Quiver plot of coordinate error with wrong arrow lengths (2024)

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Andy on 23 May 2024 at 19:29

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Commented: Voss on 24 May 2024 at 17:08

DSC03765.xlsx

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I'm working on a quiver plot that represents coordinate error in images.

However, the magnitude of the vectors is not being represented correctly: for example, some small erros are being draw as bigger lines.

The magnitudes seems to be calculated correctly, but 'idx' is always 0 or 1, although there are 4 magnitude classes; also, the lengths of arrows are wrong in the figures.

I'm plotting 5 figures, but magnitude thresholds are calculated considering the set of images to generate a common legend.

% data

x1 = xlsread('DSC03765.xlsx',1,'A14:A614');

y1 = xlsread('DSC03765.xlsx',1,'B14:B614');

errorx1 = xlsread('DSC03765.xlsx',1,'E14:E614');

errory1 = xlsread('DSC03765.xlsx',1,'F14:F614');

x2 = xlsread('DSC03765.xlsx',2,'A14:A614');

y2 = xlsread('DSC03765.xlsx',2,'B14:B614');

errorx2 = xlsread('DSC03765.xlsx',2,'E14:E614');

errory2 = xlsread('DSC03765.xlsx',2,'F14:F614');

x3 = xlsread('DSC03765.xlsx',3,'A14:A614');

y3 = xlsread('DSC03765.xlsx',3,'B14:B614');

errorx3 = xlsread('DSC03765.xlsx',3,'E14:E614');

errory3 = xlsread('DSC03765.xlsx',3,'F14:F614');

x4 = xlsread('DSC03765.xlsx',4,'A14:A614');

y4 = xlsread('DSC03765.xlsx',4,'B14:B614');

errorx4 = xlsread('DSC03765.xlsx',4,'E14:E614');

errory4 = xlsread('DSC03765.xlsx',4,'F14:F614');

x5 = xlsread('DSC03765.xlsx',5,'A14:A614');

y5 = xlsread('DSC03765.xlsx',5,'B14:B614');

errorx5 = xlsread('DSC03765.xlsx',5,'E14:E614');

errory5 = xlsread('DSC03765.xlsx',5,'F14:F614');

% calculate magnitude

magnitude1 = sqrt(errorx1.^2+errory1.^2);

magnitude2 = sqrt(errorx2.^2+errory2.^2);

magnitude3 = sqrt(errorx3.^2+errory3.^2);

magnitude4 = sqrt(errorx4.^2+errory4.^2);

magnitude5 = sqrt(errorx5.^2+errory5.^2);

magnitude_total = [];

magnitudes = {magnitude1, magnitude2, magnitude3, magnitude4, magnitude5};

% concatenate values of magnitude in one array

for i = 1:length(magnitudes)

magnitude_total = vertcat(magnitude_total, magnitudes{i});

end

% calculate min and max magnitude

mag_res = 0.05;

magnitudelim = [ ...

floor(min(magnitude_total)/mag_res) ...

ceil(max(magnitude_total)/mag_res) ...

]*mag_res;

% define a color map

n_colors = 4;

cmap = jet(n_colors);

% calculate the magnitude thresholds

mthresholds = linspace(magnitudelim(1),magnitudelim(2),n_colors+1);

% plot function

function plot_image(x, y, errorx, errory, magnitude, mthresholds, cmap, magnitudelim, n_colors, img_title)

figure

hold on

% for each color, find the indicies of the magnitudes at this color level

for ii = 1:n_colors

idx = magnitude >= mthresholds(ii) & magnitude < mthresholds(ii+1);

% generate an arrow of the corresponding color

quiver(x(idx), y(idx), errorx(idx), errory(idx), 0.5, 'Color', cmap(ii,:));

end

% set up the colorbar

colormap(cmap);

colorbar();

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Voss on 24 May 2024 at 15:36

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Ran in:

DSC03765.xlsx

By the way, here is a more succinct version, which uses readtable instead of xlsread (which is no longer recommended) and uses arrays (cell arrays, tables) instead of sequences of numbered variables (x1, x2, x3, ...):

sheet_names = sheetnames('DSC03765.xlsx');

N = numel(sheet_names);

C = cell(1,N);

for ii = 1:N

% read sheet

T = readtable('DSC03765.xlsx','Sheet',ii);

% rename table variables

T = renamevars(T,1:width(T),{'x','y','foo','bar','errorx','errory'});

% calculate magnitude

T.magnitude = sqrt(T.errorx.^2+T.errory.^2);

% store table in cell array

C{ii} = T;

end

% concatenate values of magnitude in one array

magnitude_total = vertcat(C{:}).magnitude;

% calculate min and max magnitude

mag_res = 0.05;

magnitudelim = [ ...

floor(min(magnitude_total)/mag_res) ...

ceil(max(magnitude_total)/mag_res) ...

]*mag_res;

% define a color map

n_colors = 4;

cmap = jet(n_colors);

% calculate the magnitude thresholds

mthresholds = linspace(magnitudelim(1),magnitudelim(2),n_colors+1);

nm = [570 525 850 490 550];

common_scale_factor = 50;

for ii = 1:numel(C)

plot_image(C{ii}.x, C{ii}.y, common_scale_factor*C{ii}.errorx, common_scale_factor*C{ii}.errory, ...

C{ii}.magnitude, mthresholds, cmap, magnitudelim, n_colors, nm(ii));

end

% plot function

function plot_image(x, y, errorx, errory, magnitude, mthresholds, cmap, magnitudelim, n_colors, nm)

figure

hold on

% for each color, find the indicies of the magnitudes at this color level

for ii = 1:n_colors

idx = magnitude >= mthresholds(ii) & magnitude < mthresholds(ii+1);

% generate an arrow of the corresponding color

quiver(x(idx), y(idx), errorx(idx), errory(idx), 'off', 'Color', cmap(ii,:));

end

% set up the colorbar

colormap(cmap);

colorbar();

caxis(magnitudelim);

xlim([0 2836])

ylim([0 2778])

title(sprintf('%d nm',nm));

hold off

end

Answers (1)

Voss on 24 May 2024 at 15:11

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Edited: Voss on 24 May 2024 at 15:12

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DSC03765.xlsx

"some small erros are being draw as bigger lines"

That's because each quiver plot scales its own arrows' lengths independently of any other quiver plots.

Using a scale factor of 0.5 means each quiver plot's arrows are half as long as they would be if they were automatically scaled not to overlap, as described in the documentation,

When scale is a positive number, the quiver function automatically adjusts the lengths of arrows so they do not overlap, then stretches them by a factor of scale. For example, a scale of 2 doubles the length of arrows, and a scale of 0.5 halves the length of arrows.

But this implies nothing about the relative length of one quiver plot's arrows compared to another quiver plot's arrows. Since each quiver plot's arrow lengths are scaled independently, it's impossible to enforce any relationship between multiple quiver plots' arrow lengths when using automatic scaling.

However, you can turn automatic scaling off, and manually apply a scale factor to the arrow magnitudes (i.e., multiply the U and V by some factor before sending them to quiver). Using the same factor for all quiver plots will scale them all together. See the variable common_scale_factor below, and adjust it until the plots look like what you want.

% data

x1 = xlsread('DSC03765.xlsx',1,'A14:A614');

y1 = xlsread('DSC03765.xlsx',1,'B14:B614');

errorx1 = xlsread('DSC03765.xlsx',1,'E14:E614');

errory1 = xlsread('DSC03765.xlsx',1,'F14:F614');

x2 = xlsread('DSC03765.xlsx',2,'A14:A614');

y2 = xlsread('DSC03765.xlsx',2,'B14:B614');

errorx2 = xlsread('DSC03765.xlsx',2,'E14:E614');

errory2 = xlsread('DSC03765.xlsx',2,'F14:F614');

x3 = xlsread('DSC03765.xlsx',3,'A14:A614');

y3 = xlsread('DSC03765.xlsx',3,'B14:B614');

errorx3 = xlsread('DSC03765.xlsx',3,'E14:E614');

errory3 = xlsread('DSC03765.xlsx',3,'F14:F614');

x4 = xlsread('DSC03765.xlsx',4,'A14:A614');

y4 = xlsread('DSC03765.xlsx',4,'B14:B614');

errorx4 = xlsread('DSC03765.xlsx',4,'E14:E614');

errory4 = xlsread('DSC03765.xlsx',4,'F14:F614');

x5 = xlsread('DSC03765.xlsx',5,'A14:A614');

y5 = xlsread('DSC03765.xlsx',5,'B14:B614');

errorx5 = xlsread('DSC03765.xlsx',5,'E14:E614');

errory5 = xlsread('DSC03765.xlsx',5,'F14:F614');

% calculate magnitude

magnitude1 = sqrt(errorx1.^2+errory1.^2);

magnitude2 = sqrt(errorx2.^2+errory2.^2);

magnitude3 = sqrt(errorx3.^2+errory3.^2);

magnitude4 = sqrt(errorx4.^2+errory4.^2);

magnitude5 = sqrt(errorx5.^2+errory5.^2);

magnitude_total = [];

magnitudes = {magnitude1, magnitude2, magnitude3, magnitude4, magnitude5};

% concatenate values of magnitude in one array

for i = 1:length(magnitudes)

magnitude_total = vertcat(magnitude_total, magnitudes{i});

end

% calculate min and max magnitude

mag_res = 0.05;

magnitudelim = [ ...

floor(min(magnitude_total)/mag_res) ...

ceil(max(magnitude_total)/mag_res) ...

]*mag_res;

% define a color map

n_colors = 4;

cmap = jet(n_colors);

% calculate the magnitude thresholds

mthresholds = linspace(magnitudelim(1),magnitudelim(2),n_colors+1);

% plot function

function plot_image(x, y, errorx, errory, magnitude, mthresholds, cmap, magnitudelim, n_colors, img_title)

figure

hold on

common_scale_factor = 50;

% for each color, find the indicies of the magnitudes at this color level

for ii = 1:n_colors

idx = magnitude >= mthresholds(ii) & magnitude < mthresholds(ii+1);

% generate an arrow of the corresponding color

quiver(x(idx), y(idx), common_scale_factor*errorx(idx), common_scale_factor*errory(idx), 'off', 'Color', cmap(ii,:));

end

% set up the colorbar

colormap(cmap);

colorbar();

caxis(magnitudelim);

xlim([0 2836])

ylim([0 2778])

title(img_title);

hold off

end

% plot all figures

plot_image(x1, y1, errorx1, errory1, magnitude1, mthresholds, cmap, magnitudelim, n_colors, '570nm');

plot_image(x2, y2, errorx2, errory2, magnitude2, mthresholds, cmap, magnitudelim, n_colors, '525nm');

plot_image(x3, y3, errorx3, errory3, magnitude3, mthresholds, cmap, magnitudelim, n_colors, '850nm');

plot_image(x4, y4, errorx4, errory4, magnitude4, mthresholds, cmap, magnitudelim, n_colors, '490nm');

plot_image(x5, y5, errorx5, errory5, magnitude5, mthresholds, cmap, magnitudelim, n_colors, '550nm');

(For the other question, "'idx' is always 0 or 1" because idx is a logical vector, which is used for (logical) indexing.)

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Andy on 24 May 2024 at 16:58