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

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philio63
philio63 2022-5-21
评论： philio63 2022-5-26
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!
  1 个评论
philio63
philio63 2022-5-21
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!

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采纳的回答

Adit Alware
Adit Alware 2022-5-26
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!
  1 个评论
philio63
philio63 2022-5-26
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.

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