Hello together,
stackedplot has a "vertical cursor" set as default as you can see in the picture. I even don’t know, how to name it. I couldn’t find it in the documentation.
Is there a way to control the propperties of this vertical cursor? To switch it on and off?

Thanks in advance!
Best regards.
ChristofHello together,
stackedplot has a "vertical cursor" set as default as you can see in the picture. I even don’t know, how to name it. I couldn’t find it in the documentation.
Is there a way to control the propperties of this vertical cursor? To switch it on and off?

Thanks in advance!
Best regards.
Christof Hello together,
stackedplot has a "vertical cursor" set as default as you can see in the picture. I even don’t know, how to name it. I couldn’t find it in the documentation.
Is there a way to control the propperties of this vertical cursor? To switch it on and off?

Thanks in advance!
Best regards.
Christof stackedplot, vertical cursor, properties MATLAB Answers — New Questions

​

i’m trying to import a signal like a time running signal builder block, but it doesn’t work as i’m new to this signal editor block and i tried to understand the matlab tutorial, but i can’t even import the signal as the error appears.
And the archive is a column of time from 0 to 81 seconds, and the second column of rpm that changes over time as the car goes on a track. XLSX DOCUMENT
The process is to use the rpm and link it to a lookup table, as it will have the car rpm range, and the values that will be linked with that rpm, like a heat generated from the combustion engine. As i said, i used the signal builder before and that worked as intended, but now i’m a little confused and i don’t know if the data that i’m importing is "wrong" for the purpose or is really that difficult to understand the "new" blocki’m trying to import a signal like a time running signal builder block, but it doesn’t work as i’m new to this signal editor block and i tried to understand the matlab tutorial, but i can’t even import the signal as the error appears.
And the archive is a column of time from 0 to 81 seconds, and the second column of rpm that changes over time as the car goes on a track. XLSX DOCUMENT
The process is to use the rpm and link it to a lookup table, as it will have the car rpm range, and the values that will be linked with that rpm, like a heat generated from the combustion engine. As i said, i used the signal builder before and that worked as intended, but now i’m a little confused and i don’t know if the data that i’m importing is "wrong" for the purpose or is really that difficult to understand the "new" block i’m trying to import a signal like a time running signal builder block, but it doesn’t work as i’m new to this signal editor block and i tried to understand the matlab tutorial, but i can’t even import the signal as the error appears.
And the archive is a column of time from 0 to 81 seconds, and the second column of rpm that changes over time as the car goes on a track. XLSX DOCUMENT
The process is to use the rpm and link it to a lookup table, as it will have the car rpm range, and the values that will be linked with that rpm, like a heat generated from the combustion engine. As i said, i used the signal builder before and that worked as intended, but now i’m a little confused and i don’t know if the data that i’m importing is "wrong" for the purpose or is really that difficult to understand the "new" block signal processing MATLAB Answers — New Questions

​

Error using vertcat
Dimensions of arrays being concatenated are not consistent.

Error in DNUA (line 73)
feasibleGroups = [feasibleGroups; groups_k];

>>Error using vertcat
Dimensions of arrays being concatenated are not consistent.

Error in DNUA (line 73)
feasibleGroups = [feasibleGroups; groups_k];

>> Error using vertcat
Dimensions of arrays being concatenated are not consistent.

Error in DNUA (line 73)
feasibleGroups = [feasibleGroups; groups_k];

>> cell arrays MATLAB Answers — New Questions

​

my extracted watermark image is not similar with original watermark image where there exist gray background in the extracted watermark image and the color also did not same as original.

this is my code using FWHT and SVD algorithm
% Read the watermarked image
%watermarked = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimageswatermarked_12.png’);

% Read the original host image
host = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimageshost 1.png’);
wm = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimagesw image 2.png’);

%EMBEDDING
% Resize watermark to match the host image size if necessary
wm = imresize(wm, size(host(:,:,1)));

% Extract individual color channels of the host image
h_red = host(:,:,1);
h_green = host(:,:,2);
h_blue = host(:,:,3);

% Extract individual color channels of the watermark image
wm_red = wm(:,:,1);
wm_green = wm(:,:,2);
wm_blue = wm(:,:,3);

% Apply FWHT to host image
transformed_h_red = fwht2(h_red);
transformed_h_green = fwht2(h_green);
transformed_h_blue = fwht2(h_blue);

% Apply FWHT to watermark image
transformed_wm_red = fwht2(wm_red);
transformed_wm_green = fwht2(wm_green);
transformed_wm_blue = fwht2(wm_blue);

% Apply SVD to FWHT-transformed host images
[U_h_red, S_h_red, V_h_red] = svd(transformed_h_red);
[U_h_green, S_h_green, V_h_green] = svd(transformed_h_green);
[U_h_blue, S_h_blue, V_h_blue] = svd(transformed_h_blue);

% Apply SVD to FWHT-transformed watermark images
[~, S_wm_red] = svd(transformed_wm_red);
[~, S_wm_green] = svd(transformed_wm_green);
[~, S_wm_blue] = svd(transformed_wm_blue);

% Modify the singular values of the host image by the singular values of the watermark image
alpha = 0.01; % Example scaling factor, adjust as needed
S_new_red = S_h_red + (alpha * S_wm_red);
S_new_green = S_h_green + (alpha * S_wm_green);
S_new_blue = S_h_blue + (alpha * S_wm_blue);

% Apply the inverse SVD to get the watermarked image channels
watermarked_red = U_h_red * S_new_red * V_h_red’;
watermarked_green = U_h_green * S_new_green * V_h_green’;
watermarked_blue = U_h_blue * S_new_blue * V_h_blue’;

% Apply inverse FWHT to each color channel of the watermarked image
watermarked_red = ifwht2(watermarked_red);
watermarked_green = ifwht2(watermarked_green);
watermarked_blue = ifwht2(watermarked_blue);

% Combine the RGB blocks to form the final watermarked color image
watermarked_color_image = cat(3, watermarked_red, watermarked_green, watermarked_blue);

% Scale the image data to the range [0, 1] and convert to uint8
watermarked = (255 * mat2gray(watermarked_color_image));
%watermarked = uint8(watermarked);

% Display the final watermarked color image in original size
%figure; % Open a new figure window
%imshow(watermarked, ‘InitialMagnification’, ‘fit’);
%title(‘Watermarked Image’);

% Open a dialog box to get the file path
%[filename, pathname] = uiputfile({‘*.png’;’*.jpg’;’*.bmp’;’*.tiff’}, ‘Save as’);

%if isequal(filename,0) || isequal(pathname,0)
% disp(‘User pressed cancel’)
%else
% Create the full file path
% full_filename = fullfile(pathname, filename);

% Save the watermarked color image to the chosen location
% imwrite(watermarked_color_image, full_filename);

% Display a message to indicate the image has been saved
% disp([‘Watermarked image saved as ‘, full_filename]);
%end

%END EMBED

%%
%EXTRACTION PROCESS
% Extract individual color channels of the watermarked image
%watermarked = imread(‘C:UsersUserDownloadswatermarked_12.png’);
% Read the original host image
%host = imread(‘C:UsersUserDownloadshost 1.png’);
%wm = imread(‘C:UsersUserDownloadsw image 1.png’);

%EMBEDDING
% Resize watermark to match the host image size if necessary
wm = imresize(wm, size(host(:,:,1)));

% % Extract individual color channels of the host image
% h_red = host(:,:,1);
% h_green = host(:,:,2);
% h_blue = host(:,:,3);

% Extract individual color channels of the watermark image
wm_red = wm(:,:,1);
wm_green = wm(:,:,2);
wm_blue = wm(:,:,3);

w_red = watermarked(:,:,1);
w_green = watermarked(:,:,2);
w_blue = watermarked(:,:,3);

% Extract individual color channels of the host image
h_red = host(:,:,1);
h_green = host(:,:,2);
h_blue = host(:,:,3);

% Apply FWHT to the watermarked image and the host image
transformed_w_red = fwht2(w_red);
transformed_w_green = fwht2(w_green);
transformed_w_blue = fwht2(w_blue);

transformed_wm_red = fwht2(wm_red);
transformed_wm_green = fwht2(wm_green);
transformed_wm_blue = fwht2(wm_blue);

transformed_h_red = fwht2(h_red);
transformed_h_green = fwht2(h_green);
transformed_h_blue = fwht2(h_blue);

% Apply SVD to the FWHT-transformed watermarked image
[U_w_red, S_w_red, V_w_red] = svd(transformed_w_red);
[U_w_green, S_w_green, V_w_green] = svd(transformed_w_green);
[U_w_blue, S_w_blue, V_w_blue] = svd(transformed_w_blue);

% Apply SVD to the FWHT-transformed watermarked image
[U_wm_red, S_wm_red, V_wm_red] = svd(transformed_wm_red);
[U_wm_green, S_wm_green, V_wm_green] = svd(transformed_wm_green);
[U_wm_blue, S_wm_blue, V_wm_blue] = svd(transformed_wm_blue);

% Apply SVD to the FWHT-transformed host image
[~, S_h_red, ~] = svd(transformed_h_red);
[~, S_h_green, ~] = svd(transformed_h_green);
[~, S_h_blue, ~] = svd(transformed_h_blue);

% Subtract the singular values of the host image from the singular values of the watermarked image
S_ext_red = (S_w_red – S_h_red)/alpha;
S_ext_green = (S_w_green – S_h_green)/alpha;
S_ext_blue = (S_w_blue – S_h_blue)/alpha;

% Apply the inverse SVD to acquire the extracted watermark image
extracted_red = U_wm_red * S_ext_red * V_wm_red’;
extracted_green = U_wm_green * S_ext_green * V_wm_green’;
extracted_blue = U_wm_blue * S_ext_blue * V_wm_blue’;

% Apply the inverse FWHT
extracted_red = ifwht2(extracted_red);
extracted_green = ifwht2(extracted_green);
extracted_blue = ifwht2(extracted_blue);

% Combine the RGB blocks to form the final extracted watermark image
extracted_watermark = cat(3, extracted_red, extracted_green, extracted_blue);

%%
% figure;imshow(uint8(extracted_watermark));
extracted_watermark = uint8(255 * mat2gray( (extracted_watermark)));
% extracted_watermark = uint8(extracted_watermark);
figure;imshow(extracted_watermark);

% Resize the extracted watermark image to 128 x 128
extracted_watermark = imresize(extracted_watermark, [128 128]);

% Display the host image, watermark image, watermarked image, and extracted image side by side
figure; % Open a new figure window
subplot(1, 4, 1);
imshow(host, ‘InitialMagnification’, ‘fit’);
title(‘Host Image’);

subplot(1, 4, 2);
imshow(wm, ‘InitialMagnification’, ‘fit’);
title(‘Watermark Image’);

watermarked = uint8(watermarked);
subplot(1, 4, 3);
imshow(watermarked, ‘InitialMagnification’, ‘fit’);
title(‘Watermarked Image’);

subplot(1, 4, 4);
imshow(extracted_watermark, ‘InitialMagnification’, ‘fit’);
title(‘Extracted Watermark Image’);

% Function to apply 2D FWHT
function transformed_image = fwht2(image)
% Apply the 2D FWHT
transformed_image = fwht(fwht(double(image)).’).’;
end

% Function to apply 2D inverse FWHT
function image = ifwht2(transformed_image)
% Apply the 2D inverse FWHT
image = ifwht(ifwht(double(transformed_image)).’).’;
endmy extracted watermark image is not similar with original watermark image where there exist gray background in the extracted watermark image and the color also did not same as original.

this is my code using FWHT and SVD algorithm
% Read the watermarked image
%watermarked = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimageswatermarked_12.png’);

% Read the original host image
host = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimageshost 1.png’);
wm = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimagesw image 2.png’);

%EMBEDDING
% Resize watermark to match the host image size if necessary
wm = imresize(wm, size(host(:,:,1)));

% Extract individual color channels of the host image
h_red = host(:,:,1);
h_green = host(:,:,2);
h_blue = host(:,:,3);

% Extract individual color channels of the watermark image
wm_red = wm(:,:,1);
wm_green = wm(:,:,2);
wm_blue = wm(:,:,3);

% Apply FWHT to host image
transformed_h_red = fwht2(h_red);
transformed_h_green = fwht2(h_green);
transformed_h_blue = fwht2(h_blue);

% Apply FWHT to watermark image
transformed_wm_red = fwht2(wm_red);
transformed_wm_green = fwht2(wm_green);
transformed_wm_blue = fwht2(wm_blue);

% Apply SVD to FWHT-transformed host images
[U_h_red, S_h_red, V_h_red] = svd(transformed_h_red);
[U_h_green, S_h_green, V_h_green] = svd(transformed_h_green);
[U_h_blue, S_h_blue, V_h_blue] = svd(transformed_h_blue);

% Apply SVD to FWHT-transformed watermark images
[~, S_wm_red] = svd(transformed_wm_red);
[~, S_wm_green] = svd(transformed_wm_green);
[~, S_wm_blue] = svd(transformed_wm_blue);

% Modify the singular values of the host image by the singular values of the watermark image
alpha = 0.01; % Example scaling factor, adjust as needed
S_new_red = S_h_red + (alpha * S_wm_red);
S_new_green = S_h_green + (alpha * S_wm_green);
S_new_blue = S_h_blue + (alpha * S_wm_blue);

% Apply the inverse SVD to get the watermarked image channels
watermarked_red = U_h_red * S_new_red * V_h_red’;
watermarked_green = U_h_green * S_new_green * V_h_green’;
watermarked_blue = U_h_blue * S_new_blue * V_h_blue’;

% Apply inverse FWHT to each color channel of the watermarked image
watermarked_red = ifwht2(watermarked_red);
watermarked_green = ifwht2(watermarked_green);
watermarked_blue = ifwht2(watermarked_blue);

% Combine the RGB blocks to form the final watermarked color image
watermarked_color_image = cat(3, watermarked_red, watermarked_green, watermarked_blue);

% Scale the image data to the range [0, 1] and convert to uint8
watermarked = (255 * mat2gray(watermarked_color_image));
%watermarked = uint8(watermarked);

% Display the final watermarked color image in original size
%figure; % Open a new figure window
%imshow(watermarked, ‘InitialMagnification’, ‘fit’);
%title(‘Watermarked Image’);

% Open a dialog box to get the file path
%[filename, pathname] = uiputfile({‘*.png’;’*.jpg’;’*.bmp’;’*.tiff’}, ‘Save as’);

%if isequal(filename,0) || isequal(pathname,0)
% disp(‘User pressed cancel’)
%else
% Create the full file path
% full_filename = fullfile(pathname, filename);

% Save the watermarked color image to the chosen location
% imwrite(watermarked_color_image, full_filename);

% Display a message to indicate the image has been saved
% disp([‘Watermarked image saved as ‘, full_filename]);
%end

%END EMBED

%%
%EXTRACTION PROCESS
% Extract individual color channels of the watermarked image
%watermarked = imread(‘C:UsersUserDownloadswatermarked_12.png’);
% Read the original host image
%host = imread(‘C:UsersUserDownloadshost 1.png’);
%wm = imread(‘C:UsersUserDownloadsw image 1.png’);

%EMBEDDING
% Resize watermark to match the host image size if necessary
wm = imresize(wm, size(host(:,:,1)));

% % Extract individual color channels of the host image
% h_red = host(:,:,1);
% h_green = host(:,:,2);
% h_blue = host(:,:,3);

% Extract individual color channels of the watermark image
wm_red = wm(:,:,1);
wm_green = wm(:,:,2);
wm_blue = wm(:,:,3);

w_red = watermarked(:,:,1);
w_green = watermarked(:,:,2);
w_blue = watermarked(:,:,3);

% Extract individual color channels of the host image
h_red = host(:,:,1);
h_green = host(:,:,2);
h_blue = host(:,:,3);

% Apply FWHT to the watermarked image and the host image
transformed_w_red = fwht2(w_red);
transformed_w_green = fwht2(w_green);
transformed_w_blue = fwht2(w_blue);

transformed_wm_red = fwht2(wm_red);
transformed_wm_green = fwht2(wm_green);
transformed_wm_blue = fwht2(wm_blue);

transformed_h_red = fwht2(h_red);
transformed_h_green = fwht2(h_green);
transformed_h_blue = fwht2(h_blue);

% Apply SVD to the FWHT-transformed watermarked image
[U_w_red, S_w_red, V_w_red] = svd(transformed_w_red);
[U_w_green, S_w_green, V_w_green] = svd(transformed_w_green);
[U_w_blue, S_w_blue, V_w_blue] = svd(transformed_w_blue);

% Apply SVD to the FWHT-transformed watermarked image
[U_wm_red, S_wm_red, V_wm_red] = svd(transformed_wm_red);
[U_wm_green, S_wm_green, V_wm_green] = svd(transformed_wm_green);
[U_wm_blue, S_wm_blue, V_wm_blue] = svd(transformed_wm_blue);

% Apply SVD to the FWHT-transformed host image
[~, S_h_red, ~] = svd(transformed_h_red);
[~, S_h_green, ~] = svd(transformed_h_green);
[~, S_h_blue, ~] = svd(transformed_h_blue);

% Subtract the singular values of the host image from the singular values of the watermarked image
S_ext_red = (S_w_red – S_h_red)/alpha;
S_ext_green = (S_w_green – S_h_green)/alpha;
S_ext_blue = (S_w_blue – S_h_blue)/alpha;

% Apply the inverse SVD to acquire the extracted watermark image
extracted_red = U_wm_red * S_ext_red * V_wm_red’;
extracted_green = U_wm_green * S_ext_green * V_wm_green’;
extracted_blue = U_wm_blue * S_ext_blue * V_wm_blue’;

% Apply the inverse FWHT
extracted_red = ifwht2(extracted_red);
extracted_green = ifwht2(extracted_green);
extracted_blue = ifwht2(extracted_blue);

% Combine the RGB blocks to form the final extracted watermark image
extracted_watermark = cat(3, extracted_red, extracted_green, extracted_blue);

%%
% figure;imshow(uint8(extracted_watermark));
extracted_watermark = uint8(255 * mat2gray( (extracted_watermark)));
% extracted_watermark = uint8(extracted_watermark);
figure;imshow(extracted_watermark);

% Resize the extracted watermark image to 128 x 128
extracted_watermark = imresize(extracted_watermark, [128 128]);

% Display the host image, watermark image, watermarked image, and extracted image side by side
figure; % Open a new figure window
subplot(1, 4, 1);
imshow(host, ‘InitialMagnification’, ‘fit’);
title(‘Host Image’);

subplot(1, 4, 2);
imshow(wm, ‘InitialMagnification’, ‘fit’);
title(‘Watermark Image’);

watermarked = uint8(watermarked);
subplot(1, 4, 3);
imshow(watermarked, ‘InitialMagnification’, ‘fit’);
title(‘Watermarked Image’);

subplot(1, 4, 4);
imshow(extracted_watermark, ‘InitialMagnification’, ‘fit’);
title(‘Extracted Watermark Image’);

% Function to apply 2D FWHT
function transformed_image = fwht2(image)
% Apply the 2D FWHT
transformed_image = fwht(fwht(double(image)).’).’;
end

% Function to apply 2D inverse FWHT
function image = ifwht2(transformed_image)
% Apply the 2D inverse FWHT
image = ifwht(ifwht(double(transformed_image)).’).’;
end my extracted watermark image is not similar with original watermark image where there exist gray background in the extracted watermark image and the color also did not same as original.

this is my code using FWHT and SVD algorithm
% Read the watermarked image
%watermarked = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimageswatermarked_12.png’);

% Read the original host image
host = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimageshost 1.png’);
wm = imread(‘C:Userswindow10DocumentsJAMILAHKELAS CS249FYPWatermarkingimagesw image 2.png’);

%EMBEDDING
% Resize watermark to match the host image size if necessary
wm = imresize(wm, size(host(:,:,1)));

% Extract individual color channels of the host image
h_red = host(:,:,1);
h_green = host(:,:,2);
h_blue = host(:,:,3);

% Extract individual color channels of the watermark image
wm_red = wm(:,:,1);
wm_green = wm(:,:,2);
wm_blue = wm(:,:,3);

% Apply FWHT to host image
transformed_h_red = fwht2(h_red);
transformed_h_green = fwht2(h_green);
transformed_h_blue = fwht2(h_blue);

% Apply FWHT to watermark image
transformed_wm_red = fwht2(wm_red);
transformed_wm_green = fwht2(wm_green);
transformed_wm_blue = fwht2(wm_blue);

% Apply SVD to FWHT-transformed host images
[U_h_red, S_h_red, V_h_red] = svd(transformed_h_red);
[U_h_green, S_h_green, V_h_green] = svd(transformed_h_green);
[U_h_blue, S_h_blue, V_h_blue] = svd(transformed_h_blue);

% Apply SVD to FWHT-transformed watermark images
[~, S_wm_red] = svd(transformed_wm_red);
[~, S_wm_green] = svd(transformed_wm_green);
[~, S_wm_blue] = svd(transformed_wm_blue);

% Modify the singular values of the host image by the singular values of the watermark image
alpha = 0.01; % Example scaling factor, adjust as needed
S_new_red = S_h_red + (alpha * S_wm_red);
S_new_green = S_h_green + (alpha * S_wm_green);
S_new_blue = S_h_blue + (alpha * S_wm_blue);

% Apply the inverse SVD to get the watermarked image channels
watermarked_red = U_h_red * S_new_red * V_h_red’;
watermarked_green = U_h_green * S_new_green * V_h_green’;
watermarked_blue = U_h_blue * S_new_blue * V_h_blue’;

% Apply inverse FWHT to each color channel of the watermarked image
watermarked_red = ifwht2(watermarked_red);
watermarked_green = ifwht2(watermarked_green);
watermarked_blue = ifwht2(watermarked_blue);

% Combine the RGB blocks to form the final watermarked color image
watermarked_color_image = cat(3, watermarked_red, watermarked_green, watermarked_blue);

% Scale the image data to the range [0, 1] and convert to uint8
watermarked = (255 * mat2gray(watermarked_color_image));
%watermarked = uint8(watermarked);

% Display the final watermarked color image in original size
%figure; % Open a new figure window
%imshow(watermarked, ‘InitialMagnification’, ‘fit’);
%title(‘Watermarked Image’);

% Open a dialog box to get the file path
%[filename, pathname] = uiputfile({‘*.png’;’*.jpg’;’*.bmp’;’*.tiff’}, ‘Save as’);

%if isequal(filename,0) || isequal(pathname,0)
% disp(‘User pressed cancel’)
%else
% Create the full file path
% full_filename = fullfile(pathname, filename);

% Save the watermarked color image to the chosen location
% imwrite(watermarked_color_image, full_filename);

% Display a message to indicate the image has been saved
% disp([‘Watermarked image saved as ‘, full_filename]);
%end

%END EMBED

%%
%EXTRACTION PROCESS
% Extract individual color channels of the watermarked image
%watermarked = imread(‘C:UsersUserDownloadswatermarked_12.png’);
% Read the original host image
%host = imread(‘C:UsersUserDownloadshost 1.png’);
%wm = imread(‘C:UsersUserDownloadsw image 1.png’);

%EMBEDDING
% Resize watermark to match the host image size if necessary
wm = imresize(wm, size(host(:,:,1)));

% % Extract individual color channels of the host image
% h_red = host(:,:,1);
% h_green = host(:,:,2);
% h_blue = host(:,:,3);

% Extract individual color channels of the watermark image
wm_red = wm(:,:,1);
wm_green = wm(:,:,2);
wm_blue = wm(:,:,3);

w_red = watermarked(:,:,1);
w_green = watermarked(:,:,2);
w_blue = watermarked(:,:,3);

% Extract individual color channels of the host image
h_red = host(:,:,1);
h_green = host(:,:,2);
h_blue = host(:,:,3);

% Apply FWHT to the watermarked image and the host image
transformed_w_red = fwht2(w_red);
transformed_w_green = fwht2(w_green);
transformed_w_blue = fwht2(w_blue);

transformed_wm_red = fwht2(wm_red);
transformed_wm_green = fwht2(wm_green);
transformed_wm_blue = fwht2(wm_blue);

transformed_h_red = fwht2(h_red);
transformed_h_green = fwht2(h_green);
transformed_h_blue = fwht2(h_blue);

% Apply SVD to the FWHT-transformed watermarked image
[U_w_red, S_w_red, V_w_red] = svd(transformed_w_red);
[U_w_green, S_w_green, V_w_green] = svd(transformed_w_green);
[U_w_blue, S_w_blue, V_w_blue] = svd(transformed_w_blue);

% Apply SVD to the FWHT-transformed watermarked image
[U_wm_red, S_wm_red, V_wm_red] = svd(transformed_wm_red);
[U_wm_green, S_wm_green, V_wm_green] = svd(transformed_wm_green);
[U_wm_blue, S_wm_blue, V_wm_blue] = svd(transformed_wm_blue);

% Apply SVD to the FWHT-transformed host image
[~, S_h_red, ~] = svd(transformed_h_red);
[~, S_h_green, ~] = svd(transformed_h_green);
[~, S_h_blue, ~] = svd(transformed_h_blue);

% Subtract the singular values of the host image from the singular values of the watermarked image
S_ext_red = (S_w_red – S_h_red)/alpha;
S_ext_green = (S_w_green – S_h_green)/alpha;
S_ext_blue = (S_w_blue – S_h_blue)/alpha;

% Apply the inverse SVD to acquire the extracted watermark image
extracted_red = U_wm_red * S_ext_red * V_wm_red’;
extracted_green = U_wm_green * S_ext_green * V_wm_green’;
extracted_blue = U_wm_blue * S_ext_blue * V_wm_blue’;

% Apply the inverse FWHT
extracted_red = ifwht2(extracted_red);
extracted_green = ifwht2(extracted_green);
extracted_blue = ifwht2(extracted_blue);

% Combine the RGB blocks to form the final extracted watermark image
extracted_watermark = cat(3, extracted_red, extracted_green, extracted_blue);

%%
% figure;imshow(uint8(extracted_watermark));
extracted_watermark = uint8(255 * mat2gray( (extracted_watermark)));
% extracted_watermark = uint8(extracted_watermark);
figure;imshow(extracted_watermark);

% Resize the extracted watermark image to 128 x 128
extracted_watermark = imresize(extracted_watermark, [128 128]);

% Display the host image, watermark image, watermarked image, and extracted image side by side
figure; % Open a new figure window
subplot(1, 4, 1);
imshow(host, ‘InitialMagnification’, ‘fit’);
title(‘Host Image’);

subplot(1, 4, 2);
imshow(wm, ‘InitialMagnification’, ‘fit’);
title(‘Watermark Image’);

watermarked = uint8(watermarked);
subplot(1, 4, 3);
imshow(watermarked, ‘InitialMagnification’, ‘fit’);
title(‘Watermarked Image’);

subplot(1, 4, 4);
imshow(extracted_watermark, ‘InitialMagnification’, ‘fit’);
title(‘Extracted Watermark Image’);

% Function to apply 2D FWHT
function transformed_image = fwht2(image)
% Apply the 2D FWHT
transformed_image = fwht(fwht(double(image)).’).’;
end

% Function to apply 2D inverse FWHT
function image = ifwht2(transformed_image)
% Apply the 2D inverse FWHT
image = ifwht(ifwht(double(transformed_image)).’).’;
end #imagewatermarking, #imageprocessing, #mathematics, #fwht, #svd MATLAB Answers — New Questions

​

This is the code to perform LOAM for the self driving car moving around the parking lot, now how to add kalman filter in this code given below:
% Load reference path % 60 vehicles are parked
data = load("parkingLotReferenceData.mat");

% Set reference trajectory of the ego vehicle
refPosesX = data.refPosesX;
refPosesY = data.refPosesY;
refPosesT = data.refPosesT;

% Set poses of the parked vehicles
parkedPoses = data.parkedPoses;

% Display the reference trajectory and the parked vehicle locations
sceneName = "LargeParkingLot";
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2,DisplayName="Reference Path");
scatter(parkedPoses(:,1),parkedPoses(:,2),[],"filled",DisplayName="Parked Vehicles");
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500]; % Resize figure
title("Large Parking Lot")
legend

modelName = ‘GenerateLidarDataOfParkingLot’;
open_system(modelName)
snapnow
helperAddParkedVehicles(modelName,parkedPoses)

close(hScene)

if ~ispc
error("Unreal Engine Simulation is supported only on Microsoft" + char(174) + " Windows" + char(174) + ".");
end

% Run simulation
simOut = sim(modelName);

close_system(modelName,0)

ptCloudArr = helperGetPointClouds(simOut);
groundTruthPosesLidar = helperGetLidarGroundTruth(simOut);

ptCloud = ptCloudArr(1);
nextPtCloud = ptCloudArr(2);
gridStep = 0.5;
tform = pcregisterloam(ptCloud,nextPtCloud,gridStep);
disp(tform)

egoRadius = 3.5;
cylinderRadius = 50;
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");
selectedIdx = findPointsInCylinder(nextPtCloud,[egoRadius cylinderRadius]);
nextPtCloud = select(nextPtCloud,selectedIdx,OutputSize="full");

figure
hold on
title("Cylindrical Neighborhood")
pcshow(ptCloud)
view(2)

maxPlanarSurfacePoints = 8;
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
nextPoints = detectLOAMFeatures(nextPtCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);

figure
hold on
title("LOAM Points")
show(points,MarkerSize=12)

[~,rmseValue] = pcregisterloam(points,nextPoints);
disp([‘RMSE: ‘ num2str(rmseValue)])

points = downsampleLessPlanar(points,gridStep);

figure
hold on
title(‘LOAM Points After Downsampling the Less Planar Surface Points’)
show(points,’MarkerSize’,12)

absPose = groundTruthPosesLidar(1);
relPose = rigidtform3d;
vSetOdometry = pcviewset;

viewId = 1;
vSetOdometry = addView(vSetOdometry,viewId,absPose);

% Display the parking lot scene with the reference trajectory
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2)
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500];

numSkip = 5;
for k = (numSkip+1):numSkip:numel(ptCloudArr)
prevPoints = points;
viewId = viewId + 1;
ptCloud = ptCloudArr(k);

% Select a cylindrical neighborhood of interest.
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");

% Detect LOAM points and downsample the less planar surface points
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

% Register the points using the previous relative pose as an initial
% transformation
relPose = pcregisterloam(points,prevPoints,InitialTransform=relPose);

% Update the absolute pose and store it in the view set
absPose = rigidtform3d(absPose.A * relPose.A);
vSetOdometry = addView(vSetOdometry,viewId,absPose);

% Visualize the absolute pose in the parking lot scene
plot(absPose.Translation(1),absPose.Translation(2),Color="r",Marker=".",MarkerSize=8);
xlim([-60 40])
ylim([10 60])
title("Build a Map Using Lidar Odometry")
legend(["Ground Truth","Estimated Position"])
pause(0.001)
view(2)
end

absPose = groundTruthPosesLidar(1);
relPose = rigidtform3d;
vSetMapping = pcviewset;

ptCloud = ptCloudArr(1);
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");
points = detectLOAMFeatures(ptCloud,’MaxPlanarSurfacePoints’,maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

viewId = 1;
vSetMapping = addView(vSetMapping,viewId,absPose);

voxelSize = 0.1;
loamMap = pcmaploam(voxelSize);
addPoints(loamMap,points,absPose);

% Display the parking lot scene with the reference trajectory
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2)
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500];

for k = (numSkip+1):numSkip:numel(ptCloudArr)
prevPtCloud = ptCloud;
prevPoints = points;
viewId = viewId + 1;
ptCloud = ptCloudArr(k);

% Select a cylindrical neighborhood of interest.
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");

% Detect LOAM points and downsample the less planar surface points
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

% Register the points using the previous relative pose as an initial
% transformation
relPose = pcregisterloam(points,prevPoints,MatchingMethod="one-to-one",InitialTransform=relPose);

% Find the refined absolute pose that aligns the points to the map
absPose = findPose(loamMap,points,relPose);

% Store the refined absolute pose in the view set
vSetMapping = addView(vSetMapping,viewId,absPose);

% Add the new points to the map
addPoints(loamMap,points,absPose);

% Visualize the absolute pose in the parking lot scene
plot(absPose.Translation(1),absPose.Translation(2),Color="r",Marker=".",MarkerSize=8)
xlim([-60 40])
ylim([10 60])
title("Build a Map Using Lidar Mapping")
legend(["Ground Truth","Estimated Position"])
pause(0.001)
view(2)
end

% Get the ground truth trajectory
groundTruthTrajectory = vertcat(groundTruthPosesLidar.Translation);

% Get the estimated trajectories
odometryPositions = vertcat(vSetOdometry.Views.AbsolutePose.Translation);
mappingPositions = vertcat(vSetMapping.Views.AbsolutePose.Translation);

% Plot the trajectories
figure
plot3(groundTruthTrajectory(:,1),groundTruthTrajectory(:,2),groundTruthTrajectory(:,3),LineWidth=2,DisplayName="Ground Truth")
hold on
plot3(odometryPositions(:,1),odometryPositions(:,2),odometryPositions(:,3),LineWidth=2,DisplayName="Odometry")
plot3(mappingPositions(:,1),mappingPositions(:,2),mappingPositions(:,3),LineWidth=2,DisplayName="Odometry and Mapping")
view(2)

legend
title("Compare Trajectories")

% Select the poses to compare
selectedGroundTruth = groundTruthTrajectory(1:numSkip:end,:);

% Compute the RMSE
rmseOdometry = rmse(selectedGroundTruth,odometryPositions,"all");
rmseWithMapping = rmse(selectedGroundTruth,mappingPositions,"all");
disp([‘RMSE of the trajectory estimated with Odometry: ‘ num2str(rmseOdometry)])

disp([‘RMSE of the trajectory estimated with Odometry and Mapping: ‘ num2str(rmseWithMapping)])

function ptCloudArr = helperGetPointClouds(simOut)

% Extract signal
ptCloudData = simOut.ptCloudData.signals.values;

% Create a pointCloud array
ptCloudArr = pointCloud(ptCloudData(:,:,:,2)); % Ignore first frame
for n = 1:size(ptCloudData,4)
ptCloudArr(end+1) = pointCloud(ptCloudData(:,:,:,n)); %#ok<AGROW>
end

end
function gTruth = helperGetLidarGroundTruth(simOut)

numFrames = size(simOut.lidarLocation.time,1);
gTruth = repmat(rigidtform3d,numFrames-1,1);

for i = 1:numFrames
gTruth(i).Translation = squeeze(simOut.lidarLocation.signals.values(:,:,i));
% Ignore the roll and the pitch rotations since the ground is flat
yaw = double(simOut.lidarOrientation.signals.values(:,3,i));
gTruth(i).R = [cos(yaw) -sin(yaw) 0;
sin(yaw) cos(yaw) 0;
0 0 1];
end
endThis is the code to perform LOAM for the self driving car moving around the parking lot, now how to add kalman filter in this code given below:
% Load reference path % 60 vehicles are parked
data = load("parkingLotReferenceData.mat");

% Set reference trajectory of the ego vehicle
refPosesX = data.refPosesX;
refPosesY = data.refPosesY;
refPosesT = data.refPosesT;

% Set poses of the parked vehicles
parkedPoses = data.parkedPoses;

% Display the reference trajectory and the parked vehicle locations
sceneName = "LargeParkingLot";
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2,DisplayName="Reference Path");
scatter(parkedPoses(:,1),parkedPoses(:,2),[],"filled",DisplayName="Parked Vehicles");
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500]; % Resize figure
title("Large Parking Lot")
legend

modelName = ‘GenerateLidarDataOfParkingLot’;
open_system(modelName)
snapnow
helperAddParkedVehicles(modelName,parkedPoses)

close(hScene)

if ~ispc
error("Unreal Engine Simulation is supported only on Microsoft" + char(174) + " Windows" + char(174) + ".");
end

% Run simulation
simOut = sim(modelName);

close_system(modelName,0)

ptCloudArr = helperGetPointClouds(simOut);
groundTruthPosesLidar = helperGetLidarGroundTruth(simOut);

ptCloud = ptCloudArr(1);
nextPtCloud = ptCloudArr(2);
gridStep = 0.5;
tform = pcregisterloam(ptCloud,nextPtCloud,gridStep);
disp(tform)

egoRadius = 3.5;
cylinderRadius = 50;
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");
selectedIdx = findPointsInCylinder(nextPtCloud,[egoRadius cylinderRadius]);
nextPtCloud = select(nextPtCloud,selectedIdx,OutputSize="full");

figure
hold on
title("Cylindrical Neighborhood")
pcshow(ptCloud)
view(2)

maxPlanarSurfacePoints = 8;
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
nextPoints = detectLOAMFeatures(nextPtCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);

figure
hold on
title("LOAM Points")
show(points,MarkerSize=12)

[~,rmseValue] = pcregisterloam(points,nextPoints);
disp([‘RMSE: ‘ num2str(rmseValue)])

points = downsampleLessPlanar(points,gridStep);

figure
hold on
title(‘LOAM Points After Downsampling the Less Planar Surface Points’)
show(points,’MarkerSize’,12)

absPose = groundTruthPosesLidar(1);
relPose = rigidtform3d;
vSetOdometry = pcviewset;

viewId = 1;
vSetOdometry = addView(vSetOdometry,viewId,absPose);

% Display the parking lot scene with the reference trajectory
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2)
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500];

numSkip = 5;
for k = (numSkip+1):numSkip:numel(ptCloudArr)
prevPoints = points;
viewId = viewId + 1;
ptCloud = ptCloudArr(k);

% Select a cylindrical neighborhood of interest.
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");

% Detect LOAM points and downsample the less planar surface points
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

% Register the points using the previous relative pose as an initial
% transformation
relPose = pcregisterloam(points,prevPoints,InitialTransform=relPose);

% Update the absolute pose and store it in the view set
absPose = rigidtform3d(absPose.A * relPose.A);
vSetOdometry = addView(vSetOdometry,viewId,absPose);

% Visualize the absolute pose in the parking lot scene
plot(absPose.Translation(1),absPose.Translation(2),Color="r",Marker=".",MarkerSize=8);
xlim([-60 40])
ylim([10 60])
title("Build a Map Using Lidar Odometry")
legend(["Ground Truth","Estimated Position"])
pause(0.001)
view(2)
end

absPose = groundTruthPosesLidar(1);
relPose = rigidtform3d;
vSetMapping = pcviewset;

ptCloud = ptCloudArr(1);
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");
points = detectLOAMFeatures(ptCloud,’MaxPlanarSurfacePoints’,maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

viewId = 1;
vSetMapping = addView(vSetMapping,viewId,absPose);

voxelSize = 0.1;
loamMap = pcmaploam(voxelSize);
addPoints(loamMap,points,absPose);

% Display the parking lot scene with the reference trajectory
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2)
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500];

for k = (numSkip+1):numSkip:numel(ptCloudArr)
prevPtCloud = ptCloud;
prevPoints = points;
viewId = viewId + 1;
ptCloud = ptCloudArr(k);

% Select a cylindrical neighborhood of interest.
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");

% Detect LOAM points and downsample the less planar surface points
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

% Register the points using the previous relative pose as an initial
% transformation
relPose = pcregisterloam(points,prevPoints,MatchingMethod="one-to-one",InitialTransform=relPose);

% Find the refined absolute pose that aligns the points to the map
absPose = findPose(loamMap,points,relPose);

% Store the refined absolute pose in the view set
vSetMapping = addView(vSetMapping,viewId,absPose);

% Add the new points to the map
addPoints(loamMap,points,absPose);

% Visualize the absolute pose in the parking lot scene
plot(absPose.Translation(1),absPose.Translation(2),Color="r",Marker=".",MarkerSize=8)
xlim([-60 40])
ylim([10 60])
title("Build a Map Using Lidar Mapping")
legend(["Ground Truth","Estimated Position"])
pause(0.001)
view(2)
end

% Get the ground truth trajectory
groundTruthTrajectory = vertcat(groundTruthPosesLidar.Translation);

% Get the estimated trajectories
odometryPositions = vertcat(vSetOdometry.Views.AbsolutePose.Translation);
mappingPositions = vertcat(vSetMapping.Views.AbsolutePose.Translation);

% Plot the trajectories
figure
plot3(groundTruthTrajectory(:,1),groundTruthTrajectory(:,2),groundTruthTrajectory(:,3),LineWidth=2,DisplayName="Ground Truth")
hold on
plot3(odometryPositions(:,1),odometryPositions(:,2),odometryPositions(:,3),LineWidth=2,DisplayName="Odometry")
plot3(mappingPositions(:,1),mappingPositions(:,2),mappingPositions(:,3),LineWidth=2,DisplayName="Odometry and Mapping")
view(2)

legend
title("Compare Trajectories")

% Select the poses to compare
selectedGroundTruth = groundTruthTrajectory(1:numSkip:end,:);

% Compute the RMSE
rmseOdometry = rmse(selectedGroundTruth,odometryPositions,"all");
rmseWithMapping = rmse(selectedGroundTruth,mappingPositions,"all");
disp([‘RMSE of the trajectory estimated with Odometry: ‘ num2str(rmseOdometry)])

disp([‘RMSE of the trajectory estimated with Odometry and Mapping: ‘ num2str(rmseWithMapping)])

function ptCloudArr = helperGetPointClouds(simOut)

% Extract signal
ptCloudData = simOut.ptCloudData.signals.values;

% Create a pointCloud array
ptCloudArr = pointCloud(ptCloudData(:,:,:,2)); % Ignore first frame
for n = 1:size(ptCloudData,4)
ptCloudArr(end+1) = pointCloud(ptCloudData(:,:,:,n)); %#ok<AGROW>
end

end
function gTruth = helperGetLidarGroundTruth(simOut)

numFrames = size(simOut.lidarLocation.time,1);
gTruth = repmat(rigidtform3d,numFrames-1,1);

for i = 1:numFrames
gTruth(i).Translation = squeeze(simOut.lidarLocation.signals.values(:,:,i));
% Ignore the roll and the pitch rotations since the ground is flat
yaw = double(simOut.lidarOrientation.signals.values(:,3,i));
gTruth(i).R = [cos(yaw) -sin(yaw) 0;
sin(yaw) cos(yaw) 0;
0 0 1];
end
end This is the code to perform LOAM for the self driving car moving around the parking lot, now how to add kalman filter in this code given below:
% Load reference path % 60 vehicles are parked
data = load("parkingLotReferenceData.mat");

% Set reference trajectory of the ego vehicle
refPosesX = data.refPosesX;
refPosesY = data.refPosesY;
refPosesT = data.refPosesT;

% Set poses of the parked vehicles
parkedPoses = data.parkedPoses;

% Display the reference trajectory and the parked vehicle locations
sceneName = "LargeParkingLot";
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2,DisplayName="Reference Path");
scatter(parkedPoses(:,1),parkedPoses(:,2),[],"filled",DisplayName="Parked Vehicles");
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500]; % Resize figure
title("Large Parking Lot")
legend

modelName = ‘GenerateLidarDataOfParkingLot’;
open_system(modelName)
snapnow
helperAddParkedVehicles(modelName,parkedPoses)

close(hScene)

if ~ispc
error("Unreal Engine Simulation is supported only on Microsoft" + char(174) + " Windows" + char(174) + ".");
end

% Run simulation
simOut = sim(modelName);

close_system(modelName,0)

ptCloudArr = helperGetPointClouds(simOut);
groundTruthPosesLidar = helperGetLidarGroundTruth(simOut);

ptCloud = ptCloudArr(1);
nextPtCloud = ptCloudArr(2);
gridStep = 0.5;
tform = pcregisterloam(ptCloud,nextPtCloud,gridStep);
disp(tform)

egoRadius = 3.5;
cylinderRadius = 50;
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");
selectedIdx = findPointsInCylinder(nextPtCloud,[egoRadius cylinderRadius]);
nextPtCloud = select(nextPtCloud,selectedIdx,OutputSize="full");

figure
hold on
title("Cylindrical Neighborhood")
pcshow(ptCloud)
view(2)

maxPlanarSurfacePoints = 8;
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
nextPoints = detectLOAMFeatures(nextPtCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);

figure
hold on
title("LOAM Points")
show(points,MarkerSize=12)

[~,rmseValue] = pcregisterloam(points,nextPoints);
disp([‘RMSE: ‘ num2str(rmseValue)])

points = downsampleLessPlanar(points,gridStep);

figure
hold on
title(‘LOAM Points After Downsampling the Less Planar Surface Points’)
show(points,’MarkerSize’,12)

absPose = groundTruthPosesLidar(1);
relPose = rigidtform3d;
vSetOdometry = pcviewset;

viewId = 1;
vSetOdometry = addView(vSetOdometry,viewId,absPose);

% Display the parking lot scene with the reference trajectory
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2)
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500];

numSkip = 5;
for k = (numSkip+1):numSkip:numel(ptCloudArr)
prevPoints = points;
viewId = viewId + 1;
ptCloud = ptCloudArr(k);

% Select a cylindrical neighborhood of interest.
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");

% Detect LOAM points and downsample the less planar surface points
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

% Register the points using the previous relative pose as an initial
% transformation
relPose = pcregisterloam(points,prevPoints,InitialTransform=relPose);

% Update the absolute pose and store it in the view set
absPose = rigidtform3d(absPose.A * relPose.A);
vSetOdometry = addView(vSetOdometry,viewId,absPose);

% Visualize the absolute pose in the parking lot scene
plot(absPose.Translation(1),absPose.Translation(2),Color="r",Marker=".",MarkerSize=8);
xlim([-60 40])
ylim([10 60])
title("Build a Map Using Lidar Odometry")
legend(["Ground Truth","Estimated Position"])
pause(0.001)
view(2)
end

absPose = groundTruthPosesLidar(1);
relPose = rigidtform3d;
vSetMapping = pcviewset;

ptCloud = ptCloudArr(1);
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");
points = detectLOAMFeatures(ptCloud,’MaxPlanarSurfacePoints’,maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

viewId = 1;
vSetMapping = addView(vSetMapping,viewId,absPose);

voxelSize = 0.1;
loamMap = pcmaploam(voxelSize);
addPoints(loamMap,points,absPose);

% Display the parking lot scene with the reference trajectory
hScene = figure(Name="Large Parking Lot",NumberTitle="off");
helperShowSceneImage(sceneName);
hold on
plot(refPosesX(:,2),refPosesY(:,2),LineWidth=2)
xlim([-60 40])
ylim([10 60])
hScene.Position = [100 100 1000 500];

for k = (numSkip+1):numSkip:numel(ptCloudArr)
prevPtCloud = ptCloud;
prevPoints = points;
viewId = viewId + 1;
ptCloud = ptCloudArr(k);

% Select a cylindrical neighborhood of interest.
selectedIdx = findPointsInCylinder(ptCloud,[egoRadius cylinderRadius]);
ptCloud = select(ptCloud,selectedIdx,OutputSize="full");

% Detect LOAM points and downsample the less planar surface points
points = detectLOAMFeatures(ptCloud,MaxPlanarSurfacePoints=maxPlanarSurfacePoints);
points = downsampleLessPlanar(points,gridStep);

% Register the points using the previous relative pose as an initial
% transformation
relPose = pcregisterloam(points,prevPoints,MatchingMethod="one-to-one",InitialTransform=relPose);

% Find the refined absolute pose that aligns the points to the map
absPose = findPose(loamMap,points,relPose);

% Store the refined absolute pose in the view set
vSetMapping = addView(vSetMapping,viewId,absPose);

% Add the new points to the map
addPoints(loamMap,points,absPose);

% Visualize the absolute pose in the parking lot scene
plot(absPose.Translation(1),absPose.Translation(2),Color="r",Marker=".",MarkerSize=8)
xlim([-60 40])
ylim([10 60])
title("Build a Map Using Lidar Mapping")
legend(["Ground Truth","Estimated Position"])
pause(0.001)
view(2)
end

% Get the ground truth trajectory
groundTruthTrajectory = vertcat(groundTruthPosesLidar.Translation);

% Get the estimated trajectories
odometryPositions = vertcat(vSetOdometry.Views.AbsolutePose.Translation);
mappingPositions = vertcat(vSetMapping.Views.AbsolutePose.Translation);

% Plot the trajectories
figure
plot3(groundTruthTrajectory(:,1),groundTruthTrajectory(:,2),groundTruthTrajectory(:,3),LineWidth=2,DisplayName="Ground Truth")
hold on
plot3(odometryPositions(:,1),odometryPositions(:,2),odometryPositions(:,3),LineWidth=2,DisplayName="Odometry")
plot3(mappingPositions(:,1),mappingPositions(:,2),mappingPositions(:,3),LineWidth=2,DisplayName="Odometry and Mapping")
view(2)

legend
title("Compare Trajectories")

% Select the poses to compare
selectedGroundTruth = groundTruthTrajectory(1:numSkip:end,:);

% Compute the RMSE
rmseOdometry = rmse(selectedGroundTruth,odometryPositions,"all");
rmseWithMapping = rmse(selectedGroundTruth,mappingPositions,"all");
disp([‘RMSE of the trajectory estimated with Odometry: ‘ num2str(rmseOdometry)])

disp([‘RMSE of the trajectory estimated with Odometry and Mapping: ‘ num2str(rmseWithMapping)])

function ptCloudArr = helperGetPointClouds(simOut)

% Extract signal
ptCloudData = simOut.ptCloudData.signals.values;

% Create a pointCloud array
ptCloudArr = pointCloud(ptCloudData(:,:,:,2)); % Ignore first frame
for n = 1:size(ptCloudData,4)
ptCloudArr(end+1) = pointCloud(ptCloudData(:,:,:,n)); %#ok<AGROW>
end

end
function gTruth = helperGetLidarGroundTruth(simOut)

numFrames = size(simOut.lidarLocation.time,1);
gTruth = repmat(rigidtform3d,numFrames-1,1);

for i = 1:numFrames
gTruth(i).Translation = squeeze(simOut.lidarLocation.signals.values(:,:,i));
% Ignore the roll and the pitch rotations since the ground is flat
yaw = double(simOut.lidarOrientation.signals.values(:,3,i));
gTruth(i).R = [cos(yaw) -sin(yaw) 0;
sin(yaw) cos(yaw) 0;
0 0 1];
end
end slam, loam, autonomous vehicle, kalman filter MATLAB Answers — New Questions

​

When i use matlab 2021a and unreal engine 4.23 for simulation,in unreal editor model ,the question is appear.
The details of the error are as follows:
MATLAB System block ‘SCRReferenceApplication/Simulation 3D Vehicle with Ground Following/Simulation 3D Vehicle’ error occurred when invoking ‘stepImpl’ method of ‘Simulation3DVehicleTerrainFb’. The error was thrown from ‘
‘D:Program FilesMATLABR2021atoolboxsharedsim3dblkssim3dblksSimulation3DVehicleTerrainFb.p’ at line 0
‘D:Program FilesMATLABR2021atoolboxsharedsim3dblkssim3dblksSimulation3DVehicleTerrainFb.p’ at line 0′.
The 3D vehicle no longer detects the ground. Review scene limits or initial position.When i use matlab 2021a and unreal engine 4.23 for simulation,in unreal editor model ,the question is appear.
The details of the error are as follows:
MATLAB System block ‘SCRReferenceApplication/Simulation 3D Vehicle with Ground Following/Simulation 3D Vehicle’ error occurred when invoking ‘stepImpl’ method of ‘Simulation3DVehicleTerrainFb’. The error was thrown from ‘
‘D:Program FilesMATLABR2021atoolboxsharedsim3dblkssim3dblksSimulation3DVehicleTerrainFb.p’ at line 0
‘D:Program FilesMATLABR2021atoolboxsharedsim3dblkssim3dblksSimulation3DVehicleTerrainFb.p’ at line 0′.
The 3D vehicle no longer detects the ground. Review scene limits or initial position. When i use matlab 2021a and unreal engine 4.23 for simulation,in unreal editor model ,the question is appear.
The details of the error are as follows:
MATLAB System block ‘SCRReferenceApplication/Simulation 3D Vehicle with Ground Following/Simulation 3D Vehicle’ error occurred when invoking ‘stepImpl’ method of ‘Simulation3DVehicleTerrainFb’. The error was thrown from ‘
‘D:Program FilesMATLABR2021atoolboxsharedsim3dblkssim3dblksSimulation3DVehicleTerrainFb.p’ at line 0
‘D:Program FilesMATLABR2021atoolboxsharedsim3dblkssim3dblksSimulation3DVehicleTerrainFb.p’ at line 0′.
The 3D vehicle no longer detects the ground. Review scene limits or initial position. unreal engine, simulink MATLAB Answers — New Questions

​

Hi everyone,
Im trying to add an image to my document but I keep getting an error
[ERROR] FOUserAgent – Image not found. URI: file:///Part1.jpg. (See position -1:-1)
[ERROR] FOUserAgent – Image not found. URI: file:///Part1.jpg. (No context info available)
my code is the following:
%% 1. System Description
%
% <<Part1.png>>
%

I have my image in the same folder as my .m file. Any help is appreciated. Thank you in advance!Hi everyone,
Im trying to add an image to my document but I keep getting an error
[ERROR] FOUserAgent – Image not found. URI: file:///Part1.jpg. (See position -1:-1)
[ERROR] FOUserAgent – Image not found. URI: file:///Part1.jpg. (No context info available)
my code is the following:
%% 1. System Description
%
% <<Part1.png>>
%

I have my image in the same folder as my .m file. Any help is appreciated. Thank you in advance! Hi everyone,
Im trying to add an image to my document but I keep getting an error
[ERROR] FOUserAgent – Image not found. URI: file:///Part1.jpg. (See position -1:-1)
[ERROR] FOUserAgent – Image not found. URI: file:///Part1.jpg. (No context info available)
my code is the following:
%% 1. System Description
%
% <<Part1.png>>
%

I have my image in the same folder as my .m file. Any help is appreciated. Thank you in advance! image, pdf, publish MATLAB Answers — New Questions

​

I am back here hoping that someone with eagles eyes can see if I am missing a index, because I cannot find where I am missing something. I am trying to implement the following pseudo-code

Until now, my attempt to do it is:

clear all; clc;
% Parameters
n = 9; h = 1 / (n + 1);
f = @(x) 2 * (pi^2) * sin(pi * x);p = @(x) 1;q = @(x) pi^2;

% Define the function S by
S = @(x) ( (x <= -2) ) .* 0 + …
( (x > -2) & (x <= -1) ) .* (1/4 * (2 + x).^3) + …
( (x > -1) & (x <= 0) ) .* (1/4 *((2 + x).^3 – 4 * (1 + x).^3)) + …
( (x > 0) & (x <= 1) ) .* (1/4 *((2 – x).^3 – 4 * (1 – x).^3)) + …
( (x > 1) & (x <= 2) ) .* (1/4 * (2 – x).^3) + …
( (x > 2) ) .* 0;

% Define the derivative of S by
dS = @(x) ( (x <= -2) ) .* 0 + …
( (x > -2) & (x <= -1) ) .* (3/4 * (2 + x).^2) + …
( (x > -1) & (x <= 0) ) .* (3/4 *((2 + x).^2 – 4 * (1 + x).^2)) + …
( (x > 0) & (x <= 1) ) .* ((-3)/4 *((2 – x).^2 – 4 * (1 – x).^2)) + …
( (x > 1) & (x <= 2) ) .* ((-3)/4 * (2 – x).^2) + …
( (x > 2) ) .* 0;

% Difine the cubic basis splines functions by
phi = cell(n + 2, 1);
phi{1} = @(x) S( x / h ) – 4 * S( (x + h) / h );
phi{2} = @(x) S((x – h) / h) – S((x + h) / h);
for i = 3:n
phi{i} = @(x) S((x – (i-1)*h) / h);
end
phi{n + 1} = @(x) S((x – n*h) / h) – S((x – (n + 2)*h) / h);
phi{n + 2} = @(x) S((x – (n + 1)*h) / h) – 4 * S((x – (n + 2)*h) / h);

% Difine the derivatives of cubic basis splines functions by
dphi = cell(n + 2, 1);
dphi{1} = @(x) (1 / h) * dS( x / h ) – (4 / h) * dS( (x + h) / h );
dphi{2} = @(x) (1 / h) * dS((x – h) / h) – (1 / h) * dS( (x + h) / h );
for i = 3:n
dphi{i} = @(x) (1 / h) * dS((x – (i-1)*h) / h);
end
dphi{n + 1} = @(x) (1 / h) * dS((x – n*h) / h) – (1 / h) * dS((x – (n + 2)*h) / h);
dphi{n + 2} = @(x) (1 / h) * dS((x – (n + 1)*h) / h) – (4 / h) * dS((x – (n + 2)*h) / h);

% inicialize the matrix of the linear sistem and its constant vector
A = zeros(n + 2, n + 2);
b = zeros(n + 2, 1);

% Start to build A and b
for i = 1:n+2
for j= i:min(i+3,n+2)
L = max((j-3)*h, 0); % in my mind, L and U should be ajusted to this, since i cannot start from i=0
U = min((i+1)*h, 1);
integrando_aij = @(x) (p(x) * dphi{i}(x) * dphi{j}(x)) + (q(x) * phi{i}(x) * phi{j}(x));
aij = gauss_quad(integrando_aij, L, U); % the gauss_quad function is at the end of this post. It seems to work fine to me.
A(i,j) = aij;
if i~=j
A(j,i) = aij;
end
Ld = max((i-3)*h, 0); % again, the same argument as before
Ud = min((i+1)*h, 1);
integrando_di = @(x) f(x) * phi{i}(x);
di = gauss_quad(integrando_di, Ld, Ud);
b(i) = di;
end
end

c = A b;

disp(‘Coefficients:’);
for i = 0:n+1
fprintf(‘c%d = %.6fn’, i, c(i+1));
end

%%%%%%%%%% PLOTTING GRAPHS %%%%%%%%%%%%%

% Here I just want to look to the shape of the functions that I have
% defined, just to make sure I am using rights tools

% Number of pts to plot
num_points = 1000;
x_values = linspace(0, 1, num_points);

figure (1);
hold on;

% Plot each function phi in [0, 1]
for i = 1:n+2
y_values = arrayfun(phi{i}, x_values);
plot(x_values, y_values, ‘DisplayName’, sprintf(‘\phi_%d(x)’, i-1));
end
xlabel(‘x’);
ylabel(‘phi_i(x)’);
title(‘Funções base phi_i(x) entre [0, 1]’);
legend show;
hold off;

figure (2)
% Plot an specific function, here I chose phi{11}
y_values_phi = arrayfun(phi{11}, x_values);
plot(x_values, y_values_phi);
xlabel(‘x’);
ylabel(‘phi(x)’);
title(‘Função base phi(x) entre [0, 1]’);
legend show;

figure (3)
% Plot S and its derivative
x_values_s = linspace(-3, 3, num_points);
y_values_s = arrayfun(S, x_values_s);
plot(x_values_s, y_values_s);
xlabel(‘x’);
ylabel(‘y’);
hold on
y_values_ds = arrayfun(dS, x_values_s);
plot(x_values_s, y_values_ds);
legend(‘S(x)’, ‘dS(x)’)
hold off

In the book that I am following the basis functions shoul look like

The last section of my code, suggest that I am using them right. Finally, here is the gauss_quad function that I call to solve integrals
function result = gauss_quad(f, a, b)
% 3-point Gauss quadrature
x = [-sqrt(3/5), 0, sqrt(3/5)];
w = [5/9, 8/9, 5/9];

% Transform the integration limits
t = 0.5 * ((b – a) * x + (b + a));
ft = arrayfun(f, t);

result = 0.5 * (b – a) * sum(w .* ft);
end
The coefficients should be
.
I think I have done a good work so far, and I need someone to give me a direction.I am back here hoping that someone with eagles eyes can see if I am missing a index, because I cannot find where I am missing something. I am trying to implement the following pseudo-code

Until now, my attempt to do it is:

clear all; clc;
% Parameters
n = 9; h = 1 / (n + 1);
f = @(x) 2 * (pi^2) * sin(pi * x);p = @(x) 1;q = @(x) pi^2;

% Define the function S by
S = @(x) ( (x <= -2) ) .* 0 + …
( (x > -2) & (x <= -1) ) .* (1/4 * (2 + x).^3) + …
( (x > -1) & (x <= 0) ) .* (1/4 *((2 + x).^3 – 4 * (1 + x).^3)) + …
( (x > 0) & (x <= 1) ) .* (1/4 *((2 – x).^3 – 4 * (1 – x).^3)) + …
( (x > 1) & (x <= 2) ) .* (1/4 * (2 – x).^3) + …
( (x > 2) ) .* 0;

% Define the derivative of S by
dS = @(x) ( (x <= -2) ) .* 0 + …
( (x > -2) & (x <= -1) ) .* (3/4 * (2 + x).^2) + …
( (x > -1) & (x <= 0) ) .* (3/4 *((2 + x).^2 – 4 * (1 + x).^2)) + …
( (x > 0) & (x <= 1) ) .* ((-3)/4 *((2 – x).^2 – 4 * (1 – x).^2)) + …
( (x > 1) & (x <= 2) ) .* ((-3)/4 * (2 – x).^2) + …
( (x > 2) ) .* 0;

% Difine the cubic basis splines functions by
phi = cell(n + 2, 1);
phi{1} = @(x) S( x / h ) – 4 * S( (x + h) / h );
phi{2} = @(x) S((x – h) / h) – S((x + h) / h);
for i = 3:n
phi{i} = @(x) S((x – (i-1)*h) / h);
end
phi{n + 1} = @(x) S((x – n*h) / h) – S((x – (n + 2)*h) / h);
phi{n + 2} = @(x) S((x – (n + 1)*h) / h) – 4 * S((x – (n + 2)*h) / h);

% Difine the derivatives of cubic basis splines functions by
dphi = cell(n + 2, 1);
dphi{1} = @(x) (1 / h) * dS( x / h ) – (4 / h) * dS( (x + h) / h );
dphi{2} = @(x) (1 / h) * dS((x – h) / h) – (1 / h) * dS( (x + h) / h );
for i = 3:n
dphi{i} = @(x) (1 / h) * dS((x – (i-1)*h) / h);
end
dphi{n + 1} = @(x) (1 / h) * dS((x – n*h) / h) – (1 / h) * dS((x – (n + 2)*h) / h);
dphi{n + 2} = @(x) (1 / h) * dS((x – (n + 1)*h) / h) – (4 / h) * dS((x – (n + 2)*h) / h);

% inicialize the matrix of the linear sistem and its constant vector
A = zeros(n + 2, n + 2);
b = zeros(n + 2, 1);

% Start to build A and b
for i = 1:n+2
for j= i:min(i+3,n+2)
L = max((j-3)*h, 0); % in my mind, L and U should be ajusted to this, since i cannot start from i=0
U = min((i+1)*h, 1);
integrando_aij = @(x) (p(x) * dphi{i}(x) * dphi{j}(x)) + (q(x) * phi{i}(x) * phi{j}(x));
aij = gauss_quad(integrando_aij, L, U); % the gauss_quad function is at the end of this post. It seems to work fine to me.
A(i,j) = aij;
if i~=j
A(j,i) = aij;
end
Ld = max((i-3)*h, 0); % again, the same argument as before
Ud = min((i+1)*h, 1);
integrando_di = @(x) f(x) * phi{i}(x);
di = gauss_quad(integrando_di, Ld, Ud);
b(i) = di;
end
end

c = A b;

disp(‘Coefficients:’);
for i = 0:n+1
fprintf(‘c%d = %.6fn’, i, c(i+1));
end

%%%%%%%%%% PLOTTING GRAPHS %%%%%%%%%%%%%

% Here I just want to look to the shape of the functions that I have
% defined, just to make sure I am using rights tools

% Number of pts to plot
num_points = 1000;
x_values = linspace(0, 1, num_points);

figure (1);
hold on;

% Plot each function phi in [0, 1]
for i = 1:n+2
y_values = arrayfun(phi{i}, x_values);
plot(x_values, y_values, ‘DisplayName’, sprintf(‘\phi_%d(x)’, i-1));
end
xlabel(‘x’);
ylabel(‘phi_i(x)’);
title(‘Funções base phi_i(x) entre [0, 1]’);
legend show;
hold off;

figure (2)
% Plot an specific function, here I chose phi{11}
y_values_phi = arrayfun(phi{11}, x_values);
plot(x_values, y_values_phi);
xlabel(‘x’);
ylabel(‘phi(x)’);
title(‘Função base phi(x) entre [0, 1]’);
legend show;

figure (3)
% Plot S and its derivative
x_values_s = linspace(-3, 3, num_points);
y_values_s = arrayfun(S, x_values_s);
plot(x_values_s, y_values_s);
xlabel(‘x’);
ylabel(‘y’);
hold on
y_values_ds = arrayfun(dS, x_values_s);
plot(x_values_s, y_values_ds);
legend(‘S(x)’, ‘dS(x)’)
hold off

In the book that I am following the basis functions shoul look like

The last section of my code, suggest that I am using them right. Finally, here is the gauss_quad function that I call to solve integrals
function result = gauss_quad(f, a, b)
% 3-point Gauss quadrature
x = [-sqrt(3/5), 0, sqrt(3/5)];
w = [5/9, 8/9, 5/9];

% Transform the integration limits
t = 0.5 * ((b – a) * x + (b + a));
ft = arrayfun(f, t);

result = 0.5 * (b – a) * sum(w .* ft);
end
The coefficients should be
.
I think I have done a good work so far, and I need someone to give me a direction. I am back here hoping that someone with eagles eyes can see if I am missing a index, because I cannot find where I am missing something. I am trying to implement the following pseudo-code

Until now, my attempt to do it is:

clear all; clc;
% Parameters
n = 9; h = 1 / (n + 1);
f = @(x) 2 * (pi^2) * sin(pi * x);p = @(x) 1;q = @(x) pi^2;

% Define the function S by
S = @(x) ( (x <= -2) ) .* 0 + …
( (x > -2) & (x <= -1) ) .* (1/4 * (2 + x).^3) + …
( (x > -1) & (x <= 0) ) .* (1/4 *((2 + x).^3 – 4 * (1 + x).^3)) + …
( (x > 0) & (x <= 1) ) .* (1/4 *((2 – x).^3 – 4 * (1 – x).^3)) + …
( (x > 1) & (x <= 2) ) .* (1/4 * (2 – x).^3) + …
( (x > 2) ) .* 0;

% Define the derivative of S by
dS = @(x) ( (x <= -2) ) .* 0 + …
( (x > -2) & (x <= -1) ) .* (3/4 * (2 + x).^2) + …
( (x > -1) & (x <= 0) ) .* (3/4 *((2 + x).^2 – 4 * (1 + x).^2)) + …
( (x > 0) & (x <= 1) ) .* ((-3)/4 *((2 – x).^2 – 4 * (1 – x).^2)) + …
( (x > 1) & (x <= 2) ) .* ((-3)/4 * (2 – x).^2) + …
( (x > 2) ) .* 0;

% Difine the cubic basis splines functions by
phi = cell(n + 2, 1);
phi{1} = @(x) S( x / h ) – 4 * S( (x + h) / h );
phi{2} = @(x) S((x – h) / h) – S((x + h) / h);
for i = 3:n
phi{i} = @(x) S((x – (i-1)*h) / h);
end
phi{n + 1} = @(x) S((x – n*h) / h) – S((x – (n + 2)*h) / h);
phi{n + 2} = @(x) S((x – (n + 1)*h) / h) – 4 * S((x – (n + 2)*h) / h);

% Difine the derivatives of cubic basis splines functions by
dphi = cell(n + 2, 1);
dphi{1} = @(x) (1 / h) * dS( x / h ) – (4 / h) * dS( (x + h) / h );
dphi{2} = @(x) (1 / h) * dS((x – h) / h) – (1 / h) * dS( (x + h) / h );
for i = 3:n
dphi{i} = @(x) (1 / h) * dS((x – (i-1)*h) / h);
end
dphi{n + 1} = @(x) (1 / h) * dS((x – n*h) / h) – (1 / h) * dS((x – (n + 2)*h) / h);
dphi{n + 2} = @(x) (1 / h) * dS((x – (n + 1)*h) / h) – (4 / h) * dS((x – (n + 2)*h) / h);

% inicialize the matrix of the linear sistem and its constant vector
A = zeros(n + 2, n + 2);
b = zeros(n + 2, 1);

% Start to build A and b
for i = 1:n+2
for j= i:min(i+3,n+2)
L = max((j-3)*h, 0); % in my mind, L and U should be ajusted to this, since i cannot start from i=0
U = min((i+1)*h, 1);
integrando_aij = @(x) (p(x) * dphi{i}(x) * dphi{j}(x)) + (q(x) * phi{i}(x) * phi{j}(x));
aij = gauss_quad(integrando_aij, L, U); % the gauss_quad function is at the end of this post. It seems to work fine to me.
A(i,j) = aij;
if i~=j
A(j,i) = aij;
end
Ld = max((i-3)*h, 0); % again, the same argument as before
Ud = min((i+1)*h, 1);
integrando_di = @(x) f(x) * phi{i}(x);
di = gauss_quad(integrando_di, Ld, Ud);
b(i) = di;
end
end

c = A b;

disp(‘Coefficients:’);
for i = 0:n+1
fprintf(‘c%d = %.6fn’, i, c(i+1));
end

%%%%%%%%%% PLOTTING GRAPHS %%%%%%%%%%%%%

% Here I just want to look to the shape of the functions that I have
% defined, just to make sure I am using rights tools

% Number of pts to plot
num_points = 1000;
x_values = linspace(0, 1, num_points);

figure (1);
hold on;

% Plot each function phi in [0, 1]
for i = 1:n+2
y_values = arrayfun(phi{i}, x_values);
plot(x_values, y_values, ‘DisplayName’, sprintf(‘\phi_%d(x)’, i-1));
end
xlabel(‘x’);
ylabel(‘phi_i(x)’);
title(‘Funções base phi_i(x) entre [0, 1]’);
legend show;
hold off;

figure (2)
% Plot an specific function, here I chose phi{11}
y_values_phi = arrayfun(phi{11}, x_values);
plot(x_values, y_values_phi);
xlabel(‘x’);
ylabel(‘phi(x)’);
title(‘Função base phi(x) entre [0, 1]’);
legend show;

figure (3)
% Plot S and its derivative
x_values_s = linspace(-3, 3, num_points);
y_values_s = arrayfun(S, x_values_s);
plot(x_values_s, y_values_s);
xlabel(‘x’);
ylabel(‘y’);
hold on
y_values_ds = arrayfun(dS, x_values_s);
plot(x_values_s, y_values_ds);
legend(‘S(x)’, ‘dS(x)’)
hold off

In the book that I am following the basis functions shoul look like

The last section of my code, suggest that I am using them right. Finally, here is the gauss_quad function that I call to solve integrals
function result = gauss_quad(f, a, b)
% 3-point Gauss quadrature
x = [-sqrt(3/5), 0, sqrt(3/5)];
w = [5/9, 8/9, 5/9];

% Transform the integration limits
t = 0.5 * ((b – a) * x + (b + a));
ft = arrayfun(f, t);

result = 0.5 * (b – a) * sum(w .* ft);
end
The coefficients should be
.
I think I have done a good work so far, and I need someone to give me a direction. code, homework, algorithm, integration, index MATLAB Answers — New Questions

​

So I am working on an app using app designer. The app has one UIAxes and is updated in real time with a scatter plot, based on a timer function. I also have a button that when clicked, enables me to place a rectangle ROI on the UIAxes. Those two things by themselves work nicely. However, the problem is when I create the ROI by clicking on the button and right after that enabling the real time scatter plot updates, it removes my ROI from the UIAxes. I need to have this ROI enabled on the same UIAxes as the real time scatter plot updates, for further processing. How can I fix this or do this, without app designer removing the ROI as soon as I start the scatter plot updates?

here is a video that shows the problem https://streamable.com/ry6gpv
so as you can see in the video, there are two scenarios that dont work, i would be happy if either worked, but both would be perfect scenario:
1) i start the real time scatter plot and then try to draw a roi on top, it doesnt let me or show it at all
2) i draw the roi first and then start the real time scatter plot, but it then removes my roi
so it seems no matter what the case, i cant have both at the same time. how to fix that?

I simplified the app to the bare bones, so it highlights the main problem that I need fixed, as described above. I attached the text version of the full app designer code as well as the app designer project file.

Thanks!So I am working on an app using app designer. The app has one UIAxes and is updated in real time with a scatter plot, based on a timer function. I also have a button that when clicked, enables me to place a rectangle ROI on the UIAxes. Those two things by themselves work nicely. However, the problem is when I create the ROI by clicking on the button and right after that enabling the real time scatter plot updates, it removes my ROI from the UIAxes. I need to have this ROI enabled on the same UIAxes as the real time scatter plot updates, for further processing. How can I fix this or do this, without app designer removing the ROI as soon as I start the scatter plot updates?

here is a video that shows the problem https://streamable.com/ry6gpv
so as you can see in the video, there are two scenarios that dont work, i would be happy if either worked, but both would be perfect scenario:
1) i start the real time scatter plot and then try to draw a roi on top, it doesnt let me or show it at all
2) i draw the roi first and then start the real time scatter plot, but it then removes my roi
so it seems no matter what the case, i cant have both at the same time. how to fix that?

I simplified the app to the bare bones, so it highlights the main problem that I need fixed, as described above. I attached the text version of the full app designer code as well as the app designer project file.

Thanks! So I am working on an app using app designer. The app has one UIAxes and is updated in real time with a scatter plot, based on a timer function. I also have a button that when clicked, enables me to place a rectangle ROI on the UIAxes. Those two things by themselves work nicely. However, the problem is when I create the ROI by clicking on the button and right after that enabling the real time scatter plot updates, it removes my ROI from the UIAxes. I need to have this ROI enabled on the same UIAxes as the real time scatter plot updates, for further processing. How can I fix this or do this, without app designer removing the ROI as soon as I start the scatter plot updates?

here is a video that shows the problem https://streamable.com/ry6gpv
so as you can see in the video, there are two scenarios that dont work, i would be happy if either worked, but both would be perfect scenario:
1) i start the real time scatter plot and then try to draw a roi on top, it doesnt let me or show it at all
2) i draw the roi first and then start the real time scatter plot, but it then removes my roi
so it seems no matter what the case, i cant have both at the same time. how to fix that?

I simplified the app to the bare bones, so it highlights the main problem that I need fixed, as described above. I attached the text version of the full app designer code as well as the app designer project file.

Thanks! app designer, roi, scatter plot, real time MATLAB Answers — New Questions

​

A Simulink model I have will hard crash Simulink and MATLAB when I insert a breakpoint in a MATLAB function block. However, this only happens when I run the simulation in Normal mode. When I run in Accelerator mode, the break point works fine. The model didn’t always have this problem, but I’m not sure what caused it. Unfortunately, it takes a long time to crash, reopen, and reload the large model and I haven’t been able to isolate the cause.
Is there a general reason why breakpoints in MATLAB function blocks would crash Simulink in Normal mode, but not inAccelerator? I need to run the model in Normal mode for some other features I’d like to use.A Simulink model I have will hard crash Simulink and MATLAB when I insert a breakpoint in a MATLAB function block. However, this only happens when I run the simulation in Normal mode. When I run in Accelerator mode, the break point works fine. The model didn’t always have this problem, but I’m not sure what caused it. Unfortunately, it takes a long time to crash, reopen, and reload the large model and I haven’t been able to isolate the cause.
Is there a general reason why breakpoints in MATLAB function blocks would crash Simulink in Normal mode, but not inAccelerator? I need to run the model in Normal mode for some other features I’d like to use. A Simulink model I have will hard crash Simulink and MATLAB when I insert a breakpoint in a MATLAB function block. However, this only happens when I run the simulation in Normal mode. When I run in Accelerator mode, the break point works fine. The model didn’t always have this problem, but I’m not sure what caused it. Unfortunately, it takes a long time to crash, reopen, and reload the large model and I haven’t been able to isolate the cause.
Is there a general reason why breakpoints in MATLAB function blocks would crash Simulink in Normal mode, but not inAccelerator? I need to run the model in Normal mode for some other features I’d like to use. simulink, matlab function block, crash, accelerator MATLAB Answers — New Questions

​