检查两条线是否几乎平行会产生错误的结果 [英] Checking if two lines are nearly parallel gives wrong results

问题描述

我正在使用以下方程式查找两条线是否平行.但是当线几乎平行并且最终在远处相遇时，我遇到了问题.我想要一个方程，将这两条几乎平行的线视为平行.

I'm using the following equation to find if two lines are parallel or not. But I'm having problems when the lines are nearly parallel and finally meet in the far distance. I want an equation that considers these two nearly parallel lines as parallel.

var la = new Line {X1 = 1005, Y1 = 773, X2 = 1202, Y2 = 1198};
var lb = new Line {X1 = 1239, Y1 = 1181, X2 = 1550, Y2 = 1856};

var d = (lb.Y2 - lb.Y1) * (la.X2 - la.X1) - (lb.X2 - lb.X1) * (la.Y2 - la.Y1);
if (Math.Abs(d) < 0.001)
{
    // Return if lines are parallel
}

令我惊讶的是，上述 d 的等式得出的数字远大于0.我在这里错了吗?我使用的方程式错误吗?

To my surprise the above equation for d results in a number far greater than 0. What a I getting wrong here? Am I using the wrong equation?

我正在使用这篇文章: http://paulbourke.net/geometry/pointlineplane/

I'm using this article: http://paulbourke.net/geometry/pointlineplane/

推荐答案

难以比较坡度.具有斜率7和8的两条线比具有斜率1和2的两条线彼此更靠近，尽管斜率差始终相同.

Slopes are hard to compare. Two lines with the slopes 7 and 8 are closer to each other than two lines with the slopes 1 and 2, although the slope difference is always the same.

相反，我们应该将可以计算出的角度与点积进行比较:

Instead, we should compare the resulting angle which can be calculated with the dot product:

dx1 = la.X2 - la.X1
dy1 = la.Y2 - la.Y1
dx2 = lb.X2 - lb.X1
dy2 = lb.Y2 - lb.Y1
cosAngle = abs((dx1 * dx2 + dy1 * dy2) / sqrt((dx1 * dx1 + dy1 * dy1) * (dx2 * dx2 + dy2 * dy2)))

如果直线是完美的平行线(或反平行线)， cosAngle 将为1.它将减小两条直线之间的角度的余弦值.因此，如果两线之间的夹角为10°，则 cosAngle 将为0.9848.您可以指定一个任意阈值，在该阈值之上，线被视为平行.然后

If the lines are perfect parallel (or anti-parallel), cosAngle will be 1. It will decrease by the cosine of the angle in between both lines. So if there is an angle of 10° between the lines, cosAngle will be 0.9848. You can specify an arbitrary threshold above which lines are considered parallel. Then

if(cosAngle > threshold) //threshold = cos(threshold angle)
    // parallel or anti-parallel
else
    // not parallel 

如果要区分反并行度，请不要使用 abs .负值代表反平行性.

If you want to distinguish anti-parallelness, leave the abs away. Then negative values stand for anti-parallelity.

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