**Assignment 4**

Student name: Gaurav Parmar

(#) 1. Sphere Tracing
The sphere tracing is implemented in the file renderer.py<br>
Sphere tracing iterative updates the estimate by using the current SDF value. 
The resulting gif of torus is shown below.
<table frame="vsides">
    <tbody><tr>
      <td valign="top"><img src="./part_1.gif"></td>
    </tr>
  </tbody>
</table>


(#) 2. Optimizing a Neural SDF
The MLP for the SDF is a 6 layer MLP with LeakyReLU activations. 
The final linear layer does not have this activation as the values can be negative. 
The eikonal loss encourages the norm of the gradient be close to 1.
The input (left) and final optimized surface (right) are shown below. 
<table frame="vsides">
    <tbody>
    <tr>
      <td valign="top"><img src="./part_2_input.gif"></td>
      <td valign="top"><img src="./part_2.gif"></td>
    </tr>
</tbody>
</table>


(#) 3. VolSDF
alpha: this represents the largest value of the density
beta: this reflects how fast the density will change when crossing the edge
1. A high beta value will stretch out the SDF
2. Learning the SDF will be easier if a high beta value is used
3. Conversely, a low beta value will likely learn a more accurate surface

I used the default values of alphs = beta = 10. The results are shown below
<table frame="vsides">
    <tbody>
    <tr>
      <td valign="top"><img src="./part_3_geometry.gif"></td>
      <td valign="top"><img src="./part_3.gif"></td>
    </tr>
</tbody>
</table>


(#) 4. Neural Surface Extras

(##) Rendering a Large Scene with Sphere Tracing
The scene below includes 25 objects. 
<table frame="vsides">
    <tbody><tr>
      <td valign="top"><img src="./part_4_1.gif"></td>
    </tr>
  </tbody>
</table>

(#) late days
I used 0 late days on this assigment.
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