Using OpenGL shaders to plot 4D points in 2D in C++

Question

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Visualising 4D objects in OpenGL

I have a set of 4 dimensional data points (lets call the dimensions X,Y,A, and B) that I'd like to plot in 6 different 2d plots (plot XxY, XxA, XxB, YxA, etc...).

In a previous question I asked about the proper way to store and plot this data. The solution was to use a VBO that stored the 4 dimensional vertices. Then using different vertex shaders I could select which dimensions are plotted in each of the 2d plots.

I've spent a few weeks looking around for openGL tutorials on how to do this but I haven't yet found something that makes sense.

My question is this: In c++, how can I define a shader that would allow me to plot only 2 dimensions of a 4 dimensional point in a VBO, and do I need to define a single shader for all 6 2d plots or do I need a shader for each of 6 different plots?

Finally how do I incorporate the shader into the plotting code so it gets used by openGL?

maybe, but I'm asking specifically how to do this with shaders whereas the other link is asking for a library. — slayton, Sep 28 '11 at 17:19
The algebra is the same either way. You might as well ask "how do I plot a point using OpenGL shaders" — spraff, Sep 28 '11 at 17:38
Points have 3 dimensions - not 4. So, what is your question? — BЈовић, Sep 28 '11 at 18:04
@VJo: Three-dimensional points have three dimensions, sure. Four-dimensional points will have four. — GManNickG, Sep 28 '11 at 18:35
Write down the vector equations without referring to the number of dimensions: it works in equally for any dimensionality. — spraff, Oct 04 '11 at 08:15

score 3 · Accepted Answer · answered Sep 28 '11 at 17:50

Since shaders can work with 4 dimensional vectors and 4x4 matrix, we can be smart and use only one vertex shader to do the trick. This shader will take three inputs:

the point data (a 4 floating vector),
a selection 4x4 matrix,
a projection 4x4 matrix.

All the magic is done by the selection matrix, which will map you 4 coordinates vector to planar coordinates. Let's call the point data v, the selection matrix S and P the projection matrix. The output of the vertex shader will be:

P * S * v

By setting correctly the coefficients of S, you will be able to select which component in v should appear in the result. For example, if you want to display YxB, then S will be:

S matrix

So we have:

enter image description here

P is a standard projection matrix, which will help you to place your graph correctly (offsets and scale).

Following is an example of vertex shader implementation (not tested, may contain mistakes) for OpenGl3:

#version 130

in vec4 vin;
uniform mat4 s;
uniform mat4 p;

out vec4 vout;

void main()
{
    vec4 tmp = s * vin;

    // Depending on your projection matrix,
    // you may force the 4th component to 1.
    tmp[3] = 1;

    vout = p * tmp;
}

Notes: glUniformMatrix4fv is the function to use to define S and P.

Of course, you might want to premultiply (`P * S`), instead of using two separate uniforms. — Ben Voigt, Sep 28 '11 at 18:20

score 0 · Answer 2 · answered Sep 28 '11 at 18:01

You have this input:

in vec4 Points;

You can access to vec4 components by indexing them:

Point[0]; // Equals Point.x

You can supply the following uniforms to specify which components to use for plotting:

uniform int XCoordIndex;
uniform int YCoordIndex;

gl_Position = vec4(Point[XCoordIndex], Point[YCoordIndex], 0.0, 1.0)

Using OpenGL shaders to plot 4D points in 2D in C++

2 Answers2