A survey of curve and surface methods in CAGD

Polygonization of implicit surfaces

https://www.researchgate.net/file.PostFileLoader.html?id=5328aebdd5a3f2663d8b461f&assetKey=AS%3A273573887840257%401442236505726

The Bernstein polynomial basis: A centennial retrospective

A method is presented for representing botanical trees, given three-dimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A free-form surface connects branching limbs. "Blobby" techniques are used to model the tree trunk as a series of non-circular cross sections. Bark is simulated with a bump map digitized from real world bark; leaves are textures mapped onto simple surfaces.

Modeling the mighty maple

Barycentric coordinates are unique for triangles, but there are many possible generalizations to convex polygons. In this paper we derive sharp upper and lower bounds on all barycentric coordinates over convex polygons and use them to show that all such coordinates have the same continuous extension to the boundary. We then present a general approach for constructing such coordinates and use it to show that the Wachspress, mean value, and discrete harmonic coordinates all belong to a unifying one-parameter family of smooth three-point coordinates. We show that the only members of this family that are positive, and therefore barycentric, are the Wachspress and mean value ones. However, our general approach allows us to construct several sets of smooth five-point coordinates, which are positive and therefore barycentric.

/pdf/a-general-construction-of-barycentric-coordinates-over-4fchku2ewd.pdf

A general construction of barycentric coordinates over convex polygons

https://bura.brunel.ac.uk/bitstream/2438/2287/1/TR_07_81.pdf

Peter Charrot

Papers

A pentagonal surface patch for computer aided geometric design

A C1 triangular interpolation patch for computer-aided geometric design