Barycentric coordinates and transfinite interpolation

More documents

Recommendations

Info

In this talk: 1. Barycentric coordinates 2. Generalization to polygons: Wachspress, mean value, etc. 3. Transfinite interpolation
Barycentric coordinates on a triangle v 3 T x v 1 v 2 Given x ∈ T , want λ 1 , λ 2 , λ 3 ≥ 0 such that λ 1 + λ 2 + λ 3 = 1, and λ 1 v 1 + λ 2 v 2 + λ 3 v 3 = x.
Page 1: Barycentric coordinates and transfi
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 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

Create successful ePaper yourself

Delete template?

Save as template?