Abstract We show that a sufficiently general hypersurface of degree d in $\mathbb {P}^n$ admits toric Gröbner degeneration after linear change coordinates if and only $d\leq 2n-1$ .

In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. are characterized by a functional relation between principal curvatures that implicitly defines approximate local congruences on the surface. These symmetries can be exploited to simplify surface paneling of double-curved architectural skins through mold re-use. We prese...

In this paper we will classify those translation surfaces in E involving polynomials which are Weingarten surfaces. Mathematics Subject Classification (2000): 53A05, 53A10.

We present a compact formulation of the orthogonal Weingarten formula, with the traditional quantity I(i1, . . . , i2k : j1, . . . , j2k) = ∫ On ui1j1 . . . ui2kj2k du replaced by the more advanced quantity I(a) = ∫ On Πu aij ij du, depending on a matrix of exponents a ∈ Mn(N). Among consequences, we establish a number of basic facts regarding the integrals I(a): vanishing condition, sign, poss...

A method is presented for generating a discrete piecewise constant Gaussian curvature (CGC) surface. An energy functional first formulated so that its stationary point the linear Weingarten (LW) surface, which has property such weighted sum of mean and curvatures constant. The CGC surface obtained using gradient derived from variation special type LW updating shape based on flow. filtering inco...