1. Motion Planning for
Camera Movements in
Virtual Environments
By Dennis Nieuwenhuisen and Mark H. Overmars
In Proc. IEEE Int. Conf. on
Robotics and Automation 2004
Presented by Melvin Zhang
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2. Overview
 Motivation
 Related work
 Camera configurations
 Good cinematography
 Approach
 Handling the constraints
 Motion planning for camera movements
 Creating a roadmap
 Finding shortest path
 Computing camera speed
 Computing viewing direction
 Applications and experiments
 Summary
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3. Motivation
 Camera navigation in virtual
environments
 Computer games
 Architectural walkthrough
 Urban planning
 CAD model inspection
 Drawbacks of manual control
 Difficult
 Ugly motions
 Requires attention of user
 Solution: Specify start and goal
 Automatically generate smooth
collision free motion
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4. Related work
 Support motion generated by user
 Virtual sidewalk
 Speed of motion adapted automatically
 Computation of fixed camera positions
 Following a target
 Third person view
 Trajectory may not be known beforehand
 Similar to target tracking
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5. Camera configurations
 Camera position - point in 3D
 Viewing direction - point in 3D
 Amount of roll - 1 parameter
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6. Good cinematography
 Camera not too close to obstacles
 Horizon should be straight
 Lower speed when making sharp turns
 Speed as high as possible
 Visual cues to future movements
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7. Approach
1. Create probabilistic roadmap
2. For each query, connect start and goal nodes
3. Compute shortest path
4. Smooth path
5. Compute trajectory
6. Shorten path
7. Reduce number of segments
8. Compute viewing direction
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8. Handling the constraints
 Camera should not pass to close to obstacles
 Model camera as sphere
 Horizon should be straight
 Avoid rolling the camera
 Lower speed when making sharp turns
 Compute speed base on radius of turn
 Speed as high as possible
 Path should maximize speed of camera
 Visual cues to future movements
 Viewing direction of time t set to position in time t+d
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9. Creating a roadmap
 Consider camera as
sphere
 Generate collision
free camera positions
 Connect position c, c’
by checking if cylinder
is collision free
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10. Finding shortest path
 Wide turns may be preferred over sharp turns
 Use a penalty function, p(e,e’), which depends
on angle between e and e’
 Distance for e arriving from e’ is
p(e,e’) + length(e)
 Compute shortest path
using Dijkstra’s algorithm
 Complexity is O(|V|log|V|)
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11. Smoothing the path (I)
 Path consist of straight line segments
 Smooth path must be first order continuous
 Replace vertices along path with largest collision
free circular arc using binary search
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12. Smoothing the path (II)
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13. Computing camera speed
 Smooth path is not sufficient for
smooth motion
 Speed should also change in a
continuous way
 Max speed determined by arc radius
 Use max acceleration and
deceleration to find actual speed
 Backtrack deceleration to guarantee
bottom corner
 Accelerate maximally up to threshold or
new edge
 Complexity is linear in number of
segments and arcs on path
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14. Shortening the path
 As roadmap is coarse, shortest path in graph may be
shortened
 Pick two random configurations
 Check for collision free path between them
 Compute camera speed
 Accept if new time is lower
 Remove nearby nodes to reduce number of segments
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15. Computing viewing direction (I)
 Viewing direction should also be first order
continuous
 Should indicate future motion
 At time t, look at position at time t+td
 Proved to be first order continuous
 Nearer in sharp turns and further in wide turns
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16. Computing viewing direction (II)
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17. Applications and experiments
 Implemented in CAVE C++ library
 Figure on the left is scene of Rotterdam
 Preprocessing in 2D (fixed height) took 5s (Pentium 4, 2.4 Ghz)
 Query any pair of positions in 0.5s
 Figure on the right is model of a building
 Preprocessing in 3D took 8s
 Query any pair of positions in 0.5s
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18. Demo video 1
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19. Demo video 2
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20. Future work
 Generating “human” path
 Fixed height above ground
 Possibility of climbing starts/ladders
 Following target with known trajectory
 Account for obstacle occlusions of target
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21. Summary
 Contributions
 Novel application of PRM approach for planning camera motions
 Formulated constraints imposed by theory of cinematography
 Developed various smoothing techniques to achieve a smooth
trajectory
 Further improvements
 Penalty function p(e,e’) not defined, shortest path does not take
into account camera speed
 Collision check for circular arcs is time consuming, currently
approximate arcs using number of short line segments
 Path shortening needs to repeat adding of arcs and computing
speed diagram
 Approach base on iteratively applying several heuristics to
improve the path, difficult to judge amount of improvement
 Formulate path improvement as an optimization problem?
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