A Constructive Approach to Solving Geometric Constraint Systems

This paper proposes a constructive approach to solving geometric constraint systems.The approach incorporates graph-based and rule-based approaches, and achieves interactive speed.The paper presents a graph representation of geometric conStraint syStems, and discusses in detailthe algorithm of geometric reasoning based on poinl-cluster reduction. An example is made forillustration.

Solving geometric constraints with genetic simulated annealing algorithm

This paper applies genetic simulated annealing algorithm (SAGA) to solving geometric constraint problems. This method makes full use of the advantages of SAGA and can handle under-/over- constraint problems naturally. It has advantages (due to its not being sensitive to the initial values) over the Newton-Raphson method, and its yielding of multiple solutions, is an advantage over other optimal methods for multi-solution constraint system. Our experiments have proved the robustness and efficiency of this method.

Improved Quality Prediction Model for Multistage Machining Process Based on Geometric Constraint Equation

Product variation reduction is critical to improve process efficiency and product quality, especially for multistage machining process（MMP）. However, due to the variation accumulation and propagation, it becomes quite difficult to predict and reduce product variation for MMP. While the method of statistical process control can be used to control product quality, it is used mainly to monitor the process change rather than to analyze the cause of product variation. In this paper, based on a differential description of the contact kinematics of locators and part surfaces, and the geometric constraints equation defined by the locating scheme, an improved analytical variation propagation model for MMP is presented. In which the influence of both locator position and machining error on part quality is considered while, in traditional model, it usually focuses on datum error and fixture error. Coordinate transformation theory is used to reflect the generation and transmission laws of error in the establishment of the model. The concept of deviation matrix is heavily applied to establish an explicit mapping between the geometric deviation of part and the process error sources. In each machining stage, the part deviation is formulized as three separated components corresponding to three different kinds of error sources, which can be further applied to fault identification and design optimization for complicated machining process. An example part for MMP is given out to validate the effectiveness of the methodology. The experiment results show that the model prediction and the actual measurement match well. This paper provides a method to predict part deviation under the influence of fixture error, datum error and machining error, and it enriches the way of quality prediction for MMP.

Spatial geometric constraints histogram descriptors based on curvature mesh graph for 3D pollen particles recognition

This paper presents one novel spatial geometric constraints histogram descriptors （SGCHD） based on curvature mesh graph for automatic three-dimensional （3D） pollen particles recognition. In order to reduce high dimensionality and noise disturbance arising from the abnormal record approach under microscopy, the separated surface curvature voxels are ex- tracted as primitive features to represent the original 3D pollen particles, which can also greatly reduce the computation time for later feature extraction process. Due to the good invariance to pollen rotation and scaling transformation, the spatial geometric constraints vectors are calculated to describe the spatial position correlations of the curvature voxels on the 3D curvature mesh graph. For exact similarity evaluation purpose, the bidirectional histogram algorithm is applied to the spatial geometric constraints vectors to obtain the statistical histogram descriptors with fixed dimensionality, which is invariant to the number and the starting position of the curvature voxels. Our experimental results compared with the traditional methods validate the argument that the presented descriptors are invariant to different pollen particles geometric transformations （such as posing change and spatial rotation）, and high recognition precision and speed can be obtained simultaneously.

High-resolution Remote Sensing Image Semi-global Matching Method Considering Geometric Constraints of Connection Points and Image Texture Information

Dense matching of remote sensing images is a key step in the generation of accurate digital surface models.The semi-global matching algorithm comprehensively considers the advantages and disadvantages of local matching and global matching in terms of matching effect and computational efficiency,so it is widely used in close-range,aerial and satellite image matching.Based on the analysis of the original semi-global matching algorithm,this paper proposes a semi-global high-resolution remote sensing image that takes into account the geometric constraints of the connection points and the image texture information based on a large amount of high-resolution remote sensing image data and the characteristics of clear image texture.123123The method includes 4 parts:①Precise orientation.Aiming at the system error in the image orientation model,the system error of the rational function model is compensated by the geometric constraint relationship of the connecting points between the images,and the sub-pixel positioning accuracy is obtained;②Epipolar image generation.After the original image is divided into blocks,the epipolar image is generated based on the projection trajectory method;③Image dense matching.In order to reduce the size of the cost space and calculation time,the image is pyramided and then semi-globally matched layer by layer.In the matching process,the disparity map expansion and erosion algorithm that takes into account the image texture information is introduced to restrict the disparity search range and better retain the edge characteristics of the ground objects;④Generate DSM.In order to test the matching effect,the weighted median filter algorithm is used to filter the disparity map,and the DSM is obtained based on the principle of forward intersection.Finally,the paper uses the matching results of WordView3 and Ziyuan No.3 stereo image to verify the effectiveness of this method.

GENERATION AND APPLICATION OF VARIATIONAL GEOMETRIC CONSTRAINTS NETWORK BASED ON ISO'S FEATURE

The concept of variantional geometric constraints network is presented. Basedon ISO's feature, three kinds of variational geometric constraints are defined. The concepts ofmate tree (MT) and loop circuit (LC) are presented. The generation method of well-constrainedvariational geometric constraints network (VGCN) is studied. The network can be applied ingeneration of well-constrained tolerance types and tolerance chains. A simple example is analyzed toshow the scheme to be effective.

High-resolution Remote Sensing Image Semi-global Matching Method Considering Geometric Constraints of Connection Points and Image Texture Information

Dense matching of remote sensing images is a key step in the generation of accurate digital surface models.The semi-global matching algorithm comprehensively considers the advantages and disadvantages of local matching and global matching in terms of matching effect and computational efficiency,so it is widely used in close-range,aerial and satellite image matching.Based on the analysis of the original semi-global matching algorithm,this paper proposes a semi-global high-resolution remote sensing image that takes into account the geometric constraints of the connection points and the image texture information based on the large amount of high-resolution remote sensing image data and the characteristics of clear image texture.The method includes 4 parts:(1)Precise orientation.Aiming at the system error in the image orientation model,the system error of the rational function model is compensated by the geometric constraint relationship of the connecting points between the images,and the sub-pixel positioning accuracy is obtained;(2)Epipolar image generation.After the original image is divided into blocks,the epipolar image is generated based on the projection trajectory method;(3)Image dense matching.In order to reduce the size of the cost space and calculation time,the image is pyramided and then semi-globally matched layer by layer.In the matching process,the disparity map expansion and erosion algorithm that takes into account the image texture information is introduced to restrict the disparity search range and better retain the edge characteristics of the ground objects;(4)Generate DSM.In order to test the matching effect,the weighted median filter algorithm is used to filter the disparity map,and the DSM is obtained based on the principle of forward intersection.Finally,the paper uses the matching results of WordView3 and Ziyuan No.3 stereo image to verify the effectiveness of this method.

Bio-inspired Design and Inverse Kinematics Solution of an Omnidirectional Humanoid Robotic Arm with Geometric and Load Capacity Constraints

Inspired by the driving muscles of the human arm,a 4-Degree of Freedom(DOF)concentrated driving humanoid robotic arm is proposed based on a spatial double parallel four-bar mechanism.The four-bar mechanism design reduces the inertia of the elbow-driving unit and the torque by 76.65%and 57.81%,respectively.Mimicking the human pose regulation strategy that the human arm picks up a heavy object by adjusting its posture naturally without complicated control,the robotic arm features an integrated position-level closed-form inverse solution method considering both geometric and load capacity limitations.This method consists of a geometric constraint model incorporating the arm angle(φ)and the Global Configuration(GC)to avoid joint limits and singularities,and a load capacity model to constrain the feasible domain of the arm angle.Further,trajectory tracking simulations and experiments are conducted to validate the feasibility of the proposed inverse solution method.The simulated maximum output torque,maximum output power and total energy consumption of the robotic arm are reduced by up to 2.0%,13.3%,and 33.3%,respectively.The experimental results demonstrate that the robotic arm can bear heavy loads in a human-like posture,effectively reducing the maximum output torque and energy consumption of the robotic arm by 1.83%and 5.03%,respectively,while avoiding joints beyond geometric and load capacity limitations.The proposed design provides a high payload–weight ratio and an efficient pose control solution for robotic arms,which can potentially broaden the application spectrum of humanoid robots.

RESEARCH ON SEARCH AND RECOGNI-TION FOR CONSTRAINT BASED ON COMPREHENSION OF GRAPH

A promising approach on the search for geometric constraint of directionalgraph in off-line parametric design has been put forward. The method for representation of thedirectional graph is given firstly, then the constraint model for every geometry element is putforward. By the search of geometric constraint, it sets up the topology constraint relation on thedifferent element objects, which are not related in geometry data base, and achieves the identifyfor the directional graph. The algorithm of recognizing geometric constraint is described in detail,in the meantime, the application example in off-line parametric design on dimension-driven isgiven.

Research on an algorithm for solving parameter ranges in parametric drawing systems

To solve the problem that in parametric drawing systems, unreasonable parameter values in a parametric model often result in an improper shape of a geometric object, this paper proposes a novel algebraic algorithm for determining the valid range of parameter values in certain 2-dimensional parametric drawing systems. This algorithm can solve valid range of parameters such as radius and coordinate of centre points of parametric models with only linear segments and circles. The result of the study shows that all values within the valid range provided by this algorithm can ensure that the topological shape of a geometric object does not change after reconstruction, and to some extent, this algorithm can significantly promote the efficiency of parametric drawing system design and the intel- lectual level of human-computer interaction. The analysis shows that complexity of this algorithm is O（n2）.

Topology Optimization for Harmonic Excitation Structures with Minimum Length Scale Control Using the Discrete Variable Method

Continuumtopology optimization considering the vibration response is of great value in the engineering structure design.The aimof this studyis toaddress the topological designoptimizationof harmonic excitationstructureswith minimumlength scale control to facilitate structuralmanufacturing.Astructural topology design based on discrete variables is proposed to avoid localized vibration modes,gray regions and fuzzy boundaries in harmonic excitation topology optimization.The topological design model and sensitivity formulation are derived.The requirement of minimum size control is transformed into a geometric constraint using the discrete variables.Consequently,thin bars,small holes,and sharp corners,which are not conducive to the manufacturing process,can be eliminated from the design results.The present optimization design can efficiently achieve a 0–1 topology configuration with a significantly improved resonance frequency in a wide range of excitation frequencies.Additionally,the optimal solution for harmonic excitation topology optimization is not necessarily symmetric when the load and support are symmetric,which is a distinct difference fromthe static optimization design.Hence,one-half of the design domain cannot be selected according to the load and support symmetry.Numerical examples are presented to demonstrate the effectiveness of the discrete variable design for excitation frequency topology optimization,and to improve the design manufacturability.

Analysis on steering characteristics of crawler pipeline robot

In order to improve the elbow passing performance and different diameter adaptability of pipeline robot,a supported crawler pipeline robot is designed,which adopts screw nut mechanism and hinge four-bar mechanism to adapt to the complex environment such as variable diameter pipeline and elbow.The steering characteristics passing through the elbow are studied,the kinematic of pipeline robot bending steering is established,the geometric constraint(GC)and steering constraint(SC)in the elbow are analyzed,and the steering experiment is conducted.The results show that the robot can pass through the elbow by the SC model.The SC model can reduce the motor current and energy consumption when the robot passes through the elbow.

Geometric constraint solving with geometric transformation

This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems with loops. The latter algorithm is of quadratic complexity and is complete for constraint problems about simple polygons. The key to it is to combine the idea of graph based methods for geometric constraint solving and geometric transformations coming from rule-based methods.

A stereo matching algorithm using multi-peak candidate matches and geometric constraints

Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correlation coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate matches. Multi-peak candidates are extracted corresponding to three closest feature points at first. The corresponding multi-peak candidate matches are used to construct the model polygon. Correspondence is determined based on the local geometric relations between the three feature points and the multi-peak candidates. The disparity test and the global consistency checkout are applied to eliminate the remaining ambiguous matches that are not removed by the local geometric relational test. Experimental results show that the proposed algorithm is feasible and accurate.

Image Selective Segmentation under Geometrical Constraints Using an Active Contour Approach

In this paper we propose a new model for segmentation of an image under some geometrical constraints in order to detect special regions of interest.Our work is based on the recent work by Gout et al.[Numer.Algorithms,39(2005),pp.155-173 and 48(2008),pp.105-133]using geodesic active contours models,by combining it with the idea of a piecewise constant Mumford-Shah model as with the non-selective Chan-Vese segmentation.Numerical tests show that our method is more robust than the previous works.

Distance geometric constraint filtering algorithm and its application in UWB location

This paper proposed a novel wireless location algorithm based on distance geometry （DG） constraint filtering for the time of arrival （TOA） of the signal （namely as DG-TOA）. Filtering and processing of the observed data and leading to the mathematical formulas based on DG-TOA algorithm are applied to location, also play crucial rules. Simulation results show that the proposed DG-TOA algorithm can provide more valid observation data and be more precise than least square estimate （LSE） algorithm in dense, multi-route, indoor circumstances with the ranging estimation error.

Improved quadric surfaces recognition from scanned mechanical models

This paper presents a novel algorithm for identifying quadric surfaces from scanned mechanical models. We make several important improvements over the existing variational 3D shape segmentation framework, which utilizes Lloyd＇s iteration. First, instead of using randomized initialization （which likely falls into non-optimal minimum）, the RANSAC-based initialization approach is adopted. Given a good initialization, our method converges quickly than previous approaches. Second, in order to enhance the stability and the robustness, we carefully modify the distortion-minimizing flooding algorithm by using seed regions instead of seed triangles. Third, the geometric constraints are introduced into the optimization framework. The segmentation quality is further improved. We validate the efficiency and the robustness of our proposed method on various datasets, and demonstrate that our method outperforms state-of-art approaches.

Size and Shape of Polymer Chain near a Flat Surface

The size and the shape of non-reversal random-walking polymerchains near an impenetrable, non- interacting flat surface areinvestigated by means of Monte Carlo simulation on the simple cubiclattice. It was found that both size and shape are dependent on thenormal-to-surface distance z_0 of the first segment of chain. We findthat the size and shape of chains, characterized by mean squareradius of gyration and mean asphericity parameter respectively, show similar dependence on distance z_0.

Quasi-static Deployment Simulation for Deployable Space Truss Structures

A new method was proposed for quasi-static deployment analysis of deployable space truss structures. The structure is assumed a rigid assembly, whose constraints are classified as three categories:rigid member constraint, joint-attached kinematic constraint and boundary constraint. And their geometric constraint equations and derivative matrices are formulated. The basis of the null space and M-P inverse of the geometric constraint matrix are employed to determine the solution for quasi-static deployment analysis. The influence introduced by higher terms of constraints is evaluated subsequently. The numerical tests show that the new method is efficient.

Hierarchical Geometric Constraint Model for Parametric Feature Based Modeling

A new geometric constraint model is described, which is hierarchical and suitable for parametric feature based modeling. In this model, different levels of geometric information are represented to support various stages of a design process. An efficient approach to parametric featu-re based modeling is also presented, adopting the high level geometric constraint model. The low level geometric model such as B-reps can be derived automatically from the high level geometric constraint model, enabling designers to perform their task of detailed design.