Assignment 4

1. Sphere Tracing (30pts)

Given origins, directions, and a SDF.

1. For each point that doesn't intersect with the implicit surface, query the SDF to get the distance f(p) to the closest surface.
2. If the distance is less than the threshold, mark the point as an intersected point.
3. Update the position of the unintersected point by moving f(p) along the given direction.
4. Repeat step 1 to step 3 until all points are marked as intersections or the max number of iterations is reached.

2. Optimizing a Neural SDF (30pts)

MLP:

1. Positional encoder to encode point positions (Harmonic Embedding).
2. Six linear layers following the Softplus activation function with beta = 100.
3. One linear layer without activation function to predict the distance.

Eikonal loss: MSE loss between the gradients and 1.

3. VolSDF (30 pts)

Alpha controls the constant density of the object and beta controls how smoothly density decreases near the object’s boundary.

1. How does high beta bias your learned SDF? What about low beta?

   High beta makes the reconstructions look blurred and low beta looks better.

2. Would an SDF be easier to train with volume rendering and low beta or high beta? Why?

   High one. Because an SDF with high beta will have a smooth density boundary which is easier to learn.

3. Would you be more likely to learn an accurate surface with high beta or low beta? Why?

   Low one. Because an SDF with low beta could have a clear and sharp boundary when it transforms to density. Then a more accurate surface can be optimized due to the stronger constraints.

alpha = 10.0 beta = 0.05

4. Neural Surface Extras (CHOOSE ONE! More than one is extra credit)

4.1. Render a Large Scene with Sphere Tracing (10 pts)

The scene consists of a sphere of radius 1.0 centered at (0, 0, 0), and 14 boxes of side length 0.5, and 6 toruses with R=0.25 and r = 0.1.