how to find a normal vector?

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Sierra
Sierra on 25 Jun 2022
Commented: Sierra on 25 Jun 2022
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

Accepted Answer

Matt J
Matt J on 25 Jun 2022
Edited: Matt J on 25 Jun 2022
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 Comments
Sierra
Sierra on 25 Jun 2022
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
Sierra on 25 Jun 2022
To Matt J
I thought P1 is V0, P1 in this function.

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