BSc Hons Computer Games Technology CMPCD2035 Computer Animation

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BSc (Hons) Computer Games TechnologyCMPCD2035
Computer Animation Maths for 3D Computer Games

• Dr Dave Pountney (room 611c)D.C.Pountney_at_livjm.ac
  .uk
• Abdennour El Rhalibi (room 723)
• A.Elrhalibi_at_livjm.ac.uk

School of Computing and Mathematical Sciences
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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• Maths Animation and Games
• Games involve Modelling and RT or pre-rendered
  Animation
• Camera motion
• Walking Characters
• Moving rigid object (car, ball, missile, etc)
• Flexible and soft object animation
• Object deforming or breaking
• Explosion, fire, particles
• Etc
• Object and characters in game and animation
  change some of their attributes over time in a 3D
  space
• Position / orientation
• Shape
• Colour
• Velocity, etc
• Maths allows you these represent these
  attributes, and other parameters with a concise
  notation and enable to apply operators
  (algorithms/programme) to achieve these changes
• Coordinate systems, point, angle vectors,
  matrices, space representation (matrix, Euler,
  Quaternion), curve and surfaces, equations, etc
• Trigonometry operators, matrix calculation,
  transform, interpolation techniques, numerical
  approximation, etc

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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• 3D Maths, Animation and Games Examples

Path following with approximation Techniques for
position and orientation
Calculating trajectory using force and
Intersection
Interpolation and soft objects
Path following and FK
Interpolation or simple path following
Rigid body physics, path following, and with
collision and response
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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• 3D Maths, Animation and Games Example

Interpolation and soft objects
20,000 particles in a galaxy-forming gravitation
simulation
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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• Aims
• Use matrix algebra to perform basic spatial
  transformations in 3-D.
• Use vectors to solve ray problems in computer
  graphics.
• Perform numerical methods such as interpolation.
• To use mathematical software and/or a programming
  language to perform all of the above (Derive)
• To storyboard, compose, and to render an animated
  sequence.
• Explain various animation techniques to produce
  motion for an animated sequence based on
  interpolation techniques.
• Implement animation techniques and interpolation
  algorithms using modern programming language.
• Use of 3D animation software tools (for example
  3DSMax or 3Dcanvas) to produce motion for an
  animated sequence.

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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• Syllabus
• 1. Geometry 3-D coordinate systems, vector
  algebra and vector geometry of lines, planes and
  surfaces in 3-D. Intersections of objects.
• 2. Linear algebra determinants, inverse,
  transpose, solutions of systems of equations
  matrix transformations in 3-D space. Changes of
  axes.
• 3. Interpolation Approximating Curves
  Patches linear cubic interpolation, splines,
  Bezier curves, B-splines, surface patches.
• 4. Numerical simulation of motion Euler,
  Runge-Kutta methods (applied to sports simulation
  problems).
• Use of mathematical software and algorithms to
  solve problems in each topic above.
• Computer Animation Background and History.
• Principle of Animation (2D, 3D Animation) and
  Computer Animation Software.
• StoryBoarding, scene composition and rendering.
• Real-Time vs. single Frame Animation.
• Animation Hardware.
• Display Pipeline, Matrix Transformation and
  Interpolation.
• Keyframing/Track-based Animation.
• Physics Based Animation Camera Animation, Path
  Following, Rigid Body Animation, Kinematic,
  ,....
• Emergent Behavioural Animation for example-
  Particle and flocks, plant growth.
• Use of 3D modelling tools and Opengl to apply
  some of the topics above

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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• Assessment
• Examination 40 Examination Three hours
  written exam. 3(hrs)
• Coursework 30 Coursework A Substantive piece
  of cw using DERIVE.
• Coursework 30 Coursework Group work covers
  Project using a 3D Animation Software or a
  Animation Programming task.

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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• Reading List selected Chapters from
• 3D Games Real-Time Rendering and Software
  Technology, Volume 1, by Alan Watt, Fabio
  Policarpo, Publisher Pearson Addison Wesley,
  2003
• 3D Games, Vol. 2 Animation and Advanced
  Real-Time Rendering, by Alan Watt, Fabio
  Policarpo, Publisher Pearson Addison Wesley,
  2003
• Lengyel E, (2002) Maths for 3-D Game Programming
  Computer graphics. Charles River Media Inc.
• Boardman, Ted (2001) '3D Studio MAX 4
  Fundamentals' New Riders
• Watt, Alan. Watt, Mark. (1992) 'Animation and
  Rendering Techniques, Theory and Practice'
  Addison- Wesley
• Kerlow, Issac Victor. (2000) 'The Art of 3-D
  Computer Animation and Imaging' Van Nostrand
  Reinhold
• Parent, Rick (2001) 'Computer Animation
  Algorithms and Techniques' Morgan - Kaufmann

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COMPUTER ANIMATION AND MATHEMATICS FOR 3-D
COMPUTER GAMES

• Reading List selected Chapters from

Some Course Textbook
Computer Animation Algorithms and
Techniques 1st Edition Rick Parent Published by
Morgan Kaufmann
3D Games Real-Time Rendering and Software
Technology, Volume 1 Allan Watt and Fabio
Policarpo Hardcover Edition
http//activeweb.livjm.ac.uk/modcat/ http//cwis.l
ivjm.ac.uk/timetables/