Showing papers in "Computer-aided Design in 2010"

Review: Recent development in CNC machining of freeform surfaces: A state-of-the-art review

Abstract: Freeform surfaces, also called sculptured surfaces, have been widely used in various engineering applications. Freeform surfaces are primarily manufactured by CNC machining, especially 5-axis CNC machining. Various methodologies and computer tools have been developed in the past to improve efficiency and quality of freeform surface machining. This paper aims at providing a state-of-the-art review on recent research development in CNC machining of freeform surfaces. This review primarily focuses on three aspects in freeform surface machining: tool path generation, tool orientation identification, and tool geometry selection. For each aspect, first concepts, requirements and fundamental research methods are briefly introduced. The major research methodologies developed in the past decade in each aspect are presented with details. Problems and future research directions are also discussed.

Structural optimization based on CAD-CAE integration and metamodeling techniques

Abstract: Traditional structural optimization, which identifies the best combination of geometrical parameters to improve the product's performance and to save the material, is often carried out manually. This paper presents a framework that performs the integration between commercial CAD-CAE software by using common scripting, programming languages and Application Programming Interface. The loop of design-analysis-redesign in optimization process was done automatically and seamlessly without interaction with designer. Along with CAD-CAE computer-aided tools, metamodeling techniques including response surface methodology and radial basis function were applied to structural optimization according to the number of design variables. This approach reduces the time for solving computation-intensive design optimization problems and the designers are free from monotonous repetitive tasks. Three case studies were carried out in order to verify the feasibility and general-purpose characteristics of the proposed method for the structural optimization process of mechanical components. The results show that the proposed method facilitates the structural optimization process and reduces the computing cost compared to other approaches.

Computer aided fixture design: Recent research and trends

Abstract: Widely used in manufacturing, fixtures have a direct impact upon product manufacturing quality, productivity and cost, so much attention has already been paid to the research of computer aided fixture design (CAFD) and many achievements in this field have been reported. In this paper, a literature survey of computer aided fixture design and automation over the past decade is proposed. First, an introduction is given on the fixture applications in industry. Then, significant works done in the CAFD field, including their approaches, requirements and working principles are discussed. Finally, some prospective research trends are also discussed.

A study on X-FEM in continuum structural optimization using a level set model

Abstract: In this paper, we implement the extended finite element method (X-FEM) combined with the level set method to solve structural shape and topology optimization problems. Numerical comparisons with the conventional finite element method in a fixed grid show that the X-FEM leads to more accurate results without increasing the mesh density and the degrees of freedom. Furthermore, the mesh in X-FEM is independent of the physical boundary of the design, so there is no need for remeshing during the optimization process. Numerical examples of mean compliance minimization in 2D are studied in regard to efficiency, convergence and accuracy. The results suggest that combining the X-FEM for structural analysis with the level set based boundary representation is a promising approach for continuum structural optimization.

Holistic ship design optimization

Abstract: Ship design is a complex endeavor requiring the successful coordination of many disciplines, of both technical and non-technical nature, and of individual experts to arrive at valuable design solutions. Inherently coupled with the design process is design optimization, namely the selection of the best solution out of many feasible ones on the basis of a criterion, or rather a set of criteria. A systemic approach to ship design may consider the ship as a complex system integrating a variety of subsystems and their components, for example, subsystems for cargo storage and handling, energy/power generation and ship propulsion, accommodation of crew/passengers and ship navigation. Independently, considering that ship design should actually address the whole ship's life-cycle, it may be split into various stages that are traditionally composed of the concept/preliminary design, the contractual and detailed design, the ship construction/fabrication process, ship operation for an economic life and scrapping/recycling. It is evident that an optimal ship is the outcome of a holistic optimization of the entire, above-defined ship system over her whole life-cycle. But even the simplest component of the above-defined optimization problem, namely the first phase (conceptual/preliminary design), is complex enough to require to be simplified (reduced) in practice. Inherent to ship design optimization are also the conflicting requirements resulting from the design constraints and optimization criteria (merit or objective functions), reflecting the interests of the various ship design stake holders. The present paper provides a brief introduction to the holistic approach to ship design optimization, defines the generic ship design optimization problem and demonstrates its solution by use of advanced optimization techniques for the computer-aided generation, exploration and selection of optimal designs. It discusses proposed methods on the basis of some typical ship design optimization problems with multiple objectives, leading to improved and partly innovative designs with increased cargo carrying capacity, increased safety and survivability, reduced required powering and improved environmental protection. The application of the proposed methods to the integrated ship system for life-cycle optimization problem remains a challenging but straightforward task for the years to come.

Design reuse oriented partial retrieval of CAD models

Abstract: As a huge number of 3D CAD models is generated each year, retrieval of 3D CAD models is becoming more and more important for achieving design reuse. However, the existing methods for partial retrieval of 3D CAD models are very few and far from the requirements of design reuse. In this paper, we present an approach to partial retrieval of 3D CAD models for design reuse. The criteria for determining whether a subpart of 3D CAD models is reusable for design is defined first. Based on the criteria defined, all the design reusable subparts involved in the 3D CAD models in the library are automatically extracted and stored in the library as reference models. Moreover, each design reusable subpart in the library is represented by all its local matching regions in a hierarchical way so as to support multi-mode partial retrieval. In our approach, three partial retrieval modes including normal retrieval, exact retrieval and relaxed retrieval are defined to meet various partial retrieval requirements of design reuse such as the incomplete and vague queries during the early design stage. And the multi-mode partial retrieval is achieved by performing multi-mode matching and similarity assessment between the query and the design reusable subparts in the library indexed by bitmap. Experimental results are presented to demonstrate the effectiveness of the approach.

Efficient collision detection using a dual OBB-sphere bounding volume hierarchy

Abstract: We present an efficient algorithm for collision detection between static rigid objects using a dual bounding volume hierarchy which consists of an oriented bounding box (OBB) tree enhanced with bounding spheres. This approach combines the compactness of OBBs and the simplicity of spheres. The majority of distant objects are separated using the simpler sphere tests. The remaining objects are in close proximity, where some separation axes are significantly more effective than others. We select 5 from among the 15 potential separating axes for OBBs. Experimental results show that our algorithm achieves considerable speedup in most cases with respect to the existing OBB algorithms.

Curvature continuous path generation for autonomous vehicle using B-spline curves

Abstract: In this paper we introduce a roadmap algorithm for generating collision-free paths in terms of cubic B-spline curves for unmanned vehicles used in mining operations. The algorithm automatically generates collision-free paths that are curvature continuous with an upper bounded curvature and a small slope discontinuity of curvature at knots, when we are given the locations of the obstacles, the boundary geometry of the working area, positions and directions of the vehicle at the start, loading, and the goal points. Our algorithm also allows us to find a switch back point where the vehicle reverses its direction to enter the loading area. Examples are provided to demonstrate the effectiveness of the proposed algorithms.

VR-CAD integration: Multimodal immersive interaction and advanced haptic paradigms for implicit edition of CAD models

Abstract: This paper presents an approach for the integration of Virtual Reality (VR) and Computer-Aided Design (CAD). Our general goal is to develop a VR-CAD framework making possible intuitive and direct 3D edition on CAD objects within Virtual Environments (VE). Such a framework can be applied to collaborative part design activities and to immersive project reviews. The cornerstone of our approach is a model that manages implicit editing of CAD objects. This model uses a naming technique of B-Rep components and a set of logical rules to provide straight access to the operators of Construction History Graphs (CHG). Another set of logical rules and the replay capacities of CHG make it possible to modify in real-time the parameters of these operators according to the user's 3D interactions. A demonstrator of our model has been developed on the OpenCASCADE geometric kernel, but we explain how it can be applied to more standard CAD systems such as CATIA. We combined our VR-CAD framework with multimodal immersive interaction (using 6 DoF tracking, speech and gesture recognition systems) to gain direct and intuitive deformation of the objects' shapes within a VE, thus avoiding explicit interactions with the CHG within a classical WIMP interface. In addition, we present several haptic paradigms specially conceptualized and evaluated to provide an accurate perception of B-Rep components and to help the user during his/her 3D interactions. Finally, we conclude on some issues for future researches in the field of VR-CAD integration.

Bspline approximation of circle arc and straight line for pocket machining

Abstract: This article proposes a new method of 2D curve interpolation using non-uniform cubic B-splines particularly adapted to the interpolation of sequences of straight lines and circle arcs. The purpose of this method is to calculate C2 continuous curves adapted to high feedrate pocket machining. Industrially machined pockets usually present simple forms. Generally, the tool path is defined by circle arcs and line segments that introduce slowdowns during machining. Thus, a method for approximating a sequence of line segments and circle arcs using Bspline curves is proposed. The proposed method ensures exact line interpolation, to approach the tool path precisely, to reduce the number of control points and to avoid thickening and oscillation at the connections between line segments and circle arcs. Various applications are presented and numerous tests on machine tools allow the advantages of this method to be illustrated.

A collaborative Design for Usability approach supported by Virtual Reality and a Multi-Agent System embedded in a PLM environment

Abstract: This paper details a collaborative workstation design approach integrating knowledge based on engineering process, using a Multi-Agent System (MAS) on a Virtual Reality (VR) platform. The MAS supports R&D teams to extract and re-use engineering knowledge so as to improve their efficiency in developing new products. Our research targets the development of a knowledge engineering system integrated into a PLM-Product Life cycle Management-environment linked with virtual reality tools. A PLM is a strategic business approach with a consistent set of methodologies and software solutions. It is meant to promote collaborative creation, management, delivery and proper use of this life cycle definition and information product in multinational companies. This system is used by engineers to carry out projects in a collective way while conveying a defined process. The MAS allows capitalization, and to annotate knowledge according to the actions of the designers inside a PLM environment. Then, this knowledge is used by VR tools to analyze various aspects of the virtual prototype such as manufacturing, maintenance, reliability or ergonomics. Consequently, we use expert knowledge to pilot the design process of a virtual prototype inside a three-dimensional immersive virtual reality platform. In this context, our paper describes our knowledge management approach applied to improve ergonomics and collaborative design in industrial areas.

A simple and effective geometric representation for irregular porous structure modeling

Abstract: Computer-aided design of porous structures is a challenging task because of the high degree of irregularity and intricacy associated with the geometries. Most of the existing design approaches either target designing artifacts with regular-shaped pores or reconstructing geometric models from existing porous objects. For regular porous structures, it is difficult to control the pore shapes and distributions locally; for reconstructed models, a design is attainable only if there are some existing objects to reconstruct from. This paper is motivated to present an alternative approach to design irregular porous artifacts with controllable pore shapes and distributions, yet without requiring any existing objects as prerequisites. Inspired by the random colloid-aggregation model which explains the formation mechanism of random porous media, Voronoi tessellation is first generated to partition the space into a collection of compartments. Selective compartments are then merged together to imitate the random colloid aggregations. Through this Voronoi cell merging, irregular convex and concave polygons are obtained and the vertices of which are modeled as control points of closed B-Spline curves. The fitted B-Spline curves are then employed to represent the boundaries of the irregular-shaped pores. The proposed approach drastically improved the ease of irregular porous structure modeling while at the same time properly maintained the irregularity that is widely found in natural objects. Compared with other existing CAD approaches, the proposed approach can easily construct irregular porous structures which appear more natural and realistic.

Feature suppression based CAD mesh model simplification

Abstract: Dynamic simulation and high quality FEA mesh generation need the CAD mesh model to be simplified, that is, suppressing the detailed features on the mesh without any changes to the rest. However, the traditional mesh simplification methods for graphical models can not satisfy the requirements of CAD mesh simplification. In this paper, we develop a feature suppression based CAD mesh model simplification framework. First, the CAD mesh model is segmented by an improved watershed segmentation algorithm, constructing the region-level representation required by feature recognition. Second, the form features needing to be suppressed are extracted using a feature recognition method with user defined feature facility based on the region-level representation, establishing the feature-level representation. Third, every recognized feature is suppressed using the most suitable one of the three methods, i.e. planar Delaunay triangulation, Poisson equation based method, and the method for blend features, thus simplifying the CAD mesh model. Our method provides an effective way to make CAD mesh model simplification meet the requirements of engineering applications. Several experimental results are presented to show the superiority and effectivity of our approach.

Interactive virtual try-on clothing design systems

Abstract: Clothing computer design systems include three integrated parts: garment pattern design in 2D/3D, virtual try-on and realistic clothing simulation. Some important results have been obtained in pattern design and clothing simulation since the 1980s. However, in the area of virtual try-on, only limited methods have been proposed which are applicable to some defined garment styles or under restrictive sewing assumptions. This paper presents a series of new techniques from virtually sewing up complex garment patterns on human models to visualizing design effects through physical-based real-time simulation. We first employ an hierarchy of ellipsoids to approximate human models in which the bounding ellipsoids are optimized recursively. We also present a new scheme for including contact friction and resolving collisions. Four types of user interactive operation are introduced to manipulate cloth patterns for pre-positioning, virtual sewing and later obtaining cloth simulation. In the cloth simulation, we propose a simplified cloth dynamic model and an integration scheme to realize a high quality real-time cloth simulation. We demonstrate the robustness of our proposed systems by complex garment style virtual try-on and cloth simulation.

Solid modeling of polyhedral objects by Layered Depth-Normal Images on the GPU

Abstract: We introduce a novel solid modeling framework taking advantage of the architecture of parallel computing on modern graphics hardware. Solid models in this framework are represented by an extension of the ray representation - Layered Depth-Normal Images (LDNI), which inherits the good properties of Boolean simplicity, localization and domain decoupling. The defect of ray representation in computational intensity has been overcome by the newly developed parallel algorithms running on the graphics hardware equipped with Graphics Processing Unit (GPU). The LDNI for a solid model whose boundary is represented by a closed polygonal mesh can be generated efficiently with the help of hardware accelerated sampling. The parallel algorithm for computing Boolean operations on two LDNI solids runs well on modern graphics hardware. A parallel algorithm is also introduced in this paper to convert LDNI solids to sharp-feature preserved polygonal mesh surfaces, which can be used in downstream applications (e.g., finite element analysis). Different from those GPU-based techniques for rendering CSG-tree of solid models Hable and Rossignac (2007, 2005) [1,2], we compute and store the shape of objects in solid modeling completely on graphics hardware. This greatly eliminates the communication bottleneck between the graphics memory and the main memory.

Global optimization of tool path for five-axis flank milling with a conical cutter

Abstract: In this paper, optimum positioning of the conical cutter for five-axis flank milling of slender surfaces is addressed from the perspective of approximating the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. Based on the observation that a conical surface can be treated as a canal surface, i.e. envelope surface of one-parameter family of spheres, the swept envelope of a conical cutter is represented as a sphere-swept surface. Then, an approach is presented to efficiently compute the signed distance between a point in space and the swept surface without constructing the swept surface itself. The first order differential increment of the signed point-to-surface distance with respect to the differential deformation of the tool axis trajectory surface is derived. By using the distance function, tool path optimizations for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework, and a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are given to confirm the validity and efficiency of the proposed approach. Comparing with the existing approaches, the present one improves the machining accuracy greatly. The rationale developed applies to general rotary cutters.

Five decades of Computer-Aided Ship Design

Abstract: This article will present a synoptical review of key developments in Computer-Aided Ship Design since its inception about five decades ago. Milestone events and major innovations will be identified in several categories of ship design application with the principal emphasis on the methodologies, the modeling and the integration of the ship design process. The discussion will address many specific subtasks of ship design on the common platform of a human-guided, computer-based decision process.

Detecting design intent in approximate CAD models using symmetry

Abstract: Finding design intent embodied as high-level geometric relations between a CAD model's sub-parts facilitates various tasks such as model editing and analysis. This is especially important for boundary-representation models arising from, e.g., reverse engineering or CAD data transfer. These lack explicit information about design intent, and often the intended geometric relations are only approximately present. A novel solution to this problem is presented based on detecting approximate local incomplete symmetries, in a hierarchical decomposition of the model into simpler, more symmetric sub-parts. Design intent is detected as congruencies, symmetries and symmetric arrangements of the leaf-parts in this decomposition. All elementary 3D symmetry types and common symmetric arrangements are considered. They may be present only locally in subsets of the leaf-parts, and may also be incomplete, i.e. not all elements required for a symmetry need be present. Adaptive tolerance intervals are detected automatically for matching inter-point distances, enabling efficient, robust and consistent detection of approximate symmetries. Doing so avoids finding many spurious relations, reliably resolves ambiguities between relations, and reduces inconsistencies. Experiments show that detected relations reveal significant design intent.

Three-dimensional beta-shapes and beta-complexes via quasi-triangulation

Abstract: The proximity and topology among particles are often the most important factor for understanding the spatial structure of particles. Reasoning the morphological structure of molecules and reconstructing a surface from a point set are examples where proximity among particles is important. Traditionally, the Voronoi diagram of points, the power diagram, the Delaunay triangulation, and the regular triangulation, etc. have been used for understanding proximity among particles. In this paper, we present the theory of the @b-shape and the @b-complex and the corresponding algorithms for reasoning proximity among a set of spherical particles, both using the quasi-triangulation which is the dual of the Voronoi diagram of spheres. Given the Voronoi diagram of spheres, we first transform the Voronoi diagram to the quasi-triangulation. Then, we compute some intervals called @b-intervals for the singular, regular, and interior states of each simplex in the quasi-triangulation. From the sorted set of simplexes, the @b-shape and the @b-complex corresponding to a particular value of @b can be found efficiently. Given the Voronoi diagram of spheres, the quasi-triangulation can be obtained in O(m) time in the worst case, where m represents the number of simplexes in the quasi-triangulation. Then, the @b-intervals for all simplexes in the quasi-triangulation can also be computed in O(m) time in the worst case. After sorting the simplexes using the low bound values of the @b-intervals of each simplex in O(mlogm) time, the @b-shape and the @b-complex can be computed in O(logm+k) time in the worst case by a binary search followed by a sequential search in the neighborhood, where k represents the number of simplexes in the @b-shape or the @b-complex. The presented theory of the @b-shape and the @b-complex will be equally useful for diverse areas such as structural biology, computer graphics, geometric modelling, computational geometry, CAD, physics, and chemistry, where the core hurdle lies in determining the proximity among spherical particles.

Computing the Hausdorff distance between two B-spline curves

Abstract: This paper presents a geometric pruning method for computing the Hausdorff distance between two B-spline curves It presents a heuristic method for obtaining the one-sided Hausdorff distance in some interval as a lower bound of the Hausdorff distance, which is also possibly the exact Hausdorff distance Then, an estimation of the upper bound of the Hausdorff distance in an sub-interval is given, which is used to eliminate the sub-intervals whose upper bounds are smaller than the present lower bound The conditions whether the Hausdorff distance occurs at an end point of the two curves are also provided These conditions are used to turn the Hausdorff distance computation problem between two curves into a minimum or maximum distance computation problem between a point and a curve, which can be solved well A pruning technique based on several other elimination criteria is utilized to improve the efficiency of the new method Numerical examples illustrate the efficiency and the robustness of the new method

Hull-form optimization in calm and rough water

Abstract: The paper presents a formal methodology for the hull form optimization in calm and rough water using wash waves and selected dynamic responses, respectively. Parametric hull form modeling is used to generate the variant hull forms with some of the form parameters modified, which are evaluated in the optimization scheme based on evolutionary strategies. Rankine-source panel method and strip theories are used for the hydrodynamic evaluation. The methodology is implemented in the optimization of a double-chine, planing hull form. Furthermore, a dual-stage optimization strategy is applied on a modern fast displacement ferry. The effect of the selected optimization parameters is presented and discussed.

Quasi-worlds and quasi-operators on quasi-triangulations

Abstract: Quasi-triangulation is the dual structure of the Voronoi diagram of spheres, and it has been used as a convenient and powerful geometric construct for representing the proximity among spherical particles with different radii. In this paper, we present the formalism of the quasi-triangulation based on a quasi-world model and define primitive query operators called quasi-operators for correct and efficient topology traversal on the quasi-triangulation. Algorithms for the quasi-operators are also presented based on the extended inter-world data structure. The proposed quasi-operators have the potential to be a fundamental platform on which efficient algorithms for application problems on quasi-triangulation can be correctly and easily developed. The recently announced powerful constructs of the @b-complex and the @b-shape are such examples.

Quick GPS: A new CAT system for single-part tolerancing

Abstract: This paper depicts a new CAT (Computer Aided Tolerancing) system called Quick GPS (Geometrical Product Specification), for assisting the designer when specifying the functional tolerances of a single part included in a mechanism, without any required complex function analysis. The mechanism assembly is first described through a positioning table formalism. In order to create datum reference frames and to respect assembly requirements, an ISO based 3D tolerancing scheme is then proposed, thanks to a set of rules based on geometric patterns and TTRS (Technologically and Topologically Related Surfaces). Since it remains impossible to determine tolerance chains automatically, the designer must impose links between the frames. The CAT system that we developed here proposes ISO based tolerance specifications to help ensure compliance with the designer's intentions, saving on time and eliminating errors. This paper will detail both the set of tolerancing rules and the designer's approach. The Quick GPS system has been developed in a CATIA V5 environment using CATIA VBA and CATIA CAA procedures.

A desktop virtual reality-based interactive modular fixture configuration design system

Abstract: Modular fixture configuration design is a complicated task requiring strong professional background and practical experience. However, automated or semi-automated computer aided modular fixture systems based on CAD packages still are not well accepted by the manufacturing industry due to the lack of intuitive interaction and immediate feedback compared with traditional models such as paper and physical models. In this paper, a novel Virtual Reality-based system for interactive modular fixture configuration design is presented. We use a multi-view based modular fixture assembly model to assist information representation and management. In addition, the suggested strategy is compatible with the principles of virtual environment and it is easy to reutilize the element model. Based on geometric constraints, we propose a precise 3D manipulation approach to improve intuitive interaction and accurate 3D positioning of fixture components in virtual space. Thus, the modular fixture configuration design task can precisely be performed in virtual space.

An artificial intelligence planning approach to manufacturing feature recognition

Abstract: Within manufacturing, features have been widely accepted as useful concepts, and in particular they are used as an interface between CAD and CAPP systems. Previous research on feature recognition focus on the issues of intersecting features and multiple interpretations, but do not address the problem of custom features representation. Representation of features is an important aspect for making feature recognition more applicable in practice. In this paper a hybrid procedural and knowledge-based approach based on artificial intelligence planning is presented, which addresses both classic feature interpretation and also feature representation problems. STEP designs are presented as case studies in order to demonstrate the effectiveness of the model.

VELOS: A VR platform for ship-evacuation analysis

Abstract: ''Virtual Environment for Life On Ships'' (VELOS) is a multi-user Virtual Reality (VR) system that aims to support designers to assess (early in the design process) passenger and crew activities on a ship for both normal and hectic conditions of operations and to improve ship design accordingly. This article focuses on presenting the novel features of VELOS related to both its VR and evacuation-specific functionalities. These features include: (i) capability of multiple users' immersion and active participation in the evacuation process, (ii) real-time interactivity and capability for making on-the-fly alterations of environment events and crowd-behavior parameters, (iii) capability of agents and avatars to move continuously on decks, (iv) integrated framework for both the simplified and advanced method of analysis according to the IMO/MSC 1033 Circular, (v) enrichment of the ship geometrical model with a topological model suitable for evacuation analysis, (vi) efficient interfaces for the dynamic specification and handling of the required heterogeneous input data, and (vii) post-processing of the calculated agent trajectories for extracting useful information for the evacuation process. VELOS evacuation functionality is illustrated using three evacuation test cases for a ro-ro passenger ship.

Distributed design review using tangible augmented technical drawings

Abstract: In this work we integrate augmented reality technology in a product development process using real technical drawings as a tangible interface for design review. We present an original collaborative framework for Augmented Design Review Over Network (ADRON). It provides the following features: augmented technical drawings, interactive FEM simulation, multimodal annotation and chat tools, web content integration and collaborative client/server architecture. Our framework is intended to use common hardware instead of expensive and complex virtual or augmented facilities. We designed the interface specifically for users with little or no augmented reality expertise proposing tangible interfaces for data review and visual editing for all the functions and configurations. Two case studies are presented and discussed: a real-time ''touch and see'' stress/strain simulation and a collaborative distributed design review session of an industrial component.

Cubic B-spline curve approximation by curve unclamping

Abstract: A new approach for cubic B-spline curve approximation is presented. The method produces an approximation cubic B-spline curve tangent to a given curve at a set of selected positions, called tangent points, in a piecewise manner starting from a seed segment. A heuristic method is provided to select the tangent points. The first segment of the approximation cubic B-spline curve can be obtained using an inner point interpolation method, least-squares method or geometric Hermite method as a seed segment. The approximation curve is further extended to other tangent points one by one by curve unclamping. New tangent points can also be added, if necessary, by using the concept of the minimum shape deformation angle of an inner point for better approximation. Numerical examples show that the new method is effective in approximating a given curve and is efficient in computation.

A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length

Abstract: There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profile with desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processes which make generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ahead trajectory generation method which determines the deceleration stage according to the fast estimated arc length and the reverse interpolation of each curve at every sampling time. This results in a feedrate trajectory generation with jerk-limited acceleration profiles for the NURBS curves. The feedrate profile is adjusted dynamically according to the geometrical path constraint determined by chord error for the curved path. A NURBS curve by two different kinematics conditions was used as a means to test the feasibility of the developed interpolation scheme and command generator.

A new algorithm for finding faces in wireframes

Abstract: The problem of identifying the topology implied by wireframe drawings of polyhedral objects requires the identification of face loops, loops of edges which correspond to a face in the object the drawing portrays. In this paper, we survey the advantages and limitations of known approaches, and present and discuss test results which illustrate the successes and failures of a currently popular approach based on Dijkstra's Algorithm. We conclude that the root cause of many failure cases is that the underlying algorithm assumes that the cost of traversing an edge is fixed. We propose a new polynomial-order algorithm for finding faces in wireframes. This algorithm could be adapted to any graph-theoretical least-cost circuit problem where the cost of traversing an edge is not fixed but context-dependent.