create a normal plane passing through a point P knowing the coordinates of the direction of the Normal vector to point P

HI! Is there a way to create a plane normal to a coordinate of a 'line_test' matrix (e.g. the 'P' coordinate)?

If it can be useful I have the coordinates of the direction of the Normal vector to point P ('normal_test').

line_test = importdata("line_test_1.mat");
figure
plot3(line_test(:,1),line_test(:,2),line_test(:,3),'r.','Markersize',10);
axis equal

P = line_test(10,:);
normal_test = importdata("normal_test.mat");

Answer 1

[Matt J]

a=normal(1); b=normal(2); c=normal(3);
d=dot(normal,P);

fimplicit3(@(x,y,z) a*x+b*y+z*c-d )

[Alberto Acri]

Hi @Matt J! I think the lines of code you sent me are wrong ('normal' is missing). I tried this again and it works! I changed the 'line' and 'normal' matrix.

line = importdata("line_w.mat");
normal = importdata("normal_w.mat");

row = 10;  % variabile
P = line(row,:);
plane = normal(row,:);

a=plane(1); b=plane(2); c=plane(3);

d=dot(plane,P);

figure
plot3(line(:,1),line(:,2),line(:,3),'r.','Markersize',10);
hold on
plot3(P(:,1),P(:,2),P(:,3),'b.','Markersize',15);
fimplicit3(@(x,y,z) a*x+b*y+z*c-d)
hold off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')
xlim([0 50])
ylim([-50 20])

[Alberto Acri]

Hi @Matt J! Can I ask you if it is possible to generate a plan of limited dimensions, for example a 10x10 square?