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NUS CS5247 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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NUS CS52472 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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NUS CS52473 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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NUS CS52474 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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NUS CS52475 Camera configurations Camera position - point in 3D Viewing direction - point in 3D Amount of roll - 1 parameter

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NUS CS52476 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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NUS CS52477 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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NUS CS52478 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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NUS CS52479 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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NUS CS524710 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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NUS CS524711 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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NUS CS524712 Smoothing the path (II)

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NUS CS524713 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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NUS CS524714 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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NUS CS524715 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+t d Proved to be first order continuous Nearer in sharp turns and further in wide turns

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NUS CS524716 Computing viewing direction (II)

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NUS CS524717 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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NUS CS524718 Demo video 1

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NUS CS524719 Demo video 2

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NUS CS524720 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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NUS CS524721 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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