# Research

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

Graphing:

Transforms and Matrices:

- http://en.wikipedia.org/wiki/Matrix_(mathematics)
- http://www.gamedev.net/reference/articles/article877.asp
- http://www.math.duke.edu/education/ccp/materials/linalg/lintrans/lint3.html
- http://www.senocular.com/flash/tutorials/transformmatrix/

Linear Algerbra:

- http://en.wikipedia.org/wiki/Law_of_cosines
- http://www.mathopenref.com/arclength.html
- http://liutaiomottola.com/formulae/sag.htm

Dynamics & Fluid Simulation:

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

Trigonometry:

Physics, Constraints & Collision:

Curves & Surfaces:

- http://paulbourke.net/miscellaneous/interpolation/
- http://www.ibiblio.org/e-notes/Splines/Bspline.java
- http://www.ibiblio.org/e-notes/Splines/B-spline.htm
- http://www.ibiblio.org/e-notes/Splines/Cardinal.htm

Waveforms, Harmonics and Oscillation:

- http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr.html
- http://www.myphysicslab.com/pendulum2.html#numerical
- http://homepages.gac.edu/~huber/fourier/index.html#DIRI

Inverse, Forward & Instantaneous Kinematics:

- http://graphics.cs.cmu.edu/nsp/course/15-464/Spring07/assignments/jlander_gamedev_nov98.pdf
- http://www.learnaboutrobots.com/inverseKinematics.htm
- http://www.euclideanspace.com/physics/kinematics/joints/index.htm
- http://www.andreasaristidou.com/FABRIK.html

Rotations:

Quaternions:

- http://gregegan.customer.netspace.net.au/APPLETS/21/DiracNotes.html
- http://www.math.nus.edu.sg/~matwyl/Paper/belttrick.pdf
- http://www.math.utah.edu/~palais/belt.html
- http://graphics.cs.uiuc.edu/~jch/papers/vqr.pdf

Motion Capture:

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

Stereo Â Vision, Photogrammetry etc:

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

Augemented Reality:

Gait Analysis:

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

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.