Problems encountered when using sph2cart

Here is the code：

load angles.mat
load vertices.mat
[vectors(:,1), vectors(:,2), vectors(:,3)] = sph2cart(angle_phi_theta(:,1), angle_phi_theta(:,2), 1);
quiver3(vertex_segment(:,1),vertex_segment(:,2),vertex_segment(:,3),...
    vectors(:,1),vectors(:,2),vectors(:,3),0.8,'Color','green','LineWidth',1);hold on;

The results:

Problem: I think the resulting vectors should converge uniformly or diverge uniformly, but why do they alternate like this? What went wrong?

Answer 1

[Star Strider]

Your data do not vary much. Also, what are the uints for ‘angle_phi_theta’ ? They appear to be more like degrees than radians that all MATLAB trigonometric functions (except those ending in ‘d’ such as sind) require. Using the deg2rad function produces a smooth, continuous surface for ‘vectors’, and a different result for the quiver plot. I am not sure that is an improvement, or the result you want.

load angles.mat
load vertices.mat

whos

  Name                   Size            Bytes  Class     Attributes

  angle_phi_theta      375x2              6000  double              
  ans                    1x36               72  char                
  vertex_segment       375x3              9000  double              

format long

angle_phi_theta

angle_phi_theta = 375×2

-9.148764617364000 0.407847307973360 -9.123309592460078 0.407853188681914 -9.101024233864036 0.407858337123113 -9.092495752495266 0.407860307402597 -9.083035544599770 0.407862492932790 -9.062827352976990 0.407867161499636 -9.036664952651956 0.407873205628524 -9.031272314098036 0.407874451454674 -8.997910473048979 0.407882158823446 -8.993195935993631 0.407883247992225

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

vertex_segment

vertex_segment = 375×3

24.276068429529410 -0.448447928746336 81.067888845006465 24.259140628673865 -1.111978356700450 81.053336662519229 24.230347879342876 -1.686194075643361 81.035379587412891 24.222789097806036 -1.838657154480922 81.017396569952453 24.205319637130444 -2.010328693931287 81.065814520761450 24.154085264800283 -2.518686225537345 81.100737089879914 24.071652394713709 -3.188041341858980 81.134735008918099 24.062239752877428 -3.256346875155522 81.164042492094680 23.921659335817342 -4.142426303775671 81.159891955460267 23.910847013653022 -4.207351211131320 81.151844177732812

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

●

angle_phi_theta = deg2rad(angle_phi_theta)

angle_phi_theta = 375×2

-0.159676065062961 0.007118278369530 -0.159231791067210 0.007118381007257 -0.158842838184722 0.007118470864507 -0.158693988104642 0.007118505252372 -0.158528876328942 0.007118543397069 -0.158176176849251 0.007118624878932 -0.157719556823354 0.007118730368882 -0.157625437525218 0.007118752112650 -0.157043163554385 0.007118886631612 -0.156960879360062 0.007118905641193

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

[vectors(:,1), vectors(:,2), vectors(:,3)] = sph2cart(angle_phi_theta(:,1), angle_phi_theta(:,2), 1);

figure
surf(vectors, EdgeColor='interp')
grid on
colormap(turbo)

figure
quiver3(vertex_segment(:,1),vertex_segment(:,2),vertex_segment(:,3),...
        vectors(:,1),vectors(:,2),vectors(:,3),0.8,'Color','green','LineWidth',1);hold on;

.

[bird]

Thank you very much for your answer. The values in angle_phi_theta are in radians, which does not need to be transformed. The first column roughly covers the range of 2*pi, so the problem you mentioned does not exist. The ideal result should be a cluster of vectors that "converge" all point to the Z-axis, as shown in the figure below, but in the opposite direction

[Star Strider]

The first column of ‘angle_phi_theta’ goes from -9 to -2, and I thought that was a bit unusual for radian measure although the difference spans about radians. The ‘vectors’ array, controlling the dirrection and magnitude of the arrows, is a spiral.

I am not certain that it is even possible to get the result you want. I attenpted a few experiments to see if I could come up with a result that resembles the one you want, and failed.

load angles.mat
load vertices.mat
whos

  Name                   Size            Bytes  Class     Attributes

  angle_phi_theta      375x2              6000  double              
  ans                    1x36               72  char                
  vertex_segment       375x3              9000  double              

       
format long

disp(angle_phi_theta)

  -9.148764617364000   0.407847307973360
  -9.123309592460078   0.407853188681914
  -9.101024233864036   0.407858337123113
  -9.092495752495266   0.407860307402597
  -9.083035544599770   0.407862492932790
  -9.062827352976990   0.407867161499636
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figure
plot(angle_phi_theta(:,1), angle_phi_theta(:,2))
grid

disp(vertex_segment)

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figure
plot3(vertex_segment(:,1), vertex_segment(:,2), vertex_segment(:,3))
grid
% view(0,90)
% axis('equal')
daspect([100 100 1])
xlabel('vertex\_segment(:,1)')
ylabel('vertex\_segment(:,2)')
zlabel('vertex\_segment(:,3)')
title('vertex\_segment')

[vectors(:,1), vectors(:,2), vectors(:,3)] = sph2cart(angle_phi_theta(:,1), angle_phi_theta(:,2), 1);

figure
plot3(vectors(:,1), vectors(:,2), vectors(:,3))
grid
xlabel('vectors(:,1)')
ylabel('vectors(:,2)')
zlabel('vectors(:,3)')
title('vectors')

% view(0,90)
% axis('equal')
% daspect([100 100 1])

figure
quiver3(vertex_segment(:,1),vertex_segment(:,2),vertex_segment(:,3),...
        vectors(:,1),vectors(:,2),vectors(:,3),0.8,'Color','green','LineWidth',1);hold on;
daspect([10 10 1])

a = linspace(0, 2*pi, size(vectors,1)).';
vectors = [cos(a) sin(a) 2*ones(size(a))];
% vectors = [cos(a) sin(a) cos(a)];

figure
quiver3(vertex_segment(:,1),vertex_segment(:,2),vertex_segment(:,3),...
        vectors(:,1),vectors(:,2),vectors(:,3),0.8,'Color','green','LineWidth',1);hold on;
daspect([10 10 1])

% view(0,90)

.

[bird]

Thank you very much for your answer. I have found the reason for the question, because I was busy with other things and did not reply in time. The main reason is that in the calculation of sph2cart, the Angle azimuth corresponding to the vector is sorted in counter-clockwise order, so the corresponding vertex_segment should also be sorted in counter-clockwise order. If clockwise ordering occurs, problems like mine will occur. Therefore, the vertex_segment need to be sorted in reverse order before calculation：

clear all

clc

close all

load angles.mat

load vertices.mat

vertex_segment=flipud(vertex_segment); % important

[vectors(:,1), vectors(:,2), vectors(:,3)] = sph2cart(angle_phi_theta(:,1), angle_phi_theta(:,2), 1);

quiver3(vertex_segment(:,1),vertex_segment(:,2),vertex_segment(:,3),...

vectors(:,1),vectors(:,2),vectors(:,3),0.8,'Color','green','LineWidth',1);hold on;

[Star Strider]

As always, my pleasure!

Thank you for clarifying that.

The counter-clockwise direction is the default mathematically, and MATLAB follows that convention. That ‘vertex_segment’ was oriented in the opposite direction is also the reason I could not get my simulations to work, since all my ‘vectors’ matrices were also counter-clockwise.

.

Answer 2

[Mathieu NOE]

hello

I could not find any quiver issue (tried to reproduce it my way) , but at the end I suspected maybe you need to invert the data order (between azimut and elevation) when you use sph2cart (we don't know how your data angle_phi_theta is generated )

clear all
clc
close all
load angles.mat
load vertices.mat
% [vectors(:,1), vectors(:,2), vectors(:,3)] = sph2cart(angle_phi_theta(:,1), angle_phi_theta(:,2), 1);
[vectors(:,1), vectors(:,2), vectors(:,3)] = sph2cart(angle_phi_theta(:,2), angle_phi_theta(:,1), 1);

% TMW quiver 
figure
quiver(vertex_segment(:,1),vertex_segment(:,2),...
        vectors(:,1),vectors(:,2),0.8,'Color','green','LineWidth',1);hold on;

% alternative quiver 
figure
plot(vertex_segment(:,1),vertex_segment(:,2));
hold on;
scal_factor = 3;
for k = 1:numel(vectors(:,1))
    dx = vertex_segment(k,1)+ scal_factor*[0 vectors(k,1)];
    dy = vertex_segment(k,2)+ scal_factor*[0 vectors(k,2)];
    plot(dx,dy,'r');
end

        
% final plot 
figure
quiver3(vertex_segment(:,1),vertex_segment(:,2),vertex_segment(:,3),...
        vectors(:,1),vectors(:,2),vectors(:,3),0.8,'Color','green','LineWidth',1);hold on;
    quiver3(vectors(:,1),vectors(:,2),vectors(:,3),...
        vertex_segment(:,1),vertex_segment(:,2),vertex_segment(:,3),0.8,'Color','green','LineWidth',1);hold on;

[bird]

Thank you very much for your answer, but this is not the cause of my trouble, but I have found the real problem, I have already replied in the last answer, thank you again for your enthusiasm.