# How to transform coordinates from OpenGL (3D) to Psychtoolbox (2D)

**URL:** <https://psychtoolbox.discourse.group/t/how-to-transform-coordinates-from-opengl-3d-to-psychtoolbox-2d/3750>\
**Category:** Programming Help\
**Created:** [March 16, 2021, 10:32am UTC](https://psychtoolbox.discourse.group/t/how-to-transform-coordinates-from-opengl-3d-to-psychtoolbox-2d/3750 "2021-03-16T10:32:55Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![Loomis](https://avatars.discourse-cdn.com/v4/letter/l/71e660/32.png) [@Loomis](https://psychtoolbox.discourse.group/u/Loomis)\
**Post date:** [March 16, 2021, 10:32am UTC](https://psychtoolbox.discourse.group/t/how-to-transform-coordinates-from-opengl-3d-to-psychtoolbox-2d/3750/1 "2021-03-16T10:32:55Z")

</div>

Hi, everyone,

The goal of my experimental program is to draw multiple moving cubes with simultaneous rotation and translation, which is adapted from the paradigm of Pylyshyn & Storm (1988) ([BJS: Basic MOT Demo](http://perception.yale.edu/Brian/demos/MOT-Basics.html)).

However, when I use PTB for programming, I encountered some difficult problems.

(1) I don’t know how to accurately detect the collision between cubes；  
(2) I don’t know how to transform the 3D coordinates of the cubes in OpenGL to the pixel coordinates of the window (note: My experiment needs to match the spatial position of the cubes to the position of mouse clicks).

This question is similar to this: [matlab - OpenGL 2D coordinates to Psychtoolbox (pixel) coordinates - Stack Overflow](https://stackoverflow.com/questions/43005282/opengl-2d-coordinates-to-psychtoolbox-pixel-coordinates).

PTB-INFO: Psychtoolbox-3 (Version 3.0.14 - Build date: Oct 3 2017) for Windows 10, under Matlab 2015b (64-Bit).

Demo code:

%% Initialization  
sca;close all;clearvars;  
PsychDefaultSetup(2);  
Screen(‘Preference’, ‘SkipSyncTests’, 2);  
InitializeMatlabOpenGL;  
screenid = max(Screen(‘Screens’));  
[window, windowRect] = PsychImaging(‘OpenWindow’, screenid, 0, [], 32, 2, [], 6, []);  
ifi = Screen(‘GetFlipInterval’, window);  
%% Start  
Screen(‘BeginOpenGL’, window);  
ar = windowRect(3) / windowRect(4); % width/height = aspect  
screenHeight = 30; % assume 30cm in height  
screenWidth = screenHeight \* ar;

% Enable lighting  
glEnable(GL.LIGHTING); % Enable lighting  
glEnable(GL.LIGHT0); % Define a local light source  
glEnable(GL.DEPTH\_TEST); % Enable proper occlusion handling via depth tests  
glMatrixMode(GL.PROJECTION); % set up a projection matrix  
glLoadIdentity;

% Calculate the FOV in the y direction assuming a distance to the objects of 100cm  
dist = 57;  
angle = 2 \* atand(screenHeight / dist);  
gluPerspective(angle, ar, 0.1, dist\*2); % defined FOV. Set up our perspective projection.  
glMatrixMode(GL.MODELVIEW); % Setup modelview matrix  
glLoadIdentity;  
glLightfv(GL.LIGHT0, GL.POSITION, [1 2 3 0]);

% Set camera  
cam = [0 0 0]; % Head position  
fix = [0 0 -1\*dist]; % Object position  
up = [0 1 0]; % Up orientation  
gluLookAt(cam(1), cam(2), cam(3), fix(1), fix(2), fix(3), up(1), up(2), up(3));

% color  
glClearColor(0, 0, 0, 0);  
glClear;  
glMaterialfv(GL.FRONT\_AND\_BACK,GL.AMBIENT\_AND\_DIFFUSE, [0.0 0.0 1.0 1]);  
Screen(‘EndOpenGL’, window);

%%  
% Setup the positions of the spheres using the mexhgrid command  
[cubeX, cubeY] = meshgrid(linspace(-25, 25, 2), linspace(-25, 25, 2));  
[s1, s2] = size(cubeX);  
cubeX = reshape(cubeX, 1, s1 \* s2);  
cubeY = reshape(cubeY, 1, s1 \* s2);

rotaY = rand(1, length(cubeX)) .\* 0;  
rotaZ = rand(1, length(cubeX)) .\* 0;

degPerSec = 180;  
degPerFrame = degPerSec \* ifi;  
vbl = Screen(‘Flip’, window);  
waitframes = 1;  
d = 0.1;  
ds = [d_ones(1,length(cubeX)/2), -d_ones(1,length(cubeX)/2)];  
%% Draw cubes  
while ~KbCheck  
Screen(‘BeginOpenGL’, window);  
glClear;  
for i = 1:length(cubeX)  
glPushMatrix;  
glTranslatef(cubeX(i), cubeY(i), -dist);  
glRotatef(rotaY(i), 0, 1, 0);  
glutSolidCube(2);  
glPopMatrix;  
HideCursor;  
end  
Screen(‘EndOpenGL’, window);  
vbl = Screen(‘Flip’, window, vbl + (waitframes - 0.5) \* ifi);  
rotaY = rotaY + degPerFrame;

```
if max(cubeX) - min(cubeX) <= 2 || max(cubeX) - min(cubeX) > 50
    ds = -ds;
end 
cubeX = cubeX + ds;

```

end  
sca;