MATLAB: How to find rotation matrix from 4 rectangle points

rotationtransformation

Hi,

I have 4 3d points(x, y, z). Using these points how can I calculate rotation angle? Consequently, I want to have a 4×4 transformation matrix including rotation and translation information.

4 points are in a plane and they are corners of rectangle and I set the top-left point as the origin of the rectangle coordinate. Look at the bellow pictures.

Here I only have four 3D points(Xw,Tw,Zw) based on the world coordinate. According to the 4 points, I can calculate 4 points based on the rectangle coordinate. For instance, value [Xr] in P2 is the distance between P1 and P2. And [-Yr] in P3 is the distance between P1 and P3.

Then how could I get rotation angle of the rectangle based on the world coordinate using those information?

Additional information (3d points in the world coordinate):

P1(-401.428, 485.929, 772.921)

P2(-21.4433, 475.611, 772.511)

P3(-400.982, 483.56, 403.703)

P4(-21.589, 473.028, 403.242)

Best Answer

Wouldn't the rotation matrix be

rotMatrix = pDistorted \ pStraight

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MATLAB: How to get rotation matrix from 3d points

All the rotation matrix are orthogonal. To find rotation matrix for each axis please refer rotx. For more information about Matrix rotation refer this link.

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You can use bwboundaries if all you want to do is draws outlines of the boundaries in the overlay above the original image:

format longg;
format compact;
clc;  % Clear command window.
workspace;  % Make sure the workspace panel is showing.
fontSize = 25;
% Read in a standard MATLAB gray scale demo image.
folder = 'C:\Users\Naresh\Documents\Temporary';
baseFileName = 'imfill.jpg';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
  % File doesn't exist -- didn't find it there.  Check the search path for it.
  fullFileName = baseFileName; % No path this time.
  if ~exist(fullFileName, 'file')
    % Still didn't find it.  Alert user.
    errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
    uiwait(warndlg(errorMessage));
    return;
  end
end
grayImage = imread(fullFileName);
% Get the dimensions of the image.  
% numberOfColorBands should be = 1.
[rows columns numberOfColorBands] = size(grayImage)
% Display the original gray scale image.

subplot(2, 2, 1);
imshow(grayImage, []);
axis square;
title('Original Grayscale Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'units','normalized','outerposition',[0 0 1 1]);
% Give a name to the title bar.
set(gcf,'name','Demo by ImageAnalyst','numbertitle','off') 
% Create a binary image.
binaryImage = grayImage < 128;
subplot(2, 2, 2);
imshow(binaryImage);
axis square;
title('Binary Image', 'FontSize', fontSize);
% bwboundaries() returns a cell array, where each cell contains the row/column coordinates for an object in the image.
% Plot the borders of all the coins on the original grayscale image using the coordinates returned by bwboundaries.
% Display the original gray scale image.
subplot(2, 2, 3);
imshow(grayImage, []);
title('Original Grayscale Image with Outlines from bwboundaries()', 'FontSize', fontSize);
axis square;
hold on;
boundaries = bwboundaries(binaryImage);
numberOfBoundaries = size(boundaries, 1);
for k = 1 : numberOfBoundaries
  thisBoundary = boundaries{k};
  plot(thisBoundary(:,2), thisBoundary(:,1), 'r-', 'LineWidth', 3);
end
hold off;

Best Answer

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MATLAB: How to get rotation matrix from 3d points

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