Simulate the Motion Blur effect in PBRT - PowerPoint PPT Presentation

Loading...

PPT – Simulate the Motion Blur effect in PBRT PowerPoint presentation | free to view - id: f46a3-NWRlM



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Simulate the Motion Blur effect in PBRT

Description:

The basic idea is to interpolate the camera during the period of two timestamps, ... The cameras are interpolated along the track of the transformation from a ... – PowerPoint PPT presentation

Number of Views:299
Avg rating:3.0/5.0
Slides: 15
Provided by: jin153
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Simulate the Motion Blur effect in PBRT


1
Simulate the Motion Blur effect in PBRT
  • using quaternions

2
Motivation and goals
  • The motivation of choosing this topic is that I
    found the motion blur is a very common effect in
    photographing.
  • My goal for this project is to implement a new
    camera plug-in in PBRT named motionblur to
    simulate the motion blur effect.

3
The approach
  • The basic idea is to interpolate the camera
    during the period of two timestamps, one of which
    is the shutter opening time t0 and the other is
    the shutter closing time t1. The cameras are
    interpolated along the track of the
    transformation from a position on t0 to another
    position on t1.

4
The approach
  • A naive approach is linearly interpolating the
    components of the two transformation matrices
    individually, but this will not give the accurate
    result.
  • More sophisticated approaches
  • 1. Decompose the matrices into translation and
    rotation components, linearly interpolating the
    translation components, and interpolating the
    rotation with quaternions.
  • 2. Directly interpolating the matrices without
    decomposition, using Alexas method.

5
The approach
  • The decomposition approach is used and
    implemented in this project
  • For the translation components, the linear
    interpolation is used
  • Let M0 and M1 be the transformation matrices of
    camera at shutter opening time and shutter
    closing time respectively, the translation
    components for M0 are M003, M013 and
    M023, the translation components for M1 are
    M103, M113 and M123.
  • Let M be the matrix interpolated between M0 and
    M1 at time t, where t0 lt t lt t1 and t0 0,
    t1 1, the linear interpolation of translation
    components are
  • M03 (1 t) M003 t M103
  • M13 (1 t) M013 t M113
  • M23 (1 t) M023 t M123

6
The approach
  • For the rotation, a new concept called
    quaternion is used
  • Definitions of quaternion

7
The approach
  • Convert the matrices into unit quaternions
  • First, transfer the rotation components of the
    transformation matrices M0 and M1 into matrices
    in orthogonal system and normalize them to get
    M0 and M1. For example
  • // normalize x
  • M000 M000/sqrt(M0002 M0012
    M0022 )
  • M001 M001/sqrt(M0002 M0012
    M0022 )
  • M002 M002/sqrt(M0002 M0012
    M0022 )
  • // y z cross x
  • M010 M021M002 -
    M022M001
  • M011 M022M000 -
    M020M002
  • M012 M020M001 -
    M021M000
  • // normalize y
  • M010 M010/sqrt(M0102 M0112
    M0122 )
  • M011 M011/sqrt(M0102 M0112
    M0122 )
  • M012 M012/sqrt(M0102 M0112
    M0122 )
  • // z x cross y
  • M020 M001M012 -
    M002M011
  • M021 M002M010 -
    M000M012
  • M022 M000M011 -
    M001M010
  • // normalize z

8
The approach
  • Then convert M0 and M1 into quaternions Q0
    and Q1, take M0 for example
  • Let Q0 (x, y, z), w
  • Q0.w 0.5sqrt(M000 M011
    M022 1.0)
  • Q0.x (M021 - M012)/(4 Q0.w)
  • Q0.y (M002 - M020)/(4 Q0.w)
  • Q0.z (M010 - M001)/(4 Q0.w)
  • Interpolate the quaternions
  • Let Q be the quaternion interpolated between Q0
    and Q1 at time t
  • Q Q0(sinO(1-t)/sinO) Q1(sinOt/sinO), where
    cosOQ0Q1.
  • Transfer quaternion Q (x, y, z), w back to
    transformation matrix Q
  • Finally, combine the translation components and
    rotation components together to get the
    transformation matrix that should be interpolated
    at time t.

9
The literatures
  • Cook R. L., Porter T., Carpenter L. Distributed
    Ray Tracing
  • Ken Shoemake Quaternions
  • Marc Alexa Linear Combination of Transformations
  • Matt Pharr Greg Humphreys Physically Based
    Rendering

10
Results
Translation
Scene of motion blur using decomposition approach
Scene of motion blur using naïve approach
Scene at shutter open time
Scene at shutter close time
11
Results
Rotation
Scene of motion blur using decomposition approach
Scene of motion blur using naïve approach
Scene at shutter open time
Scene at shutter close time
12
Critical Evaluation
  • The most significant problem for this project is
    how to interpolate the rotation components
    accurately. Shoemakes paper about quaternion is
    helpful to deal with this problem. I read the
    paper to understand why the quaternions are
    suitable to solve the interpolation of the
    rotation
  • Another difficulty is that when converting the
    matrices into quaternions, the map the rotation
    components in of the matrices into an orthogonal
    system first, and normalize the components along
    x, y, z axis, then they can be convert to
    quaternions using the equation mentioned above.
    Otherwise, the result will not be correct. In my
    implementation, I use a method named
    orthoNomalize to deal with it. I also wrote a
    quaternion class and overload some operator to
    deal with calculation of quaternions.

13
Critical Evaluation Critical Evaluation
  • The drawback of the approach is that we need to
    decompose the matrices into translation and
    rotation components which results with lots of
    work, also transferring between matrix and
    quaternion is complicated. Alexas paper provides
    another solution to interpolate between matrices
    directly. However, I failed to implement it due
    to the incorrect results of implementing the
    logarithm of matrix.

14
Demo
About PowerShow.com