match the original cuda implementation

[Yang-Xijie]

• before:
  • Render pixels within kBoundsRadius_old = sqrt(2) * kBoundsRadius = 2.828.
• after:
  • Set kBoundsRadius _new = sqrt(2) * kBoundsRadius _old.
  • Render pixels within kBoundsRadius_new = 3.

The calculation of alpha keeps the same.

[scier]

I can see a small visual improvement in large splats, but there's also a performance penalty -- I'm seeing 3.5% or more on fragment-bound (high resolution or low splat count) scenes. Do you have any measurements of whether this quantitatively impacts visual quality (e.g. PSNR)?

[Yang-Xijie]

Since the 3DGS models are mainly derived from https://github.com/graphdeco-inria/diff-gaussian-rasterization, it will be better for the viewer to keep the same with the training forward pass.

The radius in the original CUDA implementation bounds the 99% confidence interval (3.0) of a 2D splat (https://github.com/graphdeco-inria/diff-gaussian-rasterization/blob/59f5f77e3ddbac3ed9db93ec2cfe99ed6c5d121d/cuda_rasterizer/forward.cu#L232), which has a specific meaning.

Since the radius is modified from 2.828 to 3.0, more fragments are created from single instance, therefore introducing a slight performance penalty.