Motion Planning for Camera Movements in Virtual Environments

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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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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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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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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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Camera configurations

• Camera position - point in 3D
• Viewing direction - point in 3D
• Amount of roll - 1 parameter

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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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Approach

• Create probabilistic roadmap
• For each query, connect start and goal nodes
• Compute shortest path
• Smooth path
• Compute trajectory
• Shorten path
• Reduce number of segments
• Compute viewing direction

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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 td

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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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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 Dijkstras algorithm
• Complexity is O(VlogV)

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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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Smoothing the path (II)
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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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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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Computing viewing direction (I)

• Viewing direction should also be first order
  continuous
• Should indicate future motion
• At time t, look at position at time ttd
• Proved to be first order continuous
• Nearer in sharp turns and further in wide turns

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Computing viewing direction (II)
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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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Demo video 1
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Demo video 2
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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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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?