Measuring Volumes with LASERs
Geometry & Trigonometry
Turn a grid of laser-measured heights into a volume estimate, the method behind LiDAR and self-driving cars.
Introduction
Laser rangefinders measure distance by timing how long a light pulse takes to return after reflecting off a surface, using the speed of light. Scanning a grid of points across an object gives a grid of heights, and from that grid you can estimate the object's volume using numerical integration - the same principle self-driving cars use to build a 3D picture of the world around them from LiDAR scans.
Guiding Questions
- A laser scanner measures distances to a surface. How do you turn distance readings into a 3D shape?
- Scan (or simulate scanning) a simple object on a grid and reconstruct its profile.
- Estimate the object's volume from your grid of heights using numerical integration.
- How does grid resolution affect the volume estimate? Find the coarsest grid that stays within 5%.