Having trouble translating a polygon.

So I have plane. I need to traslate this plane to a few different points, taking 10 steps to get to the next point. My problem is that my trasnformation matrix is not the same size as the plane matrix. I am wondering how I can make this work.

Any help is appreciated.

here is my code.

clear all; close all;

x0 = 2; % defining the starting point in the coordinate system

y0 = -3;

x_plane = [0,1,1.5, 2,2.5,2.5,1.5,3,4,4,0]+x0; % building plane at the starting point

y_plane = [0,1,1.0,-1,-1.,1.0,1.0,1,2,0,0]+y0;

plane = [x_plane;y_plane;ones(size(x_plane))]; % creating array of x,y positions

%h = plot_polygon(plane); % pushing vector of positions into function

axis equal; grid on; % setting axis parameters

%set(h(1),'Marker','x','MarkerEdgeColor','k') % Setting markers to show specified points

% x and y traslations

x = [linspace(0,10,10),linspace(10,10,10),linspace(10,0,10)];

y = [linspace(0,0,10),linspace(0,10,10),linspace(10,0,10)];

for i = 1:1:length(x)

T = [1,0,x(i); 0,1,y(i); 0,0,1] %trasnformation matrix

planeNEW = plane * T

plot_polygon(planeNEW); % pushing vector of positions into function

axis equal; grid on; % setting axis parameters

clf

pause(0.5)

end

Answer 1

[Zinea]

Hi Phillip Raush,

• You trying to translate a 2D plane shape to different points using a transformation matrix which is of size 3x3.
• The transformation matrix you have is a 3x3matrix, which is the correct size for affine transformation when using homogeneous coordinates.
• The plane matrix is also correctly structured to be multiplied by the transformation matrix T.

However, there are a few issues with your code:

1. You are multiplying the ‘plane’ matrix by the transformation matrix ‘T’ in the wrong order. The correct order is to multiply ‘T’ by ‘plane’ from the left, no the right.
2. You are using ‘plot_polygon(planeNEW)’ without showing the implementation of the function. I am assuming this function plots the polygon defined by the input matrix.
3. For the translation to look like an animation, you should clear the figure before the next iteration.

You can refer to the code for the loop given below:

% Animate the plane translation 
for i = 1:length(x) 
    T = [1, 0, x(i); 0, 1, y(i); 0, 0, 1]; % Transformation matrix 
    planeNEW = T * plane; % Apply the transformation 
    plot_polygon(planeNEW); % Plot the transformed plane 
    pause(0.5); 
    if i < length(x) 
        clf; % Clear the figure for the next iteration 
    end 
end