# Quick question on parametric coordinates of triangle...

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Suppose I have a 2D triangle.  It would have 3 vertices with 2D coordinates - (ua, va), (ub, vb), (uc, vc).

How could these be represented with parametric coordinates?

For example, if it was an equilateral triangle, what would the parametric coordinates be?

I've looked around for references but never find anything that can easily be applied to triangles.  Most people post guides on parametric equations and polar coordinates, which is a different topic.

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The points wouldn't be represented by parametric coords themselves; rather, they would be used to form the local basis, or frame of reference, for a coordinate system so that other points could be specified as parametric coords.

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Don't really understand the question... an equilateral triangle can have any number of points as its vertices, depending on the centre, the length of the sides, and the rotation of the vertices around the centre. One such parameterisation of the points is (a, 0), (a cos(120 degrees), a sin(120 degrees)), (a cos(-120 degrees), a sin (-120 degrees)) for an equilateral triangle centred on the origin with one vertex at (a, 0).

Are you looking for barycentric coordinates? http://en.wikipedia.org/wiki/Barycentric_coordinate_system

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