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?

Answer 1

Since shaders can work with 4 dimensional vectors and 4×4 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 4×4 matrix,
• a projection 4×4 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:

So we have:

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.