title: How to interpolate and plot a 4-Dimensional hamburger?
body: <p>I have solved the heat equation in octave via finite difference and produced the following 3-D plot whose point colors correspond to the temperatures in each element of my three dimensional hamburger. </p>
  
  <p>My computational resources limit the resolution at which I may solve my burger. Thus the only way to get the plot I want is to make my scatter3 points huge blobs of color and it looks kind of bad. </p>
  
  <pre><code>[x,y,z] = meshgrid(1:nx,1:ny,1:nz)                       % Defines a grid to plot on
  scatter3(x(:), y(:), z(:), 40, burgermatrix(:), 's', 'filled')% Point color=value
  </code></pre>
  
  <p><a href="https://i.stack.imgur.com/xIKHg.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/xIKHg.png" alt="The Perfect Burger"></a></p>
  
  <p>What I want is a nice gorgeous smooth rectangular prism like this:</p>
  
  <p><a href="https://i.stack.imgur.com/L0gVr.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/L0gVr.png" alt="Prism"></a></p>
  
  <p>So I figure I need to somehow interpolate between the 3D points that I have. Can anyone help me figure out how to do this?</p>