p = a + β(b − a) + γ(c − a) refers to what?

p = a + β(b − a) + γ(c − a) refers to what?



In a Barycentric Coordinate System, p is any point on the plane.

(β,γ) represents its coordinates, because a is the "origin" b-a is an axis/vector, and c-a is the other.

Note that we can reorder the terms in p = a + β(b − a) + γ(c − a) to get
p = (1 − β − γ)a + βb+ γc

Often people define a new variable α to improve the symmetry of the equations: α ≡ 1 − β −γ which yields the equation:
p(α, β, γ) = αa+ βb+ γc, with the constraint that
α + β + γ =1

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