3D point source distance from a plane, and representing solution as a heat map

Im trying to determine the distance from a point coordinate in 3D space, to a surface. My goal is to represent the distance as a heat map or some sort of plot, which will show the "intensity". (Eventually, I will add a few equations to simulate light decay and then repeat with multiple point sources).

So I make a plane, and I make a point source. I can find the distance between the point source and a point on the surface, using dist=norm(star-p1).

x1=[-5 5 5 -5];
y1=[0 0 0 0];
z1=[0 0 10 10];
hold on

%2D Plane
patch(x1,y1,z1,	[0.71 0.72 .73]);
xlabel('x');
ylabel('y');
zlabel('z');
axis equal

%Point Source
star1=[0,5,5]; 
plot3(star1(1),star1(2), star1(3),'*','color','r','MarkerSize',12)

%Distance to wall
p1=[3,0,5] %Make a point on the wall
dist=norm(star1-p1) %find the distance from p1 to star

%view setup
rotate3d on 
view(-200,15);

My thinking is I need to make some sort of loop, where it makes a point coordinate along the 2D plane, and then calculates the distance, and saves this in a 2D array. (this is a big programming feat for me...)

However, is there an easier way? perhaps some function I'm oblivious to?

thanks!

[philio63]

Ok, I figured out how to "calculate the distance" and then record this on a matrix. This may be a bit sloppy:

for ii = -5:5
    hold on
    for jj = 0:10  
        
    px=[ii,0,jj];  
    plot3(px(1),px(2), px(3),'o','color','b'); 
    distance(ii+6,jj+1)=norm(star1-px)
    end
end

So I make an array of the distances, row and colums 10 x 10.

1. Now i think, how to overlay this on the 2D plane in matlab
2. surely I'm not doing this correctly, or effeciently

My output for "distance":
 8.7 	 8.1 	 7.7 	 7.3 	 7.1 	 7.1 	 7.1 	 7.3 	 7.7 	 8.1 	 8.7 
 8.1 	 7.5 	 7.1 	 6.7 	 6.5 	 6.4 	 6.5 	 6.7 	 7.1 	 7.5 	 8.1 
 7.7 	 7.1 	 6.6 	 6.2 	 5.9 	 5.8 	 5.9 	 6.2 	 6.6 	 7.1 	 7.7 
 7.3 	 6.7 	 6.2 	 5.7 	 5.5 	 5.4 	 5.5 	 5.7 	 6.2 	 6.7 	 7.3 
 7.1 	 6.5 	 5.9 	 5.5 	 5.2 	 5.1 	 5.2 	 5.5 	 5.9 	 6.5 	 7.1 
 7.1 	 6.4 	 5.8 	 5.4 	 5.1 	 5.0 	 5.1 	 5.4 	 5.8 	 6.4 	 7.1 
 7.1 	 6.5 	 5.9 	 5.5 	 5.2 	 5.1 	 5.2 	 5.5 	 5.9 	 6.5 	 7.1 
 7.3 	 6.7 	 6.2 	 5.7 	 5.5 	 5.4 	 5.5 	 5.7 	 6.2 	 6.7 	 7.3 
 7.7 	 7.1 	 6.6 	 6.2 	 5.9 	 5.8 	 5.9 	 6.2 	 6.6 	 7.1 	 7.7 
 8.1 	 7.5 	 7.1 	 6.7 	 6.5 	 6.4 	 6.5 	 6.7 	 7.1 	 7.5 	 8.1 
 8.7 	 8.1 	 7.7 	 7.3 	 7.1 	 7.1 	 7.1 	 7.3 	 7.7 	 8.1 	 8.7 

Any input to put me in the write direction would be appreciated!

Answer 1

[Adit Alware]

Hi,

I understand that you want an easier way of calculating distance of a bunch of points on plane with the star point you have created.

Your method of using a for loop to calculate distance looks fine to me. However, you can perform vectorization for the same:

px = [randi([-5,5],100,1),zeros(100,1),randi([0,10],100,1)]; % will create 100 random points on the plane
plot3(px(:,1),px(:,2), px(:,3),'o','color','b') %will plot all the points on the plane
distance = sqrt(sum(((star1-px).^2),2)) % will calculate the distance of each random point on plane with star1

Here randi([-5,5],100,1) will generate 100 random integers in the range(-5,5).

Using plot3 you can plot the generated points on your 2-D plane as shown above. However in this approach, points are not in an ordered manner.

If you want to have ordered set of points through vectorization approach you may try :

px =[floor(-5:0.1:4.9)',zeros(100,1),floor(0:0.1:9.9)'];

After this you may plot the points accordingly.

For your convinience, you can reshape the output of distance in form of a 10X10 matrix by:

distance= reshape(distance,[10,10]);

Regards!

[philio63]

Hey thanks. I'll try this out.

I did get my code to work with loops, although it is inefficient, and at high resolutions could take many minutes to solve.

So I am grateful for the advice you have given.