基于NURBS的非均质实体建模方法研究
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摘要
非均质实体是指由两种或两种以上组分材料（或空隙）在实体内部规则或非规则分布而形成的具有多重特定功能的构件。为了充分利用这种新型材料零件所具有的优良性能，首要而关键的问题是提供一套实用的复杂非均质实体的造型方法。本文将工业产品的主流表示法——NURBS（Non-Uniform Rational B-Spline）方法融入到非均质实体的造型设计之中，系统地提出了基于NURBS的非均质实体建模方法，取得了如下创新性成果：
1.针对非均质NURBS实体的特点，提出了使用齐次坐标表示点信息的NURBS材料数据结构；提出了一般非均质NURBS实体的统一建模方法，分别给出了非均质NURBS曲线、非均质NURBS曲面、非均质NURBS实体的各三种表示法；提出了特殊非均质NURBS体的构造方法及表达形式，给出了包括非均质直线段、非均质圆、非均质旋转体、非均质圆柱体、非均质圆锥体、非均质球体、非均质拉伸体、非均质一般柱体、非均质线性插值实体、非均质扫掠体、非均质摆转体、非均质孔斯体等十二种不同非均质实体的NURBS表示方法，并从理论和实际应用两个方面详细阐述了NURBS表达式中各基本要素的确定方法。
2.提出了非均质NURBS实体的分层次整合建模方法，该方法在相同的参数空间中，采用不同的NURBS表示形式分别表达几何模型与材料模型，两种模型在建模的某一层中进行整合并生成复杂非均质实体。这种方法在一定程度上减少了材料模型的存储空间，但却依旧保持材料变化上的连续性，同时增加了材料变化的多样性。
3.提出了两种非均质NURBS实体的逆向构造方法，其中张量积的插值方法适合于离散点呈较均匀的矩形网格分层次分布的情况，RBF-NURBS逆向构造法适合于离散点的几何分布是无规则的、散乱的情况。
4.开发了一套复杂非均质实体计算机辅助设计软件系统——NURBS-HO-CAD，该系统同时支持“一步法”与“两步法”的造型设计流程，具有多个非均质实体的保存与读取方式，实现了NURBS-HO-CAD与其它常规CAD/CAM软件之间的数据交换。
Heterogeneous object refers to a solid component consisting of two or more primarymaterials (or pore spaces) distributed continuously or discontinuously within an object,which often shows multiple special performance. In order to obtain the excellent propertyof such novel material parts, efficient modeling methodology for complex heterogeneousobject is primary and crucial. NURBS (Non-Uniform Rational B-Spline) method which isthe main modeling method for industrial products is applied into the heterogeneous objectdesign in this paper. Heterogeneous object modeling design based on NURBS method isintroduced systematically. The creative contributions of this paper summarized as follows.
1. According to the characteristic of heterogeneous NURBS object, NURBS material datastructure is presented which represents the point by homogeneous coordinates. Auniform modeling method for normal heterogeneous NURBS object is presented whichincludes three forms for heterogeneous NURBS curve, heterogeneous NURBS surfaceand heterogeneous NURBS object. Construction techniques and representationmethods for special heterogeneous NURBS object are introduced which includeheterogeneous line, heterogeneous circle, heterogeneous revolution object,heterogeneous cylinder object, heterogeneous cone object, heterogeneous sphere object,heterogeneous extruded object, heterogeneous general cylinder object, heterogeneouslinear interpolated object, heterogeneous sweeping object, heterogeneous swung object,heterogeneous Coons object. All the key elements in these heterogeneous NURBSexpressions are introduced in detail in terms of theory and practice.
2. A layered integrating method for heterogeneous NURBS object is presented. Geometrymodel and material model are expressed in different forms and they could be integratedin one layer in the process of modeling to generate complex heterogeneous object. Withthis method, storage space of material model could be reduced, but it still keeps thecontinuity of material distribution and increase the diversity of material transition.
3. Two inverse construction methods are presented to create heterogeneous NURBSobjects. Interpolated method of tensor product is fit for the discrete points which aredistributed in uniform rectangular grid layers. RBF-NURBS inverse constructionmethod is fit for the discrete points which are distributed irregularly and randomly.
4. A practical and multifunctional computer aided design software system is developedwhich is named as NURBS-HO-CAD. In this system, heterogeneous object could bedesigned by “one step method” or “two steps method”, and could be saved and open indifferent ways. Data exchange between NURBS-HO-CAD and other normalCAD/CAM system is realized in this novel system.
1.针对非均质NURBS实体的特点，提出了使用齐次坐标表示点信息的NURBS材料数据结构；提出了一般非均质NURBS实体的统一建模方法，分别给出了非均质NURBS曲线、非均质NURBS曲面、非均质NURBS实体的各三种表示法；提出了特殊非均质NURBS体的构造方法及表达形式，给出了包括非均质直线段、非均质圆、非均质旋转体、非均质圆柱体、非均质圆锥体、非均质球体、非均质拉伸体、非均质一般柱体、非均质线性插值实体、非均质扫掠体、非均质摆转体、非均质孔斯体等十二种不同非均质实体的NURBS表示方法，并从理论和实际应用两个方面详细阐述了NURBS表达式中各基本要素的确定方法。
2.提出了非均质NURBS实体的分层次整合建模方法，该方法在相同的参数空间中，采用不同的NURBS表示形式分别表达几何模型与材料模型，两种模型在建模的某一层中进行整合并生成复杂非均质实体。这种方法在一定程度上减少了材料模型的存储空间，但却依旧保持材料变化上的连续性，同时增加了材料变化的多样性。
3.提出了两种非均质NURBS实体的逆向构造方法，其中张量积的插值方法适合于离散点呈较均匀的矩形网格分层次分布的情况，RBF-NURBS逆向构造法适合于离散点的几何分布是无规则的、散乱的情况。
4.开发了一套复杂非均质实体计算机辅助设计软件系统——NURBS-HO-CAD，该系统同时支持“一步法”与“两步法”的造型设计流程，具有多个非均质实体的保存与读取方式，实现了NURBS-HO-CAD与其它常规CAD/CAM软件之间的数据交换。
Heterogeneous object refers to a solid component consisting of two or more primarymaterials (or pore spaces) distributed continuously or discontinuously within an object,which often shows multiple special performance. In order to obtain the excellent propertyof such novel material parts, efficient modeling methodology for complex heterogeneousobject is primary and crucial. NURBS (Non-Uniform Rational B-Spline) method which isthe main modeling method for industrial products is applied into the heterogeneous objectdesign in this paper. Heterogeneous object modeling design based on NURBS method isintroduced systematically. The creative contributions of this paper summarized as follows.
1. According to the characteristic of heterogeneous NURBS object, NURBS material datastructure is presented which represents the point by homogeneous coordinates. Auniform modeling method for normal heterogeneous NURBS object is presented whichincludes three forms for heterogeneous NURBS curve, heterogeneous NURBS surfaceand heterogeneous NURBS object. Construction techniques and representationmethods for special heterogeneous NURBS object are introduced which includeheterogeneous line, heterogeneous circle, heterogeneous revolution object,heterogeneous cylinder object, heterogeneous cone object, heterogeneous sphere object,heterogeneous extruded object, heterogeneous general cylinder object, heterogeneouslinear interpolated object, heterogeneous sweeping object, heterogeneous swung object,heterogeneous Coons object. All the key elements in these heterogeneous NURBSexpressions are introduced in detail in terms of theory and practice.
2. A layered integrating method for heterogeneous NURBS object is presented. Geometrymodel and material model are expressed in different forms and they could be integratedin one layer in the process of modeling to generate complex heterogeneous object. Withthis method, storage space of material model could be reduced, but it still keeps thecontinuity of material distribution and increase the diversity of material transition.
3. Two inverse construction methods are presented to create heterogeneous NURBSobjects. Interpolated method of tensor product is fit for the discrete points which aredistributed in uniform rectangular grid layers. RBF-NURBS inverse constructionmethod is fit for the discrete points which are distributed irregularly and randomly.
4. A practical and multifunctional computer aided design software system is developedwhich is named as NURBS-HO-CAD. In this system, heterogeneous object could bedesigned by “one step method” or “two steps method”, and could be saved and open indifferent ways. Data exchange between NURBS-HO-CAD and other normalCAD/CAM system is realized in this novel system.
引文
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