Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

Flexible G1 Interpolation of Quad Meshes

International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces

Watertight conversion of trimmed CAD surfaces to Clough-Tocher splines

The boundary representations (B-reps) that are used to represent shape in Computer-Aided Design systems create unavoidable gaps at the face boundaries of a model. Although these inconsistencies can be kept below the scale that is important for visualisation and manufacture, they cause problems for many downstream tasks, making it difficult to use CAD models directly for simulation or advanced geometric analysis, for example. Motivated by this need for watertight models, we address the problem of converting B-rep models to a collection of cubic C1C1 Clough–Tocher splines. These splines allow a watertight join between B-rep faces, provide a homogeneous representation of shape, and also support local adaptivity. We perform a comparative study of the most prominent Clough–Tocher constructions and include some novel variants. Our criteria include visual fairness, invariance to affine reparameterisations, polynomial precision and approximation error. The constructions are tested on both synthetic data and CAD models that have been triangulated. Our results show that no construction is optimal in every scenario, with surface quality depending heavily on the triangulation and parameterisation that are used.This research was supported by the Engineering and Physical Sciences Research Council through Grant EP/K503757/1.This is the final version. It was first published by Elsevier at http://www.sciencedirect.com/science/article/pii/S0167839615000795

C2 popunjavanje praznina pomoću konveksne kombinacije ploha pod rubnim ograničenjima

Two surface generation methods are presented, one for connecting two surfaces with C2 continuity while matching also two prescribed border lines on the free sides of the gap, and one for G1 filling a three-sided hole in a special case. The surfaces are generated as convex combination of surface and curve constituents with an appropriate correction function, and are represented in parametric form.Dane su dvije metode za izvođenje ploha. Jedna za povezivanje dviju ploha sa C2 neprekinutošću koja odgovara i dvjema graničnim linijama, a druga za G1 popunjavanje posebnog slučaja trostrane rupe. Plohe se izvode kao konveksna kombinacija plošnih i krivuljnih sastavnih dijelova sa odgovarajućom korektivnom funkcijom, a dane su u parametarskom obliku

A new construction of smooth surfaces from triangle meshes using parametric pseudo-manifolds

We introduce a new manifold-based construction for fitting a smooth surface to a triangle mesh of arbitrary topology. Our construction combines in novel ways most of the best features of previous constructions and, thus, it fills the gap left by them. We also introduce a theoretical framework that provides a sound justification for the correctness of our construction. Finally, we demonstrate the effectiveness of our manifold-based construction with a few concrete examples