无法为 2D 点动画创建第 3 维

Question

I have a code that animates dots moving in random directions in a 2D space (x and y axis). I tried to create a 3rd dimension (z axis) using spherical coordinates In order to draw and display the dots in a 3D space, I used the Psychtoolbox function moglDrawDots3D, as it takes 3d coordinates XYZ, but I am still getting a 2D animation, the dots on the z don't appear. I have no clue on the cause. I am very new to Matlab and animations, I'd be very grateful to get your feedback and insight. I tried to explain my code step by step below for the sake of clarity. Thank you in advance for your help!

PS: The use of the Psychtoolbox is not a necessity, if you have any other solution, I'd be happy to try it out.

AssertOpenGL;
InitializeMatlabOpenGL;
display = OpenWindow()
dots.nDots = 531;                       % number of dots
dots.color = [255,255,255];             % color of the dots
dots.size = 10;                         % size of dots (pixels)
dots.center = [0,0,0];                  % center of the field of dots (x,y,z)
dots.apertureSize = [50.8,28.5,50.8];   % size of rectangular aperture [w,h,depth] in degrees

First, random position within the aperture for each of the dots. 'dots.x' and 'dots.y' will hold the x and y positions for each dot.

[dots.x,dots.y,dots.z] = CreateUniformDotsIn3DFrustum(dots.nDots, 25, 1/screen_ratio, 0.1, 100);  

Then I converted these dot positions from a visual angle into pixel coordinates using a created function 'angle2pix'

tmp = Screen('Resolution',0);                       % (1) Screen's 'Resolution' function determine the screen resolution.
display.resolution = [tmp.width,tmp.height];
display.width = 50.8;                               % (2) Width of the screen in cm.
display.dist = 50;                                  % (3) Distance of the screen from the observer in cm.     

This generates pixel positions, but they're centered at [0,0], which is the top left corner

pixpos.x = angle2pix(display,dots.x);               % Convert the x position of the dots from visual angle to pixel.
pixpos.y = angle2pix(display,dots.y);               % Convert the y position of the dots from visual angle to pixel.
pixpos.z = ones(1, dots.nDots) * -1;               

I defined some timing and motion parameters for the animation

dots.speed = 3;                             % degrees/second
dots.duration = 10;                         % seconds                                                         
dots.theta_deg = randi(360,1,dots.nDots);   % degrees 
dots.phi_deg = 30;                          % degrees 
dots.theta_rad = dots.theta_deg * pi /180;  % direction converted to radians
dots.phi_rad = dots.phi_deg * pi /180;      % direction converted to radians                                                   

I calculated the distance travelled by the dot, by determining the x,y and z positions using spherical coordinates and then their derivate.

dx = dots.speed* sin(-dots.phi_rad-dots.theta_rad)/display.frameRate;
dy = -dots.speed* cos(dots.phi_rad + dots.theta_rad)/display.frameRate;
dz = -dots.speed*cos(dots.theta_rad)/display.frameRate; 

I try to fit the dots within the aperture by calculating the left, right top, bottom and depth(forward and backward) of the aperture (in degrees)

The total number of frames for the animation is determined by the duration (seconds) multiplied by the frame rate (frames/second). The function secs2frames performs the calculation

nFrames = secs2frames(display,dots.duration);

l = dots.center(1)-dots.apertureSize(1)/2;
r = dots.center(1)+dots.apertureSize(1)/2;
b = dots.center(2)-dots.apertureSize(2)/2;
t = dots.center(2)+dots.apertureSize(2)/2;
d_forward = dots.center(3)- dots.apertureSize(3)/2;
d_backward = dots.center(3)+ dots.apertureSize(3)/2;

New random starting positions

[dots.x,dots.y,dots.z] = CreateUniformDotsIn3DFrustum(dots.nDots, 25, 1/screen_ratio, 0.1, 100);   

Make the dots move

try

    for i=1:nFrames

        %convert from degrees to screen pixels     
        pixpos.x = angle2pix(display,dots.x)+ display.resolution(1)/2;
        pixpos.y = angle2pix(display,dots.y)+ display.resolution(2)/2;
        pixpos.z = ones(1, dots.nDots) * -1;

        moglDrawDots3D(display.windowPtr, [pixpos.x;pixpos.y;pixpos.z],dots.size, dots.color, dots.center,1);

update the dot position

        dots.x = dots.x + dx;
        dots.y = dots.y + dy;    
        dots.z = dots.z + dz;   

Move the dots that are outside the aperture back one aperture width

     dots.x(dots.x<l) = dots.x(dots.x<l) + dots.apertureSize(1);
        dots.x(dots.x>r) = dots.x(dots.x>r) - dots.apertureSize(1);
        dots.y(dots.y<b) = dots.y(dots.y<b) + dots.apertureSize(2);
        dots.y(dots.y>t) = dots.y(dots.y>t) - dots.apertureSize(2);
        dots.z(dots.z<d_forward) = dots.z(dots.z<d_forward) + dots.apertureSize(3);
        dots.z(dots.z>d_backward) = dots.z(dots.z>d_backward) - dots.apertureSize(3);
        Screen('Flip',display.windowPtr);
    end

catch ME
    Screen('CloseAll');
    rethrow(ME)
end
Screen('CloseAll');                                                                    

Answer 1

You asked for a suggestion on how to do this differently, so here's a demonstration of a simple 3D animation:

function q56758294
%% Generate some data
N_OBJS = 20;
P = rand(N_OBJS,3) .* ones(1,1,3);

%% Create the figure
figure(); 
hP(1) = plot3(P(:,1,1), P(:,2,1), P(:,3,1), 's', 'Color', [0 0 0]+0.8); hold on;
hP(2) = plot3(P(:,1,2), P(:,2,2), P(:,3,2), 's', 'Color', [0 0 0]+0.6);
hP(3) = plot3(P(:,1,3), P(:,2,3), P(:,3,3), 's', 'Color', [0 0 0]);
AX_LIMS = [-1 1]*3;
drawnow; set(gca, 'XLim', AX_LIMS, 'YLim', AX_LIMS, 'ZLim', AX_LIMS); grid on;

%% Animate:
FPS = 12;
for ind1 = 1:500
  % Update coordinates:
  dP = randn(N_OBJS,3)*0.1;
  P(:,:,1) = P(:,:,2);
  P(:,:,2) = P(:,:,3);
  P(:,:,3) = P(:,:,3) + dP;
  
  % Update plot objects:
  for ind2 = 1:3
    set( hP(ind2), 'XData', P(:,1,ind2), 'YData', P(:,2,ind2), 'ZData', P(:,3,ind2) );
  end
  
  pause(FPS^-1);
end

Which results in:

---

If you want white circles on a black background, replace the figure creation code with the following:

figure('Color', 'k'); 
hP(1) = plot3(P(:,1,1), P(:,2,1), P(:,3,1), '.', 'Color', [0 0 0]+0.2, 'MarkerSize', 20); hold on;
hP(2) = plot3(P(:,1,2), P(:,2,2), P(:,3,2), '.', 'Color', [0 0 0]+0.4, 'MarkerSize', 20);
hP(3) = plot3(P(:,1,3), P(:,2,3), P(:,3,3), '.', 'Color', [0 0 0]+1.0, 'MarkerSize', 20);
AX_LIMS = [-1 1]*3;
drawnow; set(gca, 'XLim', AX_LIMS, 'YLim', AX_LIMS, 'ZLim', AX_LIMS, 'Color', 'k',...
  'XColor', 'k', 'YColor', 'k', 'ZColor', 'k');

Which then results in:

---

To export a plot as a movie file, you would need to use getframe inside the loop, and then use VideoWriter as explained in this example .

Also, I've added the "trails" for aesthetic purposes, but these are easy to remove if you don't need them.