Signed Distance Functions Quiz

Answers and explanations appear as you take the quiz.

1. What does a signed distance function return for a given 3D point?
   • The distance to the nearest surface, with a sign for inside/outside
   • The color of the surface at that point
   • The number of triangles near that point
   • The brightness of the scene
2. Where is the actual surface of an SDF located?
   • Where the function is maximized
   • At the zero level set (distance equals zero)
   • Where the sign is always positive
   • At the center of the bounding box
3. Where does a true signed distance function satisfy the unit-gradient eikonal condition?
   • At every point, including all nonsmooth points
   • Only at the zero level set
   • At differentiable points, which is almost everywhere for common surfaces
   • Only outside the shape
4. How does sphere tracing use the SDF value?
   • It always steps by a tiny fixed amount
   • It steps backward to avoid the surface
   • It ignores the SDF and samples randomly
   • It steps forward by the SDF value, the safe distance to the nearest surface
5. What does DeepSDF use to represent a specific shape?
   • A compact latent code fed into a neural network
   • A full triangle mesh stored in memory
   • A single RGB image
   • A list of camera positions
6. What is one useful property of an SDF representation compared with a fixed triangle mesh?
   • It guarantees exact geometry regardless of training data or sampling
   • It is a continuous function that can be queried at chosen resolutions, subject to representation accuracy and compute
   • It always uses less memory than every possible mesh
   • It eliminates the need to compute surface normals
7. How can a signed distance function support robot collision checking?
   • It identifies the material composition of each obstacle
   • It predicts the robot's battery life from its pose
   • It gives a distance to nearby surfaces that can help determine clearance from obstacles
   • It converts a robot path into a camera image
8. In the NeuS reconstruction method, what representation is learned for a scene surface?
   • A fixed list of RGB colors with no geometry
   • An unordered set of camera exposure settings
   • A text caption for each image without a 3D representation
   • The surface is represented as the zero-level set of a neural signed distance function