即:
P_R1=(X_R1,Y_R1,Z_R1);
同理:
P_R2=(X_R2,Y_R2,Z_R2);
两条直线的公垂线:(public vertical vector)
DV_PVV=(DV_1) X( DV_2);
在两条直线任意选的点的方向向量:
DV_RP=(P_R1-P_R2);
任选直线的方向向量与公垂线向量的数量积:即此直线在公垂线上的投影(d=|n*AB|/|N|):
当DIS小于某个给定阈值时,求最近点。
直线1的对称性方程:
令公垂线与直线1交于点m,交线与点n;
有
直线2:
并且把m、n带入公垂线方程,有:
把用公垂线表示的点m和n,分别带入直线1和2的对称性方程,消除点m和n, 有:
直线1:
直线2:
上述两式相减:
求出t_1m,t_2n,则m和n
最近点:
#include
using namespace cv;
Point3d two_space_linear_collision_get_nearest_point(double A_0e, double B_0e, double C_0e, double D_0e, double A_0f, double B_0f, double C_0f, double D_0f,
double A_1e, double B_1e, double C_1e, double D_1e, double A_1f, double B_1f, double C_1f, double D_1f)
{
//直线0的A面的D,A,B,C
double line0_flatE_d = D_0e;
Mat line0_flatE = (Mat_(1, 3) << A_0e, B_0e, C_0e);
//直线0的B面的D,A,B,C
double line0_flatF_d = D_0f;
Mat line0_flatF = (Mat_(1, 3) << A_0f, B_0f, C_0f);
//直线1的A面的D,A,B,C
double line1_flatE_d = D_1e;
Mat line1_flatE = (Mat_(1, 3) << A_1e, B_1e, C_1e);
//直线1的B面的D,A,B,C
double line1_flatF_d = D_1f;
Mat line1_flatF = (Mat_(1, 3) << A_1f, B_1f, C_1f);
//两条直线0,1的direction vector(raws = 1, cols = 3)
Mat direction_line0 = line0_flatE.cross(line0_flatF);
Mat direction_line1 = line1_flatE.cross(line1_flatF);
//line0的randpoint
Point3d randPoint0(0.0, 0.0, 0.0);
randPoint0.z = 800;
Mat randPoint0_in = (Mat_(2, 2) << line0_flatE.at(0, 0), line0_flatE.at(0, 1),
line0_flatF.at(0, 0), line0_flatF.at(0, 1));
Mat randPoint0_out = randPoint0_in.inv()*(Mat_(2, 1) << -line0_flatE_d - randPoint0.z*line0_flatE.at(0, 2),
-line0_flatF_d - randPoint0.z*line0_flatF.at(0, 2));
randPoint0.x = randPoint0_out.at(0, 0);
randPoint0.y = randPoint0_out.at(1, 0);
//line1上randpoint
Point3d randPoint1(0.0, 0.0, 0.0);
randPoint1.z = 800;
Mat randPoint1_in = (Mat_(2, 2) << line1_flatE.at(0, 0), line1_flatE.at(0, 1),
line1_flatF.at(0, 0), line1_flatF.at(0, 1));
Mat randPoint1_out = randPoint1_in.inv()*(Mat_(2, 1) << -line1_flatE_d - randPoint1.z*line1_flatE.at(0, 2),
-line1_flatF_d - randPoint1.z*line1_flatF.at(0, 2));
randPoint1.x = randPoint1_out.at(0, 0);
randPoint1.y = randPoint1_out.at(1, 0);
//Public vertical vector(rows=1,cols=3)
Mat publicVerticalRay = direction_line0.cross(direction_line1);
//任选点的方向向量
Mat randRay = (Mat_(3, 1) << randPoint0.x - randPoint1.x, randPoint0.y - randPoint1.y, randPoint0.z - randPoint1.z);
Mat cross_rand_mult = publicVerticalRay*randRay;
//公垂线的模
double public_vertical_vector_length = sqrtf(publicVerticalRay.at(0, 0)*publicVerticalRay.at(0, 0)
+ publicVerticalRay.at(0, 1)*publicVerticalRay.at(0, 1)
+ publicVerticalRay.at(0, 2)*publicVerticalRay.at(0, 2));
//两直线的最小距离d=|公向量*任选向量|/|公向量|
double minDistance = std::abs(cross_rand_mult.at(0, 0)) / public_vertical_vector_length;
Point3d point_3d(0.0,0.0,0.0);
if (minDistance<50)
{
Mat two_line_t_in = (Mat_(3, 3) << publicVerticalRay.at(0, 0), -direction_line0.at(0, 0), direction_line1.at(0, 0),
publicVerticalRay.at(0, 1), -direction_line0.at(0, 1), direction_line1.at(0, 1),
publicVerticalRay.at(0, 2), -direction_line0.at(0, 2), direction_line1.at(0, 2));
Mat two_line_t = two_line_t_in.inv()*randRay;
Point3d node0, node1;
node0.x = two_line_t.at(1, 0)*direction_line0.at(0, 0) + randPoint0.x;
node0.y = two_line_t.at(1, 0)*direction_line0.at(0, 1) + randPoint0.y;
node0.z = two_line_t.at(1, 0)*direction_line0.at(0, 2) + randPoint0.z;
node1.x = two_line_t.at(2, 0)*direction_line1.at(0, 0) + randPoint1.x;
node1.y = two_line_t.at(2, 0)*direction_line1.at(0, 1) + randPoint1.y;
node1.z = two_line_t.at(2, 0)*direction_line1.at(0, 2) + randPoint1.z;
point_3d = (node0 + node1) / 2;
}
else
{
point_3d = Point3d(0.0,0.0,0.0);
}
return point_3d;
}
Have a good day~
注:编写比较匆忙,如有偏差请谅解,未经许可请勿转载