A novel method for sculptured surface subdivision

In this work,a novel method for sculptured surface subdivision to improve the machinery’s ability and efficiency in 5-axis CNC machining complex surface is introduced.The method subdivides automatically a monolithic convex or concave or simultaneously complex sculptured surface into a number of surface patches and achieves the goal of similar normal directions and small difference between the curvatures in every patch by using weight fuzzy cluster algorithm which takes the curvatures and normal vectors of the sculptured surface into account simultaneously.The inclination angle variation between every two Cutter Contact Points (CC Points) is decreased in every patch to avoid large-angle rotation of tool to save machining time when a flat-end mill is used.This work contributes to automating 5-axis CNC tool path generation for sculptured part machining and forming a foundation for further research.     

An adjustable subdivision surface modeling scheme

Based on triangle and quadrilateral meshes, this paper presents an adjustable subdivision surface scheme. The scheme can produce subdivision surface of Cl continuity of limit surface Since an adjustable parameter is introduced to the scheme, the surface modeling is flexible. Depended on given initial data, the limited surface shape can be adjusted and controlled through selecting appropriate parameters. The method is effective in generating smooth surfaces.     

A bound on the distance between Loop subdivision surface and its control mesh

By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions,we obtain a bound on the distance between Loop subdivision surface patch and its control mesh.The bound can be used to compute the numbers of subdivision for a given tolerance.Finally,two examples are listed in this paper to demonstrate the applications of the bound.     

A direct approach for subdivision surface fitting from a dense triangle mesh

This article presents a new and direct approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topology- and feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface with exactly the same topological structure and sharp features as that of the simplified mesh is finally fitted from a subset of vertices of the original dense mesh. During the fitting process, both the position masks and subdivision rules are used for setting up the fitting equation. Some examples are provided to demonstrate the proposed approach.     

Surface modeling with ternary interpolating subdivision

In this paper, a new interpolatory subdivision scheme, called ternary interpolating subdivision, for quadrilateral meshes with arbitrary topology is presented. It can be used to deal with not only extraordinary faces but also extraordinary vertices in polyhedral meshes of arbitrary topologies. It is shown that the ternary interpolating subdivision can generate a C¹-continuous interpolatory surface. Some applications with open boundaries and curves to be interpolated are also discussed.     

基于凸包特征的细分曲面求交研究

主要针对具有凸包特征的细分曲面提出了一种有效的求交的方法,该方法适用于任意具有凸包特征的细分曲面中.该方法主要是利用二部图跟踪两个细分曲面中可能相交的面.在应用二部图的基础上,选择半边数据结构,应用轴向包围盒法进行相交检测,使得具有凸包特征的细分曲面的求交得以实现.     

给定Gauss曲率函数的旋转曲面的设计

旋转曲面的设计在CAD/CAM及CAGD中有重要作用.由于给定Gauss曲率函数的嵌入旋转曲面存在性问题已经得到较好的证明,故使得曲面的设计成为可能.给出了一种给定Gauss曲率函数的嵌入旋转曲面设计算法,该算法通过求解一个二阶微分方程,并适当选取初始条件,得到旋转曲面的位置矢量.最后,通过两个实例表明,该算法是可行的,为旋转曲面的工程设计与曲面造型提供了一个新方法.     

Blending parametric patches with subdivision surfaces

In this paper the problem of blending parametric surfaces using subdivision patches is discussed.A new approach,named removing-boundary,is presented to generate piecewise-smooth subdivision surfaces through discarding the outmost quadrilaterals of the open meshes derived by each subdivision step.Then the approach is employed both to blend parametric bicubic B-spline surfaces and to fill n-sided holes.It is easy to produce piecewise-smooth subdivision surfaces with both convex and concave corners on the boundary,and limit surfaces are guaranteed to be C^2 continuous on the boundaries except for a few singular points by the removing-boundary approach Thus the blending method is very efficient and the blending surface generated is of good effect.     

带折痕的Loop细分曲面等距面处理算法

Loop细分曲面不同细分层次的网格面可作为不同加工工序的加工模型.现有等距面生成算法因未考虑折痕和边界的特殊情况,当折痕或边界存在时将会生成与预期结果有较大差别的等距面.给出了折痕等尖锐特征处极限等距位置的计算方法,以及根据尖锐特征点极限位置反求初始网格等距位置的Gauss-Jacobi迭代公式,并证明了其迭代收敛性.采用文中算法得到的等距网格面令人满意.     

Feature-Adaptive Rendering of Loop Subdivision Surfaces on Modern GPUs

We present a novel approach for real-time rendering Loop subdivision surfaces on modern graphics hardware. Our algorithm evaluates both positions and normals accurately, thus providing the true Loop subdivision surface. The core idea is to recursively refine irregular patches using a GPU compute kernel. All generated regular patches are then directly evaluated and rendered using tile hardware tessellation unit. Our approach handles triangular control meshes of arbitrary topologies and incorporates common subdivision surface features such as semi-sharp creases and hierarchical edits. While surface rendering is accurate up to machine precision, we also enforce a consistent bitwise evaluation of positions and normals at patch boundaries. This is particularly useful in the context of displacement mapping which strictly requires inatching surface normals. Furthermore, we incorporate efficient level-of-detail rendering where subdivision depth and tessellation density can be adjusted on-the-fly. Overall, our algorithm provides high-quality results at real-time frame rates, thus being ideally suited to interactive rendering applications such as video games or authoring tools.     

Multiresolution free-form deformation with subdivision surface of arbitrary topology

A new free-from deformation method is presented in this paper. Object deformation is controlled by a mesh of arbitrary topology, namely a control mesh. The subdivision surface determined by the control mesh spans an intermediate deformation space. The object is embedded into the space by the nearest point rule. When the shape of the control mesh is changed, the object embedded in the intermediate deformation space will be deformed accordingly. Since the subdivision surface has a multiresolution property, the proposed deformation method naturally has a multiresolution property. A technique for generating control meshes is also introduced in the paper. Compared with previous deformation methods with arbitrary topology control tools, the proposed method has the advantages of flexible control and computational efficiency.     

Interpolating meshes of boundary intersecting curves by subdivision surfaces

C ⁰ (creases) or C ¹ continuity across the interpolated curves.     

Evaluation of piecewise smooth subdivision surfaces

Published online: 23 July 2002     

On increasing the developability of a trimmed NURBS surface

Developable surfaces are desired in designing products manufactured from planar sheets. Trimmed non-uniform rational B-spline (NURBS) surface patches are widely adopted to represent 3D products in CAD/CAM. This paper presents a new method to increase the developability of an arbitrarily trimmed NURBS surface patch. With this tool, designers can first create and modify the shape of a product without thinking about the developable constraint. When the design is finished, our approach is applied to increase the developability of the designed surface patches. Our method is an optimisation-based approach. After defining a function to identify the developability of a surface patch, the objective function for increasing the developability is derived. During the optimisation, the positions and weights of the free control points are adjusted. When increasing the developability of a given surface patch, its deformation is also minimised and the singular points are avoided. G⁰ continuity is reserved on the boundary curves during the optimisetion, and the method to reserve G¹ continuity across the boundaries is also discussed in this paper. Compared to other existing methods, our approach solves the problem in a novel way that is close to the design convention, and we are dealing with the developability problem of an arbitrarily trimmed NURBS patch.     

Bounded curvature triangle mesh subdivision with the convex hull property

Published online: 3 July 2002     

n-Dimensional multiresolution representation of subdivision meshes with arbitrary topology

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topological subdivision process that is a key issue to robustly and soundly define mesh hierarchies. It fully supports multiresolution edition what allows the implementation of most mesh processing algorithms – like filtering or compression – for n-dimensional meshes with arbitrary topologies.We illustrate this model, in dimension 3, with an new truly multiresolution representation of subdivision volumes. It allows us to extend classical subdivision schemes to arbitrary polyhedrons and to handle adaptive subdivision with an elegant solution to compliance issues. We propose an implementation of this model as an effective and relatively inexpensive data structure.     

Smooth multiple B-spline surface fitting with Catmull%ndash;Clark subdivision surfaces for extraordinary corner patches

This paper presents an algorithm for simultaneously fitting smoothly connected multiple surfaces from unorganized measured data. A hybrid mathematical model of B-spline surfaces and Catmull–Clark subdivision surfaces is introduced to represent objects with general quadrilateral topology. The interconnected multiple surfaces are G ² continuous across all surface boundaries except at a finite number of extraordinary corner points where G ¹ continuity is obtained. The algorithm is purely a linear least-squares fitting procedure without any constraint for maintaining the required geometric continuity. In case of general uniform knots for all surfaces, the final fitted multiple surfaces can also be exported as a set of Catmull–Clark subdivision surfaces with global C ² continuity and local C ¹ continuity at extraordinary corner points. Published online: 14 May 2002 Correspondence to: W. Ma     

Ridge extraction of a smooth 2-manifold surface based on vector field

This paper presents a general scheme to compute ridges on a smooth 2-manifold surface from the standpoint of a vector field. A ridge field is introduced. Starting with an initial ridge, which may or may not be umbilical, a ridge line is then traced by calculating an associated integral curve of this field in conjunction with a new projection procedure to prevent it from diverging. This projection is the first that can optimize a ridge guess to lie on a ridge line uniquely and accurately. In order to follow this scheme, we not only develop practical ridge formulae but also address their corresponding computational procedures for an analytical surface patch, especially for an implicit surface. In contrast to other existing methods, our new approach is mathematically sound and characterized by considering the full geometric structures and topological patterns of ridges on a generic smooth surface. The resulting ridges are accurate in the numerical sense and meet the requirement of high accuracy with complete topology. Although the objective of this paper is to develop a mathematically sound framework for ridges on a smooth surface, we give a comprehensive review of relevant works on both meshes and smooth surfaces for readers.