We present a second order smooth filling of an n-valent Catmull-Clark spline ring with n biseptic patches. While an underdetermined biseptic solution to this problem has appeared previously, we make several advances in this paper. Most notably, we cast the problem as a constrained minimization and introduce a novel quadratic energy functional whose absolute minimum of zero is achieved for bicub...

We describe a method to generate blend surfaces which t with continuous curvature to the primary surfaces. This blend surface is obtained as the bicubic tensor spline minimizing a variational problem. Among all the bicubic tensor splines which give a curvature continuous blend surface, the one is chosen which minimizes a bilinear functional. In Section 2 we summarize and extend the results of a...

nalyzing and interrogating designed surfaces remains an important and widely researched issue in computer-aided geometric design (CAGD). Treating families of characteristic curves— such as contour lines, lines of curvature, asymptotic lines, isophotes, and reflection lines—on the surface proves a popular method of doing this. All these curves have something in common: s They reflect the surface...

We present a method to speed up walkthroughs of static scenes. It involves the creation of a continuousC1 radiosity reconstruction for adaptively sampled regions. This representation is a unified solution to handle unrestricted quadtrees and T-vertices, and allows for the generation of multiple different levels-of-detail of the radiosity function, which is represented as texture maps. The metho...

In this paper we introduce an intermediate representation of surfaces that we call semi-implicit. We give a general definition in the language of projective complex algebraic geometry, and we begin its systematic study with an effective view point. Our last section will apply this representation to investigate the intersection of two bi-cubic surfaces, these surfaces are widely used in Computer...

Many data mining tasks can be reformulated as optimization problems, in the solution of which approximation by surfaces plays a key role. The paper proposes a new efficient computational algorithm for spline surfaces over uniform grids. The algorithm is based on a recent result on approximation of a biquartic polynomial by bicubic ones, that ensures C2 continuity of the corresponding four bicub...

This paper gives a construction to complete, at extraordinary points, an otherwise bi-cubic spline surface – so that the resulting surface is curvature continuous everywhere. To fill the n-sided gap in the bi-cubic surface, a cap is constructed from n spline patches, each consisting of 2× 2 pieces of polynomial degree bi-5. Particular care is taken to continue the curvature distribution from th...

New algorithms for the classical problem of fairing cubic spline curves and bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abnormal portions, the algorithms (automatically or interactively) identify thèbad' data points and replace them with new points produced by minimizing the strain energy of the new curve or surface. The proposed algorith...

To generate analysis-suitable T-splines for arbitrary topologies, in this paper we introduce a new method to deal with extraordinary nodes in the T-mesh. Knot interval duplication method is used to extract knot vectors for the extraordinary nodes and spoke nodes. From defined bicubic weighted T-spline basis functions, the extracted Bézier coefficients are modified to obtain a gap-free T-spline ...

Polycube G-splines form a 2-manifold guided by a mesh of quadrilateral faces such that at most six quads meet at each vertex. In particular, this replicates the layout of the quad faces of a polycube. Polycube G-splines are piecewise bicubic and polycube Gspline surfaces are almost everywhere tangent-continuous (G) based on rational linear reparameterization. They can be constructed in two diff...