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點到直線的距離直線的交點及夾角
2022-07-05 22:18:00 【alex1801】
1、點到直線的距離
P到直線AB的距離。
//P為線外一點,AB為線段兩個端點
float getDist_P2L(CvPoint pointP, CvPoint pointA, CvPoint pointB)
{
//求直線方程
int A = 0, B = 0, C = 0;
A = pointA.y - pointB.y;
B = pointB.x - pointA.x;
C = pointA.x*pointB.y - pointA.y*pointB.x;
//代入點到直線距離公式
float distance = 0;
distance = ((float)abs(A*pointP.x + B*pointP.y + C)) / ((float)sqrtf(A*A + B*B));
return distance;
}
2、直線的交點
利用點斜式錶達直線,然後求解兩條直線組成的方程組。
解得:
x0 = (b2 - b1) / (k1 - k2 + 1e-4)
y0 = k1 * x0 + b1
3、直線的夾角
已知直線 l1:y=k1x+b1,l2:y=k2x+b2,求這兩條直線的夾角。
結論:
l1 到 l2 的轉向角為 θ,則 tanθ=(k2- k1)/(1+ k1*k2)
l1 與 l2 的夾角為 θ,則 tanθ=∣(k2- k1)/(1+ k1*k2)∣
注意:兩直線的夾角指的是兩直線所成的小於90°的銳角,顯然夾角公式中的“角”並不都是兩直線的夾角。
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