1. Motion Planning for Camera Movements in Virtual Environments Authors: D. Nieuwenhuisen, M. Overmars Presenter: David Camarillo

2. Introduction Manual Navigation in VE Difficult to do efficiently Can lead to disorientation and motion sickness Prevents operator from focusing on higher level task Automatic Navigation User only need specify goal position Smooth path generated according to cinematography

3. Theory of Cinematography Distance to prevent fear of collision Horizon maintained to prevent “drunk” view Lower speed in sharp turns Maximize camera speed to a bound Visual cues as to future directions

4. Strategy 1. Create PRM based only on position (pre- processed) 2. On query, add start (s) and goal (g) as nodes 3. Find path in roadmap with minimum time 4. Smooth path (continuous) 5. Compute time-trajectory (continuous) 6. Shorten path by randomly connecting nodes 7. Remove near nodes for fewer segments 8. Smooth viewing direction

5. Create Roadmap (PRM) Nodes are spheres to maintain halo Create random nodes Check for path to n nearest nodes Must have collision free cylinder On query, connect s and g as any other node

6. Find Path in Roadmap with Minimum Time Shortest distance has sharp turns that will take more time Cost function for an edge: Use Dijkstra’s shortest path algorithm Time O(n log(n))

7. Smooth Path Make 1 st order continuous (spatial derivative defined) Add circular arcs A collision free arc will always exist Binary search to find largest collision free arc Collision checking of arc computationally expensive

8. Smooth Path

9. Compute Time-Trajectory Max position speed should depend on curvature of path Experimentally determined s max (r) Want continuous trajectory, s(r) Use max acceleration and deceleration for speed graph Backtrack deceleration to guarantee bottom corner Accelerate maximally up to threshold or new edge

10. Shorten Path We now have continuous path from PRM Since coarse map, not shortest path Test shorter paths 1) Connect two random points on path 2) If collision free, add default circle arcs 3) Calculate speed diagram and compare 4) If improved, keep and calculate arc radii Results in too many edges (many speed changes) Remove close nodes

11. Smooth Viewing Direction Want viewing direction 1 st order continuous Time derivative defined Look at W(t+t d ) Continuity guaranteed Distance ahead depends on depends on speed Sharp turns look at nearer point

12. Implementation Movies http://robotics.stanford.edu/~latombe/cs 326/2004/class16/class16.htm Video 1 Video 2

13. Future Research Following human paths Third-person view with partially known trajectory Must account for obstacle occlusion