Better Rendering

Problem

Rendering particles as circles:

• looks noisy
• is physically inaccurate/misleading
• creates aliasing (especially at smaller resolutions)
• clobbers quality when video compression is used

Goal

• Use SPH to interpolate, then visualize
  • storing acceleration datastructure each frame takes too much memory
  • rendering each frame when simulating disallows responsive zooming/panning etc.
  • an SPH query per pixel is expensive

Solution

• particles are quads with side length \(4h\)
• instanciate a quad at each particle location
• give each quad a white texture with SPH kernel weight in alpha channel
  • Cubic Spline Kernel for \(h=1\) used: \(W(q) = \frac{5}{14\pi} \max(0, 2-q)^3 -4 \max(0, 1-q)^3\)
  • calculate pixel centre’s distance from texture centre: \(d\)
  • normalize to \(\hat{d} \in [0;\sqrt{2}]\)
  • for \(h=1\) in 2D the kernel support is \(2\) and \(W(0)=0.45\)
  • use \(r=255, g=255, b=255, \alpha = 255*\left\lfloor\frac{W(2\hat{d})}{0.45}\right\rfloor\)
• tint the texture according to particle velocity/density/etc in a material

\(\Longrightarrow\) abuse OpenGL to perform SPH sums!