Barycentric coordinates and transfinite interpolation

More documents

Recommendations

Info

Hermite <strong>interpolation</strong> Two methods: ◮ Use MV weight function (with Chris Dyken / Solveig Bruvoll) ◮ Radial minimization (with Christian Schulz)
Method 1: weight function The cubic interpolant p to the data f (0), f ′ (0), f (1), f ′ (1), can be expressed as p(x) = g 0 (x) + ψ(x)g 1 (x), where g 0 (x) = (1 − x)f (0) + xf (1), ψ(x) = x(1 − x), g 1 (x) = (1 − x)m 0 + xm 1 , <strong>and</strong> m 0 = f ′ (0) − f (1) + f (0), m 1 = −f ′ (1) + f (1) − f (0).
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 and 22: Examples of MV interpolants
Page 23 and 24: On arbitrary curves p ( x, θ) 2 p
Page 25: Application: mesh deformation, Ju,
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?