How to draw a Plane perpendicular to a line and then generate multiple planes at regular intervals

If I have a line defined by

P1 = [1, -1, 3];

P2 = [2, 3, 4];

How can I draw a plane perpendicular to this line please. I have read the previous posts on this but I m not clear how to draw the surface. Plane can be initially at the mid point of the line.

Then I want to be able to generate multiple planes at regular intervals .

Thanks

Answer 1

[Arya Chandan Reddy]

Hi, I understand that you are trying to generate a plane perpendicular to the line joining those two points. In 3d geometry any plane is defined by the equation ax + by + cz = d , where [a b c] is the direction of plane's normal ( which is perpendicular to the plane )

Hence, direction of normal is P2 - P1. [a b c]

And the dot product of normal and the mid point gives d.

surf helps us plot the planar surface and plot3 to plot 3-d line.

Here is the code

P1 = [1, -1, 3]; 
P2 = [2, 3, 4];  
midpoint = (P1 + P2) / 2;
normal = P2 - P1;

% Create a grid of points for the plane
[X, Y] = meshgrid(-10:10, -10:10);
Z = (-normal(1) * X - normal(2) * Y + dot(normal, midpoint)) / normal(3);

% Plot the plane
figure;
hold on;
surf(X, Y, Z,'FaceAlpha', 0.5);
plot3([P1(1), P2(1)], [P1(2), P2(2)], [P1(3), P2(3)], 'r', 'LineWidth', 2);
hold off;

xlabel('X');
ylabel('Y');
zlabel('Z');
title('Plane Perpendicular to Line Joining Two Points');
grid on;
axis equal;

Refer the documentation for better understanding

Hope it helps.

[Mel A]

Thanks very much, That is what I was looking for. Based on that I was able to define multiple oter planes along the line, and working on defining intersection points of several other lines with the plane.

Thank you very much!

[Mel A]

Hi @Arya Chandan Reddy Sorry to reach out again, I was able to do my next step from this. But the the moment I change P1 and P2 values I get an error. Only change I ve done is replaced the numbers of Z equation with elements of P1 and P2. It works fine if I keep P1 and P2 same numbers, even If I change one gives me an error.

Index exceeds the number of array elements. Index must not exceed 3. Thanks

P1 = [1, -1, 3];

P2 = [2, 3, 4];

normal = P2 - P1;

midpoint = (P2+P1)/2;

[X, Y] = meshgrid(-10:10, -10:10);

Z = (-normal(P1(1,1)) * X - normal(P2(1,1)) * Y + dot(normal, midpoint)) / normal(P2(1,2));

hold on;

surf(X, Y, Z,'FaceAlpha', 0.1, 'FaceColor',"yellow");

plot3([P1(1), P2(1)], [P1(2), P2(2)], [P1(3), P2(3)], 'r', 'LineWidth', 2);

hold off;

xlabel('X');

ylabel('Y');

zlabel('Z');

title('Plane Perpendicular to Line Joining Two Points');

grid on;

axis equal;

[Dyuman Joshi]

Why are you using the elements of P1 and P2 as indices for normal array while defining Z?

[Mel A]

Thanks, yes I get the point. I ve modified it, works fine