JS画几何图形之六【过直线外一点作垂线】

//过直线外一点画垂线
function drawVerticalLine(point, line){
    //画辅助线-start
    var color = ‘DarkRed‘; //垂线的颜色
    var color2 = "#ccc"; //其它辅助线的颜色
    drawPoint({
        pw:2,ph:2,color:‘DarkRed‘,point: line[0]
    });
    drawPoint({
        pw:2,ph:2,color:‘DarkRed‘,point: line[1]
    });
    drawLine(point, line[0], {color: color2});
    drawLine(point, line[1], {color: color2});
    //画辅助线-end
    
    drawPoint({
        pw:2,ph:2,color:‘DarkRed‘,point: point
    });
    
    
    var v_1_0 = line[1][1]-line[0][1]; 
    var h_1_0 = line[1][0]-line[0][0]; 
    var c_square = Math.pow(v_1_0,2) + Math.pow(h_1_0,2); 
    var c = Math.sqrt(c_square); //计算直线上两点之间的距离
    
    var a_b_slope = 0;
    var hasSlope = true;
    if(v_1_0 == 0){
        hasSlope = false;
    }
    a_b_slope = v_1_0/h_1_0; //直线的斜率
    
    var point_pos = 1; //定义point与直线的位置关系
    //当直线的斜率大于0时，如果点在直线上方，point_pos = 1，如果点在直线下方，point_pos = 3
    //当直线的斜率小于0时，如果点在直线上方，point_pos = 2，如果点在直线下方，point_pos = 4
    if(hasSlope){
        var a_b_intercept = line[1][1]-a_b_slope*line[1][0];
        var p_intercept = point[1]-a_b_slope*point[0];
        if(a_b_slope >= 0){
            if(p_intercept > a_b_intercept){
                point_pos = 3;
            }else{
                point_pos = 1;
            }
        }else{
            if(p_intercept < a_b_intercept){
                point_pos = 2;
            }else{
                point_pos = 4;
            }
        }
    }
    //A为直线与水平线的夹角（锐角）
    var sinA = Math.abs(v_1_0)/c; //sinA
    var cosA = Math.abs(h_1_0)/c; //cosA
    //C为垂线在顺时针方向上与水平线的夹角
    var sinC = 0;
    var cosC = 0;
    //D为过point与line的平行线与水平线的夹角
    var sinD = 0;
    var cosD = 0;
    switch(point_pos){
    case 1:
        sinC = cosA;
        cosC = -sinA;
        sinD = -cosC;
        cosD = sinC;
        break;
    case 2:
        sinC = cosA;
        cosC = sinA;
        sinD = cosC;
        cosD = -sinC;
        break;
    case 3:
        sinC = -cosA;
        cosC = sinA;
        sinD = cosC;
        cosD = -sinC;
        break;
    case 4:
        sinC = -cosA;
        cosC = -sinA;
        sinD = -cosC;
        cosD = sinC;
        break;
        default:
    }
    //过point画line的平行线
    drawLine(point, [point[0]+c*cosD, point[1]+c*sinD], {color: ‘Red‘});
    drawLine(point, [point[0]+c*(-cosD), point[1]+c*(-sinD)], {color: ‘Red‘});
    
    var point_v_1 = point[1]-line[1][1];
    var point_h_1 = point[0]-line[1][0];
    var point_dist_1 = Math.sqrt(Math.pow(point_v_1,2)+Math.pow(point_h_1,2)); //point到line上一点的距离
    var point_v_0 = point[1]-line[0][1];
    var point_h_0 = point[0]-line[0][0];
    var point_dist_0 = Math.sqrt(Math.pow(point_v_0,2)+Math.pow(point_h_0,2)); //point到line上另外一点的距离
    var s = (c+point_dist_1+point_dist_0)/2;
    var area = Math.sqrt(s*(s-c)*(s-point_dist_0)*(s-point_dist_1)); //以point、line[0]和line[1]为顶点的三角形的面积
    var h = 2*area/c; //三角形的高
    
    var vpoint = [point[0]+h*cosC, point[1]+h*sinC]; //垂点
    drawLine(point, vpoint); //画垂线
}