gradient computation

[ZhipengCai]

Hi, thanks for the great work. I have a question regarding to the gradient computation in

ngp_pl/models/csrc/volumerendering.cu

Lines 137 to 152 in e9d9c37

	// compute gradients by math...
	dL_drgbs[s][0] = dL_drgb[ray_idx][0]*w;
	dL_drgbs[s][1] = dL_drgb[ray_idx][1]*w;
	dL_drgbs[s][2] = dL_drgb[ray_idx][2]*w;
	dL_dsigmas[s] = deltas[s] * (
	dL_drgb[ray_idx][0]*(rgbs[s][0]*T-(R-r)) +
	dL_drgb[ray_idx][1]*(rgbs[s][1]*T-(G-g)) +
	dL_drgb[ray_idx][2]*(rgbs[s][2]*T-(B-b)) +
	dL_dopacity[ray_idx]*(1-O) +
	dL_ddepth[ray_idx]*(t*T-(D-d))
	);
	dL_drgb_bg[0] = dL_drgb[ray_idx][0]*(1-O);
	dL_drgb_bg[1] = dL_drgb[ray_idx][1]*(1-O);
	dL_drgb_bg[2] = dL_drgb[ray_idx][2]*(1-O);

Can you explain slightly on how you get the formula of dL_dsigmas[s]? i.e., why does
dL_dsigmas[s] = deltas[s] * (
dL_drgb[ray_idx][0](rgbs[s][0]T-(R-r)) +
dL_drgb[ray_idx][1](rgbs[s][1]T-(G-g)) +
dL_drgb[ray_idx][2](rgbs[s][2]T-(B-b)) +
dL_dopacity[ray_idx](1-O) +
dL_ddepth[ray_idx](t*T-(D-d))
)

[kwea123]

I have a simple writeup here. Feel free to ask any question if there is still any.
https://app.conceptboard.com/board/2hua-puao-fets-rpcd-x7no

[kwea123]

TODO: add note about gradient w.r.t. the weights that is added recently.

[jnhwkim]

@kwea123 I found that the definition of opacity is different in the ConceptBoard. Please take a look at my PR #133.