MATLAB: Generate some points on the plane restricted by 3 points (triangle)

MATLABplanepointstriangle

Assume that

are the vertices of a triangle in space. How can i generate some points on this triangle?

Best Answer

This is one of the way

n = 500; % number of random points
p1 = [1 1 2];
p2 = [5 7 3];
p3 = [8 2 1];
ps = [p1; p2; p3];
p12 = p2-p1;
p23 = p3-p2;
P = [p12; p23];
x = sqrt(rand(500, 1));
x = [x x.*rand(500, 1)];
P_new = x*P+p1;
ax = axes();
hold(ax);
view(3);
grid(ax);
plot3(ps(:,1), ps(:,2), ps(:,3), '+', 'MarkerSize', 10, 'LineWidth', 2)
plot3(P_new(:,1), P_new(:,2), P_new(:,3), 'r+', 'MarkerSize', 5, 'LineWidth', 1)

Related Solutions

MATLAB: How to move a point parallel to a created plane

Assuming your points are called p1, p2 and p3: One simple approach would be to define a coordinate system (non-orthonormal) with axes (p2-p1) and (p3-p1) as in-plane axes and the cross-product of these axes as third axis. You can then move the point inside this coordinate system and transfrom it in the world system for plotting and further calculations. The z-axis of this triangle-system is perpendicular to the triangle plane.

clearvars
close all
clc
p1 = [8 3 7]';
p2 = [5 9 2]';
p3 = [3 8 1]';
points = [p1 p2 p3];
% Transformation from world frame to triangle frame
% non-orthonormal transformation (normalization possible)
T = [p2-p1 p3-p1 cross(p2-p1,p3-p1) p1; 0 0 0 1];
% Move the point in the Triangle frame and transform to world frame
point_in_triangle_system = [1 1 0 1]'; % the last "1" is for homogenization
point_in_world_system = T*point_in_triangle_system;
% plot triangle and point
fill3(points(1,:),points(2,:),points(3,:),'b','FaceAlpha',0.5)
hold on
plot3(point_in_world_system(1),point_in_world_system(2),point_in_world_system(3),'kx')

If you provide your code, some more specific help is possible; Furthermore, I am pretty sure that Robotics System Toolbox contains functions for the transformation.

MATLAB: “Subscript indices must either be real positive integers or logicals.” Error with analytic function

In MATLAB, you need to put * for every multiplication. Change your statement like this.

p_new = p+((p*(1-p))*(s*(1-2*p)+t*(1-p))/(1+2*s*p*(1-p)-t*(1-p)*(1-p)));

Best Answer

Related Solutions

MATLAB: How to move a point parallel to a created plane

MATLAB: “Subscript indices must either be real positive integers or logicals.” Error with analytic function

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