Weishi Li

Adaptive knot placement in B-spline curve approximation

An adaptive knot placement algorithm for B-spline curve approximation to dense and noisy data points is presented in this paper. In this algorithm, the discrete curvature of the points is smoothed to expose the characteristics of the underlying curve. With respect to the integration of the smoothed curvature, knots are placed adaptively to satisfy a heuristic rule. Several experimental results are included to demonstrate the validity of this algorithm.

Target curvature driven fairing algorithm for planar cubic B-spline curves

This paper presents a new algorithm for fairing planar cubic B-spline curves. Target curvature plots prescribed by designers according to design intent are used to identify bad points and bad curve segments. The corresponding control points are then modified using local constrained optimization. The objective function is a weighed combination of two components, which are associated with the fairness in the sense of energy minimization and the coherence to the original design, respectively. Hence, designers have more control over the fairing process by using appropriate weights for the two components. Several numerical examples are provided to demonstrate the effectiveness of the algorithm.

Fast variational design of multiresolution curves and surfaces with B-spline wavelets

Abstract Multiresolution modeling provides a powerful tool for complex shape editing. To achieve a better control of deformations and a more intuitive interface, variational principles have been used in such multiresolution models. However, when handling multiresolution constraints, the existing methods often result in solving large optimization systems. Hence, the computational time may become too excessive to satisfy the requirements for interactive design in CAD. In this paper, we present a fast approach for interactive variational design of multiresolution models. By converting all constraints at different levels to a target level, the optimization problem is formulated and solved at the lower level. Thus, the unknown coefficients of the optimization system are significantly reduced. This improves the efficiency of variational design. Meanwhile, to avoid smoothing out the details of the shape in variational modeling, we optimize the change in the deformation energy instead of the total energy of the deformed shape. Several examples and the experimental results are given to demonstrate the effectiveness and efficiency of this approach.

A point inclusion test algorithm for simple polygons

An algorithm for testing the relationship of a point and a simple polygon is presented. The algorithm employs a “visible edge” of the polygon from the point to determine whether the point is in the polygon or not according to the relationship of the orientation of the polygon and the triangle formed by the point and the visible edge. The algorithm is efficient and robust for floating point computation.

A Heuristic Knot Placement Algorithm for B-Spline Curve Approximation

AbstractA new knot placement algorithm for B-spline curve approximating to dense and noisy data points is presented in this paper. In this algorithm, the discrete curvature of the points, in contrast to the points themselves as in the traditional approaches, is smoothed to expose the curvature characteristics of the underlying curve of the data. With respect to the smoothed curvature, knots are placed to satisfy a heuristic rule. Experimental results are included to demonstrate the validity of this algorithm.

Detail-preserving variational design of B-spline curves and surfaces

Multiresolution models provide a powerful tool for complex shape multiresolution editing. However, it is still hard and not intuitive to modify the overall shape of a model while preserving its details by manipulating its control points at lower resolution levels. A better control of deformations and a more intuitive interface should allow the user to control the deformation of a model by manipulating the model directly. This can be achieved by using variational modeling techniques. This paper presents a variational framework for multiresolution model design. The modeled shape is represented as a multiresolution B-spline curve or surface, which can be interactively deformed by direct user inputs. The focus of this paper is on handling multiresolution constraints and preserving surface details throughout the deformation process. To avoid smoothing out the details of the shape in variational modeling, we optimize the deformation energy alone instead of the total energy of the deformed shape. To accelerate the convergence of the iterative energy minimization process, a wavelet-based iterative method is used to compute the solution in a hierarchical fashion.

Adaptive mesh smoothing for feature preservation

A simple algorithm is presented in this paper to preserve the feature of the mesh while the mesh is smoothed. In this algorithm, the bilateral filter is modified to incorporate local first-order properties of the mesh to enhance the effectiveness of the filter in preserving features. The smoothing process is error-bounded to avoid over-smoothing the mesh. Several examples are given to demonstrate the effectiveness of this algorithm in preserving the feature while removing noise from the mesh.

Feature-preserving smoothing algorithm for polygons and meshes

A feature-preserving smoothing algorithm for irregularly sampled meshes is presented in this paper. Low-pass bilateral filter is employed in this algorithm. The parameters of the filter are assigned adaptively for each vertex. Local first-order properties are also incorporated into the filter to further preserve the sharp features of the mesh. A similar technique is also used for polygon smoothing. Several examples are given to graphically and numerically demonstrate the quality of our results.

Manufacturable surface reconstruction from complex contours

To retrieve the geometric information contained in CT images, a surface reconstruction method, which is based on the similarity between the corresponding contours of adjacent sections, is presented in this paper. The correspondence of the contours of adjacent sections is determined by incorporating the topological rules and overlaps of the convex hulls of the contours. Then, the similar vertices of the corresponding contours are matched using a two‐phase strategy, consisting of overall matching followed by local matching. Dissimilar portions are extracted to construct the triangulable spatial dissimilar polygons. Finally, triangular meshes interpolating the contours are obtained by triangulating the dissimilar polygons and similar portions separately. The reconstructed surface models can be used in rapid prototyping as well as visualization. Experimental results demonstrate the validity of the method in reconstructing the surface from severe dissimilar contours.

ORIENTATION AND POINT INCLUSION TESTS FOR SIMPLE POLYGONS

This paper presents two robust algorithms for calculating the orientation and inclusion of simple polygons, respectively. By finding a maximum vertex of a simple polygon, a very fast convex vertex searching method is proposed and the orientation of the polygon can be uniquely determined. To decide the relationship between a point and a simple polygon, the concept of visible edge is put forward and an efficient visible edge searching algorithm is presented.