Triangular Bernstein-Bézier patches

Computer Aided Geometric Design

Volumn 3, Issue 2, 1986, Pages 83-127

  Farin, Gerald ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Bernstein polynomials; B zier methods; scattered data interpolation; triangular schemes

Indexed keywords

EID: 46149129389     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-8396(86)90016-6     Document Type: Review

References (75)

1. A trivariate Clough-Tocher scheme for tetrahedral data
2. 2 Clough-Tocher scheme
3. On the dimension of piecewise polynomial functions
4. A case study of multivariate piecewise polynomials
5. Smooth interpolation in triangles
6. Representation and approximation of surfaces
7. Surfaces in computer aided geometric design: a survey with new results
8. 1 quintic interpolation over triangles: two explicit representations
9. The ß-spline: a local representation based on shape parameters and fundamental geometric measures
10. Multivariate spline algorithms
11. Letter to the Editor
12. A survey of curve and surface methods in CAGD
13. B-net basics
14. Construction of Bézier points of quadrilaterals from those of triangles
15. A new proof for the convexity of the Bernstein-Bézier surfaces over triangles
16. An improved condition for the convexity of Bernstein-Bézier polynomials over triangles
17. Convexity and variation diminishing property of Bernstein polynomials over triangles
18. On bivariate vertex splines
19. Subdivision algorithms for the generation of box spline surfaces
20. Subsplines über Dreiecken
21. r polynomials
22. Smooth interpolation to scattered 3D data
23. 1 continuity of polynomial surface patches
24. A modified Clough-Tocher interpolant
25. 1 surface strips
26. Triangular spline interpolation/Generalized triangular splines
27. Subdivision algorithms for Bézier triangles
28. Variation diminishing properties of Bernstein polynomials over triangles
29. Piecewise interpolation theory and finite element analysis
30. Geometry cells and surface definition by finite elements
31. Techniques for Visual Continuity
32. Smooth closed surfaces with discrete triangular interpolants
33. Synthesis methods of curves and surfaces in interactive CAD
34. Assembling triangular and rectangular patches and multivariate splines
35. Continuity of curvature between adjacent Bézier patches
36. A geometric proof of the variation diminishing property of B-spline approximation
37. A visually continuous, transfinite triangular interpolant
38. On cubic and quartic Clough-Tocher elements
39. Adaptive contouring of three-dimensional surfaces
40. Adaptive contouring of a trivariate interpolant
41. Tangent plane continuity between triangular Bézier patches
42. Piecewise quadratic surface fitting for contour plotting
43. Piecewise quadratic approximation on triangles
44. Unterteilungsalgorithmen für multivariate splines
45. Simple concepts don't work as the definition of variation diminishing
46. Multivariate interpolation
47. Geometric continuity: A parametrization independent measure of continuity for CAGD
48. The use of piecewise forms for the numerical representation of shape
49. Bases de Bernstein et approximants splines
50. k
51. 1-Flächen zur Interpolation unregelmässig verteilter Daten
52. A comparison of three curve intersection algorithms
53. Mehrfach differenzierbare Bézierkurven und Bézierflächen
54. 2 interpolant over triangles
55. The positivity and convexity for Bernstein polynomials over triangles
56. Interpolation polynomials on the triangle