We propose an angle-based mesh representation, which is invariant under translation, rotation, and uniform scaling, to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh, from which the mesh can be reconstructed uniquely up to translation, rotation, and uniform scaling. The reconstruction process requires solving three sparse linear systems: the first system encodes the length of edges between vertices on the mesh, the second system encodes the relationship of local frames between two adjacent vertices on the mesh, and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation, we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via handle translation, rotation, and uniform scaling. Several detail-preserving mesh editing examples are presented to demonstrate the effectiveness of the proposed method.

We introduce a kind of shape-adjustable spline curves defined over a non-uniform knot sequence. These curves not only have the many valued properties of the usual non-uniform B-spline curves, but also are shape adjustable under fixed control polygons. Our method is based on the degree elevation of B-spline curves, where maximum degrees of freedom are added to a curve parameterized in terms of a non-uniform B-spline. We also discuss the geometric effect of the adjustment of shape parameters and propose practical shape modification algorithms, which are indispensable from the user’s perspective.

A method of blending circular quadrics with parametric patches is proposed in this paper. It needs n rational bicubic Bezier patches and two S-patches to blend n (n > 2) quadrics. The blend is G1continuous. Explicit formulae of control points of both Beacutezier patches and S-patches are derived from the corresponding G1-continuity conditions. In addition, the shape can be intuitively modified by adjusting the free parameters of the blending surfaces.

In this paper, we investigate the direct manipulation problem of free form deformation with rational DMS spline volume (RDMS-FFD). For the weights based direct manipulation method, the solution of the weights can be achieved by solving a linear system; for the control points based method, the explicit solution of displacements of the control points can be obtained, and some properties are also derived from the results. For the constraint points inside the control lattices, we use the weights based methods; for the constraint points outside the control lattices, the control points based method is adopted. Several examples are presented to show the effectiveness of the proposed methods.

A new kind of Bézier-like basis with a frequency parameter, called ω-Bezier basis, is presented. It unifies and extends the Bézier basis, C-Bézier basis and H-Bézier basis defined over polynomial space, trigonometric polynomial space and hyperbolic polynomial space respectively. The ω-Bezier basis is defined in the space spanned by {cosωt, sinωt, 1, t,..., tk-2}, where ω = α, αϵR, κ is an arbitrary nonnegative integer. The ω-Bezier basis persists all desirable properties of the existing Bézier-like bases. Furthermore, it also has some special properties advantageous for modeling free form curves and surfaces, for example shape adjustability relative to the frequency parameter.

Abstract Recently, animations with deforming objects have been frequently used in various computer graphics applications. Morphing of objects is one of the techniques which realize shape transformation between two or more existing objects. In this paper, we present a novel morphing approach for 3D triangular meshes with the same topology. The basic idea of our method is to interpolate the mean curvature flow of the input meshes as the curvature flow Laplacian operator encodes the intrinsic local information of the mesh. The in‐between meshes are recovered from the interpolated mean curvature flow in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Our approach can generate visual pleasing and physical plausible morphing sequences and avoid the shrinkage and kinks appeared in the linear interpolation method. Experimental results are presented to show the applicability and flexibility of our approach. Copyright © 2007 John Wiley & Sons, Ltd.

The C-Bezier curve is introduced to CAD/CAM to deal with circular arcs, cylinders, and cones. It can precisely represent these conic curves in a Bezier-like way. A conjecture of Q.Y. Chen and G.Z. Wang (2003) is that the sequence of control polygons associated with the C-Bezier representation of a curve converges to the curve itself as the curve degree n goes to infinity. In this paper we prove this conjecture.