how to find a normal vector?

Question

Sierra 2022-6-25

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1747980-how-to-find-a-normal-vector

评论： Sierra 2022-6-25

采纳的回答： Matt J

在 MATLAB Online 中打开

for example, there are 2 points. P0(4,3,2) ,P1(8,5,4) and the vector ->P0P1

I know that In three dimension, there are infinite number of vectors perpendicular to a given vector.

but i know the point which is on the plane.

To use this function, I need to find a normal vector of the plane.

In my case, P1 point wil be the V0 and P1 for this function.

[I,check]=plane_line_intersect(n,V0,P0,P1)
%       n: normal vector of the Plane 
%       V0: any point that belong   s to the Plane 
%       P0: end point 1 of the segment P0P1
%       P1:  end point 2 of the segment P0P1

https://kr.mathworks.com/matlabcentral/fileexchange/17751-straight-line-and-plane-intersection

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2022-6-25

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1747980-how-to-find-a-normal-vector#answer_993280

编辑：Matt J 2022-6-25

在 MATLAB Online 中打开

In my case, P1 point wil be the V0 and P1 for this function.

You need 3 distinct, non-colinear points in a the plane to calculate its normal. If V0,P0,V1 are such points, then you would do,

normal=cross(P1-P0,V-P0)

10 个评论
显示 8更早的评论隐藏 8更早的评论

Sierra 2022-6-25

在 MATLAB Online 中打开

Thanks Matt J

as i said, i know one point which is on a plane. to do cross product i made two arbitrary point.

but when i used the function, it only returns x and y value. all z value is zero

do you have any idea to solve this problem?

Here is my code

intersection_point = [];
for i = 1:length(mean_trajectory_double)
    O = [mean_trajectory_double(i,1),mean_trajectory_double(i,2),mean_trajectory_double(i,3)];
    P = [mean_trajectory_double(i,1)+1,mean_trajectory_double(i,2)+1,mean_trajectory_double(i,3)-1000];
    Q = [mean_trajectory_double(i,1)+2,mean_trajectory_double(i,2)+2,mean_trajectory_double(i,3)+1000];
    OP = Q-O;
    OQ = P-O;
    normalvector = cross(OP,OQ);
    for j = 1:length(RKSI_Arr_33R)
        for k = 1:length(RKSI_Arr_33R(j).Latitude)-1
            [I,check]=plane_line_intersect([normalvector(1) normalvector(2) normalvector(3)]...
                ,[mean_trajectory_double(i,1) mean_trajectory_double(i,2) mean_trajectory_double(i,3)]...
                ,[RKSI_Arr_33R(j).Longitude(k) RKSI_Arr_33R(j).Latitude(k)  RKSI_Arr_33R(j).BAlt(k)]...
                ,[RKSI_Arr_33R(j).Longitude(k+1) RKSI_Arr_33R(j).Latitude(k+1)  RKSI_Arr_33R(j).BAlt(k+1)]);
        end
    end
    intersection_point = [intersection_point;I];
end

O is the point I know already and P, Q is what i made.

mean_trajectory_double(i,1) is longitude

mean_trajectory_double(i,2) is latitude

mean_trajectory_double(i,3) is altitude

I changed the P and Q's altitude several time, but it always returend zero.

and in making two arbitrary point(P,Q), if there are better way, tell me please.

Thanks.

Sierra 2022-6-25

在 MATLAB Online 中打开

Thanks Torsten, your code worked perfectly.

but I have one problem in 'z' value.

intersection_point = cell(30,3)
        lon = [];
        lat = [];
        alt = [];
for i = 1:length(mean_trajectory_double)-1
    P0 = [mean_trajectory_double(i,:)];
    P1 = [mean_trajectory_double(i+1,:)];
    normal_to_plane = (-P0 + P1);
    P2_in_plane = P1.' + in_plane(:,1);
    P3_in_plane = P1.' + in_plane(:,2);
        lon = [];
        lat = [];
        alt = [];
      
    for j = 1:100
        for k = 1:100
            [I,check]=plane_line_intersect([normal_to_plane(1) normal_to_plane(2) normal_to_plane(3)]...
                ,[mean_trajectory_double(i,1) mean_trajectory_double(i,2) mean_trajectory_double(i,3)]...
                ,[RKSI_Arr_33R(j).Longitude(k) RKSI_Arr_33R(j).Latitude(k)  RKSI_Arr_33R(j).BAlt(k)]...
                ,[RKSI_Arr_33R(j).Longitude(k+1) RKSI_Arr_33R(j).Latitude(k+1)  RKSI_Arr_33R(j).BAlt(k+1)]);
        end
                lon = [lon;I(1)];
                lat = [lat;I(2)];
                alt = [alt;I(3)];
    end
              
    intersection_point{i,1} = [lon];
    intersection_point{i,2} = [lat];
    intersection_point{i,3} = [alt];
end

there is no problem in x(lon),y(lat) value. but z(alt) value print same number.

Sierra 2022-6-25

To Matt J

I thought P1 is V0, P1 in this function.

请先登录，再进行评论。

how to find a normal vector?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

10 个评论
显示 8更早的评论隐藏 8更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

how to find a normal vector?

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

采纳的回答

10 个评论 显示 8更早的评论隐藏 8更早的评论

更多回答（0 个）

另请参阅

类别

标签

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

10 个评论
显示 8更早的评论隐藏 8更早的评论