Free Form Interactive Design
CCV RELATED PUBLICATIONS

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G. Xu, H. Huarng, C. Bajaj
C1 Modeling with A-patches from Rational Travariate Functions (ps) (pdf)

C. Bajaj, J. Chen, G. Xu
"Modeling with Cubic A-patches''
ACM Transactions on Graphics, 14, 2, April,(1995), 103-133.
Proceedings: Graphics Interface '94, (1994), Vancouver, Canada, Canadian Information Processing Society, 174-191. 0. (Presented as: "Free-Form Surface Design with A-Patches") ( ps.gz ) (pdf )

Rational A-Patch
We approximate a manifold triangulation in IR3 using smooth implicit algebraic surface patches, which we call A-patches. Here each A-patch is a real iso-contour of a trivariate rational function defined within a tetrahedron. The rational trivariate function provides increased degrees of freedom so that the number of surface patches needed for free-form shape modeling is significantly reduced compared to earlier similar approaches. Furthermore, the surface patches have quadratic precision, that is they exactly recover quadratic surfaces. We give conditions under which a C1 smooth and single sheeted surface patch is isolated from the multiple sheets.
Triangular A-Patch
Of these sets the first image is polygon the second is smooth
Our approach is to model a smooth surface from a surface triangulation by implicit triangular surface patches which are subsets of zero contours of trivariate functions defined as a collection of irregular triangular prisms. Comparing with the earlier approaches of modeling by implicit surfaces, this scheme uses fewer patches, and can easily capture sharp features. The construction is adaptive in recovering the detail structures.

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