This paper presents a novel parameterization method for a non-closed triangular mesh. For every flattened 1-ring neighbors, we choose a local coordinate frame, and the local geometry structure is represented as local parametric coordinates. Then the global optimal parametric coordinates are attained by aligning all the local parametric planes while preserving the local structure as much as possible. The boundary conditions are not necessary in our method, thus no high distortion appears around the boundary, and distortion is uniformly distributed over parametric domain. In addition, our method can operate directly on mesh surface which has holes without any preprocessing of surface partition. Furthermore, linear constraints are allowed in the parameterization in a least squares sense.

Abstract We present Easy Mesh Cutting, an intuitive and easy‐to‐use mesh cutout tool. Users can cut meaningful components from meshes by simply drawing freehand sketches on the mesh. Our system provides instant visual feedback to obtain the cutting results based on an improved region growing algorithm using a feature sensitive metric. The cutting boundary can be automatically optimized or easily edited by users. Extensive experimentation shows that our approach produces good cutting results while requiring little skill or effort from the user and provides a good user experience. Based on the easy mesh cutting framework, we introduce two applications including sketch‐based mesh editing and mesh merging for geometry processing. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Geometric algorithms, languages, and systems

This paper presents a novel approach for surface smoothing with feature preservation on arbitrary meshes. Laplacian operator is performed in a global way over the mesh. The surface smoothing is formulated as a quadratic optimization problem, which is easily solved a sparse linear system. The cost function to be optimized penalizes deviations from the global Laplacian operator while maintaining the overall shape of the original mesh. The features of the original mesh can be preserved by adding feature constraints and barycenter constraints in the system. Our approach is simple, non-iterative, fast, and does not cause surface shrinkage and distortion. Many experimental results are presented to show the applicability and flexibility of the approach.

This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with C/sup 1/ continuity around a common corner vertex. A C/sup 1/ continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with C/sup 1/ continuity around a corner is then developed. Our approach is easy and fast with the virtue of cubic reproduction, local shape controllability, C/sup 2/ continuous at the corner vertex. Some experimental results are presented to show the applicability and flexibility of the approach.

Subdivision, intersection and triangulation of a surface are the basic and common operations in computer aided design and computer graphics. A complicated surface can be approximated by some triangular patches. The key technique of this problem is the estimation of approximation error. This work has been done in some papers by estimating second derivatives of the surface, thus very complicated computation must be executed and hence time is overly consumed. Avoiding this estimation and exerting the influence of the control points of the surfaces, this paper gives a formula for computing the exact distance between a degree 2 Bernstein-Bezier triangular surface and its base triangle. Also, this paper gives estimates of maximal distance between a degree 2 or 3 rational Bernstein-Bezier triangular surface and its base triangle with a high precision. These results are easy for programming, simple for computing, and effective for improving the subdivision/triangulation algorithms of common rational Bezier surfaces in a design system.

We present an algorithm for bounding a piece of strip-shaped point cloud without self-intersections with an interval B-spline curve. Firstly we calculate the boundary points of the point cloud, and then bound it with an interval B-spline curve of which two pieces of boundary curves interpolate these boundary points. For the algorithm there are important applications in product shape verification, model design, NC machining, sea-route reconnaissance and weather forecasting, etc. Moreover, the center curve of the interval B-spline curve can serve quite well as the reconstructing curve from the point cloud.

This paper presents the algorithms for calculating the control points of Hermite polynomial approximation to rational Bezier curves and the recursive formulae between different degree Hermite polynomial approximations based on the close relationship between hybrid polynomial approximation and Hermite polynomial approximation. The error bound for the Hermite polynomial approximation is also obtained.

This paper presents an algorithm for determiningthe paths along which corresponding vertices travel in a 2-D shape blending.Rather than considering the vertex paths explicitly, the algorithm defines the intermediate shapes by interpolating the intrinsic definitions of the initial and final shapes.The algorithm produces shape blends which generally are more satisfactory than those produced using linear or cubic curve paths.Particularly, the algorithm can avoid the shrinkage that normally occurs when rotating rigid bodies are linearly blended, and avoids kinks in the blend when there were none in the key polygons.