自由特征及对象族特征造型研究
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摘要
在语义特征模型中,特征语义由形状信息和功能信息构成,这种建模系统不仅能完整定义特征的语义信息,而且能在模型的整个设计周期内维护特征语义的有效性,使设计人员在产品开发所有阶段设计有正确语法和一致语义的模型。随着CAD技术的不断发展,工业设计模型越来越复杂,精确度越来越高,这些需求驱动特征造型技术不断发展。当前语义特征造型技术还不成熟,很多技术难点还未攻克。本文针对语义特征建模系统,对自由特征及对象族特征造型关键技术进行研究,主要研究内容如下：
详细阐述了一种自由特征模型参数化方法,通过封装参数和约束创建任意形状的体特征。通过在基准曲面上确定多个自由特征定义点,执行插值运算构造与基准曲面正交的横截面,对横截面执行蒙皮算法和扫掠算法,创建封闭自由体特征。算法实例表明,此方法构造的自由特征与基准曲面之间是G2连续的。为提高自由特征建模效率,提出一种语义特征造型中针对自由特征几何约束问题的求解算法。通过分析约束图,识别出四面体和三角形子问题；利用图分析算法将自由特征定义点上的距离约束和角度约束映射到四面体和三角形约束图上；利用局部传播法求解各子问题,先求解三角形约束,再利用手向性规则求解四面体约束；将各子问题的解组合为问题的全局解。
提出一种新的陈述式语义特征模型,即陈述式对象族理论模型,给出模型的表示方法、拓扑形态以及几何形态。定义了模型的基本元素,以及模型成员的几何信息和拓扑信息,详细说明了对象族的不同特征和不同属性。基于组重写方法和自由度分析法,提出一种求解陈述式对象族模型的几何约束求解算法。将模型分类,给出每类模型的重写规则。在刚性组或非刚性组系统中,穷举地应用重写规则的较小集合执行本算法,一直到没有可用的重写规则为止,最后得到组的集合即为系统的求解策略。该算法不仅能识别刚性子问题,而且能识别只能通过自由度方法求解的子问题,可以确定系统是完备约束的、过约束的、还是欠约束的。
针对陈述式对象族模型拓扑约束问题,提出一种新的求解方法。将所有拓扑约束通过映射函数映射成为布尔约束,利用布尔约束求解器求解问题的解。首先假设求解器已经找到一个解,将此解作为一个参数,通过增加子句,将解中的值取反赋予系统中第一个自由变量。如果没有找到新解,确定下一个自由变量,一直到没有自由变量为止。如果向系统中成功增加取反子句,可找到一个解。通过递归应用本算法找到更多解。如果不能向系统变量中增加取反子句,此时算法退出。如果还可以增加,则调用递归算法。为使递归算法更加高效,在返回解之前,删除算法中所有单位子句。
针对陈述式对象族模型拓扑改变问题,提出一种跟踪拓扑变化的算法。算法首先建立参数和拓扑之间的关系,通过几何形态建立与几何约束系统相关联的参数化模型和拓扑实体,确定系统中哪些实体依赖变量参数。通过增加几何约束构造每个依赖实体的退化实例,利用几何约束求解器求解该退化实例,计算出变量参数对应的临界值。重复此过程,一直找到所有的临界变量。
陈述式对象族模型中有效性约束的两个重要方法是几何约束和拓扑约束,用户在维护模型有效性时可能因为参数选取不当产生无效模型。针对此问题,提出一种为单个参数确定恰当参数范围算法,在这个范围内任意数值都符合有效性要求。算法首先对拓扑约束图进行分析,找到角度约束和距离约束,将约束增加到相应几何约束中；再分析由几何约束求解器创建的结构图,找到一个或多个退化子问题的临界参数值；最后测试所有区间中的具体数值,从而确定准确参数范围。
Feature semantics consist of shape information and function information in semantic feature model,it is not only to define completely feature semantic, but also to maintain model's validity in total life cycle in semantic feature modeling system, therefore, users design model which is right in grammar and consistent in semantics in all of development stages. With the development of CAD technology, industrial design model has been more and more complexity, and its accuracy has also been higher and higher, feature modeling technology has been driven by these requirements to develop. At present, semantic feature modeling technology is immature, and has lots of technique difficulties to be conquered. To semantic feature modeling system, key technologies about freeform feature and family of object feature are researched in this thesis, and the main contents are as follows:
A parameterization algorithm of freeform feature was proposed in this thesis, parameters and constraints were encapsulated to create freeform shape volume feature in this method. Several freeform feature definition points were specified on a base surface, and interpolation algorithms were computed on these points to construct cross-section located on and orthogonal with the base surface, then these cross-sections were computed with skinning algorithm. The algorithm's example indicated that G2continuity between freeform feature created by this method and base surface can be guaranteed. To improve efficiencies of freeform feature modeling, a geometric constraint solving algorithm of semantic feature modeling was presented in this thesis. In this algorithm, feature dependency graph was analyzed to recognize tetrahedron and triangle sub-problems. Distance constraints and angle constraints on freeform feature definition points were mapped to a constraint graph of tetrahedron and triangle by a kind of graph analysis algorithms. Then each sub-problem was solved by local propagation method, triangle constraint was solved, and tetrahedron constraint was solved by hand-direction rules. Finally, solves of every sub-problem were combined into a global solve.
A new kind of declarative semantic feature model was proposed in this thesis, and geometric representation, topological structure and geometric structure were provided. Basic elements, geometric information and topological information were defined, different properties of different features and family of object were specified. Based on cluster rewrite approach and degree of freedom analyzing method, geometric constraint solving algorithm of declarative family of object feature model was proposed. Feature models were divided three types, namely, rigid cluster, scalable cluster and radial cluster in this algorithm. Rewrite rules were described, rules were to exhaustively applied a small set of rewrite rules to a system of rigid and non-rigid clusters, and the set of clusters remaining when no more rewrite rules can be applied represent the generic solution of the system. From the generic solution, modeling system could compute particular solutions, and determine whether the system is well-constrained, under-constrained or over-constrained.
A topological constraint solving method of declarative family of object model was presented in this thesis, all topological constraints were mapped to boolean constraints by mapping functions, then constraint problems were solved in solver. The algorithm for finding all solutions assumes that a solution has already been found by the solver, and is given as an argument to the algorithm, along with the solver state, and a third argument representing the number of fixed variables. The algorithm attempts to fix the first free variable in the system to the complementary value of the value in the given solution. It does this by adding a unit-clause to the system. If this results in an un-satisfiable problem, then instead the variable is fixed to the value found in the solution. As long as no new solution is found, the next free variable in the system is fixed, until no free variables remain.
To topological change problem in declaring family of object models, a tracking topological change algorithm was proposed in this thesis. Relations between parameter and topology were built, and created a system of geometric constraints to relate the parameters of a model to topological entities in the geometric representation. From the decomposition of this system into its rigid subsystems, we determine which entities are dependent on the variant parameter. For each dependent entity, degenerate cases were constructed by adding geometric constraints to the system. The degenerate cases were solved using a geometric constraint solver, and from the solutions the corresponding values of the variant parameter were computed, i.e. the critical values. This process was repeated for different topological variants of the model, until all critical values had been found.
Geometric constraint and topological constraint are two important representations of validity constraint in declarative family of object model. Invalid models are produced because of un-available parameters when users are maintaining feature models, an approach for automatically determining the allowable range for parameters of geometric constraints was presented in this thesis, and each parameter value is available in this range. Firstly, topological constraint graph was analyzed to find angle constraint and distance constraint, and add these constraints to geometric constraints. Then structure graph created by geometric constraint solver was analyzed to find one or more critical parameter value of degenerate sub-problems. Finally, parameter ranges in all ranges were tested to determine accurate parameter value.
详细阐述了一种自由特征模型参数化方法,通过封装参数和约束创建任意形状的体特征。通过在基准曲面上确定多个自由特征定义点,执行插值运算构造与基准曲面正交的横截面,对横截面执行蒙皮算法和扫掠算法,创建封闭自由体特征。算法实例表明,此方法构造的自由特征与基准曲面之间是G2连续的。为提高自由特征建模效率,提出一种语义特征造型中针对自由特征几何约束问题的求解算法。通过分析约束图,识别出四面体和三角形子问题；利用图分析算法将自由特征定义点上的距离约束和角度约束映射到四面体和三角形约束图上；利用局部传播法求解各子问题,先求解三角形约束,再利用手向性规则求解四面体约束；将各子问题的解组合为问题的全局解。
提出一种新的陈述式语义特征模型,即陈述式对象族理论模型,给出模型的表示方法、拓扑形态以及几何形态。定义了模型的基本元素,以及模型成员的几何信息和拓扑信息,详细说明了对象族的不同特征和不同属性。基于组重写方法和自由度分析法,提出一种求解陈述式对象族模型的几何约束求解算法。将模型分类,给出每类模型的重写规则。在刚性组或非刚性组系统中,穷举地应用重写规则的较小集合执行本算法,一直到没有可用的重写规则为止,最后得到组的集合即为系统的求解策略。该算法不仅能识别刚性子问题,而且能识别只能通过自由度方法求解的子问题,可以确定系统是完备约束的、过约束的、还是欠约束的。
针对陈述式对象族模型拓扑约束问题,提出一种新的求解方法。将所有拓扑约束通过映射函数映射成为布尔约束,利用布尔约束求解器求解问题的解。首先假设求解器已经找到一个解,将此解作为一个参数,通过增加子句,将解中的值取反赋予系统中第一个自由变量。如果没有找到新解,确定下一个自由变量,一直到没有自由变量为止。如果向系统中成功增加取反子句,可找到一个解。通过递归应用本算法找到更多解。如果不能向系统变量中增加取反子句,此时算法退出。如果还可以增加,则调用递归算法。为使递归算法更加高效,在返回解之前,删除算法中所有单位子句。
针对陈述式对象族模型拓扑改变问题,提出一种跟踪拓扑变化的算法。算法首先建立参数和拓扑之间的关系,通过几何形态建立与几何约束系统相关联的参数化模型和拓扑实体,确定系统中哪些实体依赖变量参数。通过增加几何约束构造每个依赖实体的退化实例,利用几何约束求解器求解该退化实例,计算出变量参数对应的临界值。重复此过程,一直找到所有的临界变量。
陈述式对象族模型中有效性约束的两个重要方法是几何约束和拓扑约束,用户在维护模型有效性时可能因为参数选取不当产生无效模型。针对此问题,提出一种为单个参数确定恰当参数范围算法,在这个范围内任意数值都符合有效性要求。算法首先对拓扑约束图进行分析,找到角度约束和距离约束,将约束增加到相应几何约束中；再分析由几何约束求解器创建的结构图,找到一个或多个退化子问题的临界参数值；最后测试所有区间中的具体数值,从而确定准确参数范围。
Feature semantics consist of shape information and function information in semantic feature model,it is not only to define completely feature semantic, but also to maintain model's validity in total life cycle in semantic feature modeling system, therefore, users design model which is right in grammar and consistent in semantics in all of development stages. With the development of CAD technology, industrial design model has been more and more complexity, and its accuracy has also been higher and higher, feature modeling technology has been driven by these requirements to develop. At present, semantic feature modeling technology is immature, and has lots of technique difficulties to be conquered. To semantic feature modeling system, key technologies about freeform feature and family of object feature are researched in this thesis, and the main contents are as follows:
A parameterization algorithm of freeform feature was proposed in this thesis, parameters and constraints were encapsulated to create freeform shape volume feature in this method. Several freeform feature definition points were specified on a base surface, and interpolation algorithms were computed on these points to construct cross-section located on and orthogonal with the base surface, then these cross-sections were computed with skinning algorithm. The algorithm's example indicated that G2continuity between freeform feature created by this method and base surface can be guaranteed. To improve efficiencies of freeform feature modeling, a geometric constraint solving algorithm of semantic feature modeling was presented in this thesis. In this algorithm, feature dependency graph was analyzed to recognize tetrahedron and triangle sub-problems. Distance constraints and angle constraints on freeform feature definition points were mapped to a constraint graph of tetrahedron and triangle by a kind of graph analysis algorithms. Then each sub-problem was solved by local propagation method, triangle constraint was solved, and tetrahedron constraint was solved by hand-direction rules. Finally, solves of every sub-problem were combined into a global solve.
A new kind of declarative semantic feature model was proposed in this thesis, and geometric representation, topological structure and geometric structure were provided. Basic elements, geometric information and topological information were defined, different properties of different features and family of object were specified. Based on cluster rewrite approach and degree of freedom analyzing method, geometric constraint solving algorithm of declarative family of object feature model was proposed. Feature models were divided three types, namely, rigid cluster, scalable cluster and radial cluster in this algorithm. Rewrite rules were described, rules were to exhaustively applied a small set of rewrite rules to a system of rigid and non-rigid clusters, and the set of clusters remaining when no more rewrite rules can be applied represent the generic solution of the system. From the generic solution, modeling system could compute particular solutions, and determine whether the system is well-constrained, under-constrained or over-constrained.
A topological constraint solving method of declarative family of object model was presented in this thesis, all topological constraints were mapped to boolean constraints by mapping functions, then constraint problems were solved in solver. The algorithm for finding all solutions assumes that a solution has already been found by the solver, and is given as an argument to the algorithm, along with the solver state, and a third argument representing the number of fixed variables. The algorithm attempts to fix the first free variable in the system to the complementary value of the value in the given solution. It does this by adding a unit-clause to the system. If this results in an un-satisfiable problem, then instead the variable is fixed to the value found in the solution. As long as no new solution is found, the next free variable in the system is fixed, until no free variables remain.
To topological change problem in declaring family of object models, a tracking topological change algorithm was proposed in this thesis. Relations between parameter and topology were built, and created a system of geometric constraints to relate the parameters of a model to topological entities in the geometric representation. From the decomposition of this system into its rigid subsystems, we determine which entities are dependent on the variant parameter. For each dependent entity, degenerate cases were constructed by adding geometric constraints to the system. The degenerate cases were solved using a geometric constraint solver, and from the solutions the corresponding values of the variant parameter were computed, i.e. the critical values. This process was repeated for different topological variants of the model, until all critical values had been found.
Geometric constraint and topological constraint are two important representations of validity constraint in declarative family of object model. Invalid models are produced because of un-available parameters when users are maintaining feature models, an approach for automatically determining the allowable range for parameters of geometric constraints was presented in this thesis, and each parameter value is available in this range. Firstly, topological constraint graph was analyzed to find angle constraint and distance constraint, and add these constraints to geometric constraints. Then structure graph created by geometric constraint solver was analyzed to find one or more critical parameter value of degenerate sub-problems. Finally, parameter ranges in all ranges were tested to determine accurate parameter value.
引文
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