JS画几何图形之五【过圆外一点作切线】

//画切线

//point 圆外的一点

//dot 圆心

//r 半径

function drawCircleTangent(point, dot, r){

    //画辅助线-start

    var color = 'DarkRed'; //切线的颜色

    var color2 = "#ccc"; //其它辅助线的颜色

    drawLine(dot, [dot[0]+9*r,dot[1]], {color: color2}); // 延长圆心所在的水平线

    drawLine(dot, [dot[0],dot[1]-4*r], {color: color2}); // 画出圆心所在的垂直线

    drawPoint({

        pw:2,ph:2,color:'DarkRed',point: [dot[0]+9*r,dot[1],'x']

    });

    drawPoint({

        pw:2,ph:2,color:'DarkRed',point: [dot[0],dot[1]-4*r,'y']

    });

    drawLine(point, [point[0],dot[1]], {color: color2}); // 画point到x轴的垂直线

    drawLine(point, dot, {color: color2}); // 连接point与dot

    drawLine([point[0]-2*r, point[1]], [point[0]+2*r, point[1]], {color: color2}); //画point所在的水平线

    //画辅助线-end

    //point.push('point');

    drawPoint({

        pw:2,ph:2,color:'DarkRed',point: point

    });

    //dot.push('centre');

    var r_square = Math.pow(r,2); // r的平方

    var point_v = point[1]-dot[1]; //point到x轴的距离的平方

    var point_h = point[0]-dot[0]; //point到y轴的距离的平方

    var c_square = Math.pow(point_v,2) + Math.pow(point_h,2); //point到圆心的距离的平方

    var c = Math.sqrt(c_square); //point到圆心的距离

    var sinA = Math.abs(point_v)/c; //sinA

    var cosA = Math.abs(point_h)/c; //cosA

    var b_square = c_square-r_square; //point到切点的距离的平方

    var b = Math.sqrt(b_square); //point到切点的距离

    var sinB = b/c; //sinB

    var cosB = r/c; //cosB

    //以圆心为坐标圆点，确定point所在的象限

    var quadrant  = 1; //默认值

    var pm_h = point_h == 0? point_h: point_h/Math.abs(point_h); //水平方向

    var pm_v = point_v == 0? point_v: point_v/Math.abs(point_v); //垂直方向

    var hv = pm_h*pm_v; //相乘，-1时point在一三象限，+1时point在二四象限，0时point在轴上

    switch(hv){

        case 1:

            if((pm_h+pm_v)==-2){

                quadrant = 2; //第二象限

            }else{

                quadrant = 4; //第四象限

            }

            break;

        case -1:

            if((pm_h-pm_v)==-2){

                quadrant = 3; //第三象限

            }

            break;

        case 0:

            if((pm_h+pm_v)==-1){ //point在x轴的负半轴或者y轴的正半轴时，断定point在第二象限

                quadrant = 2;

            }

            if((pm_h+pm_v)==1){ //point在x轴的正半轴或者y轴的负半轴时，断定point在第四象限

                quadrant = 4;

            }

            break;

        default:

    }

    var sinC = 0;

    var conC = 0;

    var sinD = 0;

    var conD = 0;

    switch(quadrant){

        case 1:

            sinC = cosB*cosA+sinB*sinA; //sinC = sin(90+(B-A)) = cos(B-A) = cosB*cosA+sinB*sinA

            conC = -(sinB*cosA-cosB*sinA); //cosC = cos(90+(B-A)) = -sin(B-A) = -(sinB*cosA-cosB*sinA)

            sinD = -(cosA*cosB-sinA*sinB); //sinD = sin(270-(A+B))

            conD = -(sinA*cosB+cosA*sinB); //conD = cos(270-(A+B))

            break;

        case 2:

            sinC = -(cosB*cosA-sinB*sinA); //sinC = sin(-90+(A+B))

            conC = sinA*cosB+cosA*sinB; //conC = cos(-90+(A+B))

            sinD = cosA*cosB+sinA*sinB; //sinD = sin(90+(A-B))

            conD = -(sinA*cosB-cosA*sinB); //conD = cos(90+(A-B))

            break;

        case 3:

            sinC = -(cosA*cosB+sinA*sinB); //sinC = sin(-90+(A-B))

            conC = -(sinA*cosB-cosA*sinB); //conC = cos(-90+(A-B))

            sinD = (cosA*cosB-sinA*sinB);

            conD = sinA*cosB+cosA*sinB;

            break;

        case 4:

            sinC = cosA*cosB-sinA*sinB;

            conC = -(sinA*cosB+cosA*sinB)

            sinD = -(cosA*cosB+sinA*sinB); //sinD = sin(270+(A-B))

            conD = (sinA*cosB-cosA*sinB); //conD = cos(270+(A-B))

            break;

        default:

    }

    var tangentPointA = [point[0]+b*conC, point[1]+b*sinC]; //切点A位置

    drawLine(point, tangentPointA, {color: color}); //画出切线

    drawLine(dot, tangentPointA, {color: color2}); //连接圆点与切点

    //drawArc(point, 17, (quadrant ==1 ||quadrant==4?180:0)-(quadrant ==2 ||quadrant==3?(-1):1)*Math.asin(sinC)*180/Math.PI, 0);

    var tangentPointB = [point[0]+b*conD, point[1]+b*sinD]; //切点B位置

    drawLine(point, tangentPointB, {color: color}); //画出切线

    drawLine(dot, tangentPointB, {color: color2}); //连接圆点与切点

    //drawArc(point, 27, (quadrant ==1 ||quadrant==4?180:0)-(quadrant ==2 ||quadrant==3?(-1):1)*Math.asin(sinD)*180/Math.PI, 0);

    drawPoint({ //描切点

        pw:3,ph:3,color:'DarkRed',point: tangentPointA

    });

    drawPoint({ //描切点

        pw:3,ph:3,color:'DarkRed',point: tangentPointB

    });

    //画辅助弧

    //(quadrant ==1 ||quadrant==4?360:0)

    drawArc(point, b, 60, (quadrant ==1 ||quadrant==4?180:0)-(quadrant ==2 ||quadrant==3?(-1):1)*Math.asin(sinC)*180/Math.PI-5);

}