Barycentric coordinates and transfinite interpolation

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Non-convex curves? Angle formulation p ( x, θ) x θ For a convex curve, the MV interpolant is g(x) = ∫ 2π 0 / ∫ f (p(x, θ)) 2π ‖p(x, θ) − x‖ dθ 1 ‖p(x, θ) − x‖ dθ. 0
On arbitrary curves p ( x, θ) 2 p 3 ( x, θ) p 1 ( x, θ) x θ where g(x) = ∫ 2π 0 n(x,θ) ∑ j=1 φ(x) = Hormann: φ(x) > 0. / (−1) j−1 ‖p j (x, θ) − x‖ f (p j(x, θ)) dθ φ(x), ∫ 2π 0 n(x,θ) ∑ j=1 (−1) j−1 ‖p j (x, θ) − x‖ dθ.
Page 1 and 2: Barycentric coordinates and transfi
Page 3 and 4: Barycentric coordinates on a triang
Page 5 and 6: Properties ◮ Lagrange property:
Page 7 and 8: Properties ◮ Lagrange property:
Page 9 and 10: To find λ and µ: let a = v 00 −
Page 11 and 12: Proof: Meyer et al. 2002 Let A i =
Page 13 and 14: Application: barycentric mappings R
Page 15 and 16: Theorem (F. & Kosinka). Wachspress
Page 17 and 18: Proof: With e i = (v i − x)/‖v
Page 19 and 20: Transfinite interpolation, Warren e
Page 21: Examples of MV interpolants
Page 25 and 26: Application: mesh deformation, Ju,
Page 27 and 28: Method 1: weight function The cubic
Page 29 and 30: To use this construction we need to
Page 31 and 32: Method 2: radial minimization MV in
Page 33 and 34: Example of radial minimization

Barycentric coordinates and transfinite interpolation

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