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Question(b): Describe at least two different usages of braycentric coordinates in Computer Graphics applications.
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Barycentric coordinates systems are coordinate systems in which the locations of points is specified by reference to simplex.
Barycentric coordinates are used in computer graphics for many years, they have found useful applications in many area to bname a few:
Function interpolation,Surface smoothing,Simulation and ray intersection tests, Shading, Image warping
Due to the linear accuracy they offer, barycentric coordinates they are extensively used in the finite element applications.
Complex barycentric coordinates are especially useful for 2D shape and image deformation.
In a typical application scenario, the user defines a source contour, usually a polygon, and deforms it to a target contour by moving its
vertices.

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Source : 
Wikipedia: https://en.wikipedia.org/wiki/Barycentric_coordinate_system#Applications
Caltech : http://www.geometry.caltech.edu/pubs/MHBD02.pdf
Johns Hopkins University: https://www.cs.jhu.edu/~misha/ReadingSeminar/Papers/Weber09.pdf

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