**Assignment 3: Volume Rendering and Neural Radiance Fields**

Student name: Kangle Deng


(##) Differentiable Volume Rendering
(###) Ray sampling

<img src="./imgs/grid.png">
<img src="./imgs/rays.png">

(###) Point sampling

<img src="./imgs/sample_points.png">

(###) Volume rendering

<img src="./imgs/part_1.gif">
<img src="./imgs/depth.png">


(##) Optimizing a basic implicit volume

(###) Loss and training

Box center: (0.25, 0.25, 0.00). 
Box side lengths: (2.00, 1.50, 1.50).

<img src="./imgs/part_2.gif">

(##) Optimizing a Neural Radiance Field (NeRF)

<img src="./imgs/part_3.gif">

(##) NeRF Extras

(###) View Dependence

<img src="./imgs/part_4_1.gif">

Notice that densities should not be view-dependent. Adding view dependence to color will improve the ability to model the specular effects, but will hurt the generalization for novel viewpoints to some extent.

(###) High Resolution Imagery

I trained the model with view dependence with 128, 256, 512 point samples per ray repectively. The training time scale linearly with the number of point samples.

Below are the results (128, 256, 512):

<img src="./imgs/part_4_3.gif">
<img src="./imgs/part_4_3_2.gif">
<img src="./imgs/part_4_3_3.gif">




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