Barycentric coordinates and transfinite interpolation

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Application: curve deformation
Theorem (F. & Kosinka). Wachspress mappings are injective Idea of proof: express Jacobian as ∣ ∑ λ i λ j λ k ∣∣∣∣∣ J = 2 ∂ 1 λ i ∂ 1 λ j ∂ 1 λ k A(v i, ′ v j, ′ v k ′ 1≤i
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: Application: barycentric mappings R
Page 17 and 18: Proof: With e i = (v i − x)/‖v
Page 19 and 20: Transfinite interpolation, Warren e
Page 21 and 22: Examples of MV interpolants
Page 23 and 24: On arbitrary curves p ( x, θ) 2 p
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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