MATLAB: Data points inside a pyramid

inside pointspyramidtriangular base

Hello all, I have a triangular base pyramid having four points (three for triangular base and one for height). how can I get the inside points of the pyramid ? Thank you .

Best Answer

We're going round in circles. Your solid (which is a tetrahedron by the way, not a pyramid) is uniquely defined by 4 four points, the ones you start with. This is the "minimum set of points which can represent" it.

As with any geometric shape, there are an infinity of "inside data point". It's of course not possible to return an infinity of points.

Or are you asking for a way to check that a given point is inside the tetrahedron?

Related Solutions

MATLAB: How to determine whether point lies within pyramid volume

Because the pyramid is regular, the algorithm is easy:

 E0 = [ 0,  0, 1];
 E1 = [ 1,  1, 0];
 E2 = [-1,  1, 0];
 E3 = [-1, -1, 0];
 E4 = [ 1, -1, 0];
 
 % Define the parameters of the pyramid:
 Pyramid.Z    = E0(3);
 Pyramid.Base = [min(E(:, 1)), max(E(:, 1)), min(E(:, 2)), max(E(:,2))]
 
 % Choose random points in the cuboid surrounding the pyramid:
 P = rand(10000, 3) .* [2, 2, 1] - [1, 1, 0];
 
 % Select points inside the pyramid:
 T = inPyramid(P, Pyramid);
 P = P(T, :);
 
 % Show the result:
 figure;
 plot3(P(:,1), P(:,2), P(:,3), '.')
 hold on
 plot3(E0(1), E0(2), E0(3), 'ro');
 plot3(E1(1), E1(2), E1(3), 'ro');
 plot3(E2(1), E2(2), E2(3), 'ro');
 plot3(E3(1), E3(2), E3(3), 'ro');
 plot3(E4(1), E4(2), E4(3), 'ro');
 xlabel('x')
 ylabel('y')
 zlabel('z')

For a point with at Z==0, you have to check, if it is inside the square. This square is shrinking linearily with the height until Z==1.

 function T = inPyramid(P, Pyramid)
 % P: 3D position as [N x 3] matrix
 % Pyramid: Struct, .Z: Height of pyramid
 %          .Base: minimum and maximum of X and Y positions at the
 %          base as [1 x 4] vector
 S = Pyramid.Base .* (Pyramid.Z - P(:, 3)) / Pyramid.Z;
 T = (P(:, 3) >= 0 & P(:, 3) <= Pyramid.Z) &     ... % Inside Z range
     (P(:, 1) >= S(:, 1) & P(:, 1) <= S(:, 2)) & ... % Inside X range
     (P(:, 2) >= S(:, 3) & P(:, 2) <= S(:, 4));      % Inside Y range
 end

This is elementary maths only.

A constructive approach instead of this rejection method:

https://www.mathworks.com/matlabcentral/answers/327990-generate-random-coordinates-inside-a-convex-polytope

MATLAB: How to call the function which contains input functions

Best approach:

Do not put input statements in functions that are going to be called repeatedly.

But if you must, then:

function [S] = pyramid(V,H)
if ~exist('V', 'var') || isempty(V)
  V = input('Enter the value of volume of square pyramid:');   
end
if ~exist('H', 'var') || isempty(H)
  H = input('Enter the value of height of square pyramid:');
end
S = sqrt(3*V/H);     
fprintf('The length of the side of square pyramid is: %f\n',S);
end

Then if you call pyramid without passing any parameters then it will prompt you for the parameters, and if you pass in parameters then it will use them.

Best Answer

Related Solutions

MATLAB: How to determine whether point lies within pyramid volume

MATLAB: How to call the function which contains input functions

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