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Research

Welcome to Research, please leave a comment if any of the links are broken:

Transforms and Matrices:

  1. http://www.isner.com/Transform/IsnerTransformManip_04.htm
  2. http://en.wikipedia.org/wiki/Matrix_(mathematics)
  3. http://www.gamedev.net/reference/articles/article877.asp
  4. http://www.math.duke.edu/education/ccp/materials/linalg/lintrans/lint3.html
  5. http://www.senocular.com/flash/tutorials/transformmatrix/
  6. http://www.d3coy.com

Linear Algerbra:

  1. http://www.mathhelpforum.com/math-help/
  2. http://en.wikipedia.org/wiki/Law_of_cosines
  3. http://www.mathopenref.com/arclength.html
  4. http://liutaiomottola.com/formulae/sag.htm

Dynamics & Fluid Simulation:

  1. http://www.cs.ubc.ca/~rbridson/fluidsimulation/
  2. http://graphics.stanford.edu/~fedkiw/
  3. http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr.html#c5
  4. http://www.myphysicslab.com/

Trigonometry:

  1. http://www.clarku.edu/~djoyce/trig/
  2. http://en.wikipedia.org/wiki/Law_of_cosines

Physics, Constraints & Collision:

  1. http://www.teknikus.dk/tj/gdc2001.htm
  2. http://www.gamedev.net/reference/programming/features/verlet/
  3. http://compsci.ca/v3/viewtopic.php?t=14897

Curves & Surfaces:

  1. http://paulbourke.net/geometry/bezier/cubicbezier.html
  2. http://www.ibiblio.org/e-notes/Splines/Bspline.java
  3. http://www.ibiblio.org/e-notes/Splines/B-spline.htm
  4. http://www.ibiblio.org/e-notes/Splines/Cardinal.htm
  5. http://pages.cpsc.ucalgary.ca/~samavati/cpsc589/pdfs/surfaces.pdf

Waveforms, Harmonics and Oscillation:

  1. http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr.html
  2. http://www.myphysicslab.com/pendulum2.html#numerical
  3. http://www.haverford.edu/physics-astro/Teaching_websites/final/DDHO/
  4. http://homepages.gac.edu/~huber/fourier/index.html#DIRI

Inverse, Forward & Instantaneous Kinematics:

  1. http://graphics.cs.cmu.edu/nsp/course/15-464/Spring07/assignments/jlander_gamedev_nov98.pdf
  2. http://www.adventuresinstorytelling.com/VCK/VCK_abstract.pdf
  3. http://www.learnaboutrobots.com/inverseKinematics.htm
  4. http://www.euclideanspace.com/physics/kinematics/joints/index.htm

Quaternions:

  1. http://gregegan.customer.netspace.net.au/APPLETS/21/DiracNotes.html
  2. http://books.elsevier.com/companions/0120884003/vq/Belt-Trick/index.html
  3. http://www.math.nus.edu.sg/~matwyl/Paper/belttrick.pdf
  4. http://www.math.utah.edu/~palais/belt.html
  5. http://graphics.cs.uiuc.edu/~jch/papers/vqr.pdf
  6. http://www.isner.com/tutorials/quatSpells/quaternion_spells_14.htm
  7. http://isg.cs.tcd.ie/projects/DualQuaternions/

Motion Capture:

  1. http://www.cs.wisc.edu/graphics/Courses/cs-838-1999/Jeff/BVH.html
  2. http://www.dcs.shef.ac.uk/intranet/research/resmes/CS0111.pdf

Stereo  Vision, Photogrammetry etc:

  1. http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT11/node12.html
  2. http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/OWENS/LECT10/node3.html
  3. http://www8.cs.umu.se/kurser/TDBD19/VT05/epipolar-4.pdf
  4. http://www.cse.unr.edu/~bebis/CS791E/Notes/EpipolarGeonetry.pdf
Surface Capture:
  1. http://www.di3d.com/index.php

Augemented Reality:

  1. http://www.robots.ox.ac.uk/ActiveVision/Projects/index.html
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2 Comments

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  1. Ricardo #
    November 5, 2014

    I would like to know more about belt trick…could you give me more references.

    • November 5, 2014

      It essentially means double twisted belt can be unwound just by moving the ends, compared to a single twisted belt which can never be unwound by only moving the ends.
      The research can be found here: http://www.cs.indiana.edu/~hansona/quatvis/Belt-Trick/index.html

      And it’s also covered in a great book called ‘visualizing Quatetnions’ – your essentially creating a belt across the unit sphere with each slice along the belt representing a new coardinate frame – this means your actually interpolating through multiple quatetnions across the hyper sphere.

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