In the previous chapter, we showed a heat map of a 2D Gaussian distribution with varying standard deviation over time. Now, we will continue with more advanced rendering of the same dataset in 3D and demonstrate the effectiveness of visualizing multi-dimensional data with OpenGL. The code base from the previous chapter will be modified to enable 3D rendering.
Instead of rendering the 2D Gaussian distribution function on a plane, we take the output of the Gaussian function as the z (height) value as follows:
Here A is the amplitude of the distribution centered at , and are the standard deviations (spread) of the distribution in the x and y directions. In our example, we will vary the spread of the distribution over time to change its shape in 3D. Additionally, we will apply a heat map to each vertex based on the height for better visualization effect.