerLine*r1/(r1+r2);float l2 = centerLine*r2/(r1+r2);//圆心连线与圆1的交点points[5] = ratioPoint(c1, points[4], r1/l1);float angle = (float) Math.acos(r1/l1);//第1个圆的切点points[0] = rotatePoint(points[5], c1, angle);points[1] = rotatePoint(points[5], c1, -angle);//圆心连线与圆2的交点points[6] = ratioPoint(points[4], c2, (l2-r2)/l2);//第2个圆的切点points[2] = rotatePoint(points[6], c2, -angle);points[3] = rotatePoint(points[6], c2, angle);return points;}return null;}//根据点 a, b, c位置距离为ab, bc, ac获取b点在ac上的垂点d，返回垂点dpublic static PointF getVerticalPoint( PointF a, PointF b, PointF c){float ab =getPointDistance(a, b);float ac =getPointDistance(a, c);float bc =getPointDistance(b, c);return getVerticalPoint(ab, ac, bc, a, c);}public static PointF getVerticalPoint(float ab,float ac, float bc, PointF a, PointF c){float angle = getAngle(ab, ac, bc);float ratio = (float) (Math.cos(angle)*ab)/ac;return ratioPoint(a, c, ratio);}//返回两点之间的距离public static float getPointDistance(PointF a, PointF b){return (float) Math.sqrt(Math.pow(a.x-b.x,2)+Math.pow(a.y-b.y, 2));}//根据点 a, b, c位置距离为ab, bc, ac获取a点角度public static float getAngle(float ab,float ac, float bc){return (float) Math.acos((ab*ab+ac*ac-bc*bc)/(2*ab*ac));}//获取一个点，起始点到该点长度除以起始点到结束点长度的比例为ratiopublic static PointF ratioPoint(PointF startPoint, PointF endPoint, float ratio){if(startPoint == null){startPoint = new PointF(0, 0);}PointF ret = new PointF();float x = endPoint.x-startPoint.x;float y = endPoint.y-startPoint.y;ret.x = x*ratio+startPoint.x;ret.y = y*ratio+startPoint.y;return ret;}//空间一个点围绕center点旋转angle角度后的位置public static PointF rotatePoint(PointF point, PointF center, float angle){if(center == null){center = new PointF(0, 0);}PointF ret = new PointF();//获取相对位置float x = point.x-center.x;float y = point.y-center.y;//根据选择矩阵旋转后加上中心点位置ret.x = (float) ((x*Math.cos(angle)-y*Math.sin(angle))+center.x);ret.y = (float) ((x*Math.sin(angle)+y*Math.cos(angle))+center.y);return ret;}
}

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两圆的外切线与内切线的切点算法

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