面向特征的传统艺术图案建模技术研究
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摘要
随着世界各国对传统文化遗产保护的重视,传统文化遗产的数字化建模也越来越受到学者的关注。传统艺术图案作为文化遗产的一部分,有着很高的审美价值和应用价值。对于传统艺术图案而言,其建模过程就是通过对图案的形状以及艺术特征进行分析和归纳,在计算机中存储和处理,并在需要的时候展示给用户。传统艺术图案建模的意义,一方面是对传统艺术图案的保护和继承;通过建模可以有效的保存这些传统的艺术图案,而且在建模过程中需要对传统艺术图案进行分析,也是对传统艺术图案特定规律特征的归纳和总结;另一方面也需要相应的图形学算法来满足建模过程中的各种需求,这在一定意义上也促进了图形学算法的发展。传统艺术图案数字化的结果还可以用于娱乐、动画等产业,体现出实际的应用价值。
本文的面向特征的传统艺术图案建模方法,是针对剪纸这一类艺术图案做研究,率先提出了三维剪纸图形这一艺术形式并完成了一个三维剪纸图形的编辑系统。三维剪纸图形是用二维剪纸图案装饰的具备二维剪纸特征的三维几何模型,其建模是指用参数控制的矢量几何图案来表示剪纸特征图案,并通过网格模型的表面编辑方法解决二维剪纸图案在三维网格模型表面映射问题。本文的贡献如下;
(1)本文率先提出了一种面向特征的剪纸艺术图案的矢量几何图案构造方法。剪纸图案包含不同变化特征的纹样和结构信息,因此很难用简单的模型来表示。我们用面向特征的建模方法对样本艺术图案做分析,根据图案的差异与相似关系能够准确的抽取其特征,并建立特征模型,来表示图案之间异同以及变化关系,并用矢量几何图案来表示剪纸图案。这些矢量几何图案作为基本的单元构成组件库,在组件库中用户可以选择基本单元并组合生成新剪纸图案。
(2)本文提出了面向矢量几何图案的分层网格模型表面编辑算法,它将层次定义为模型表面可重叠的面片区域,与不同层次对应的矢量几何图案可以互相重叠的在模型表面编辑。而传统的模型分片方法得到的是无交叠的区域,它引入的边界约束限制了表面编辑时矢量几何图案在模型表面的排布。分层的网格模型表面编辑方法消除了这个限制,能够准确的映射矢量几何图案到网格模型表面并实现矢量几何图案快速的移动、修改、复制、粘贴和删除功能。此外现有的分层网格模型表面编辑方法只修改模型的几何信息,而没有修改模型的拓扑结构。本文的方法将矢量几何图案在各自对应层次上分别进行几何信息与拓扑结构的融合,同时更新和保持层次与结果模型拓扑关系的对应,在合并所有的层次后得到正确拓扑结构的结果模型。
(3)在参数化方法这一领域,本文提出了一种基于网格模型微分属性控制的参数化优化方法,可以结合不同参数化方法的优点,综合得到优化的参数化映射结果。传统的参数化方法将问题都定义为针对特定变形函数最小化的约束求解问题。然而对于顶点曲率变化比较大的曲面,现有参数化方法很难保证参数域上顶点扭曲变形程度以及映射前后顶点分布密度的一致性。我们首先定义了顶点的变形度量,用于衡量不同参数化方法结果在参数平面上由顶点引起变形扭曲,然后在微分几何理论基础上,计算每个顶点在扭曲变形最小的参数平面上的微分坐标,并以此来构造梯度场,最后在新的参数域上重建网格模型,得到扭曲变形和顶点分布密度经过优化的参数化结果。
(4)本文提出了三维剪纸图形生成算法,使用分层的网格模型表面编辑的方法将剪纸图案映射到三维网格模型表面,从而得到具有剪纸艺术特征和丰富表现力的三维网格模型-三维剪纸图形。此外本文对现有的剖面图绘制算法做了改进,能够准确的绘制剪纸图案所特有的镂空效果,同时提供了半自动的编辑方法以方便用户快速的生成三维剪纸图形。
The importance of traditional culture heritage protection is growing rapidly world wide, researchers are paying more attention on the modeling of traditional culture heritage. As part of traditional culture heritage, traditional artistic designs are of big values both aesthetically and practically. The modeling process of traditional artistic design includes analyzing the shape as well as artistic characteristics, implementing storing them in computer and showing them to users if necessary. Such modeling research prompots the research how those designs are organized and transform them into methmatical expressions. Potential applications of the resultant models are advertisement, computer animation and entertainment industry. In this dissertation
we present a novel artistic effect named 3D paper-cut, on which 3D mesh models are decorated with 2D paper-cut patterns. We model the paper-cut pattern with feature-oriented modeling paradigm and store them with vector graphics form. We solve the mapping problem that may arise between paper-cut patterns and mesh model during mesh surface editing phase. Specifically we make the following contributions:
(1) We present a feature oriented paper-cut pattern modeling pardigm. The paper-cut patterns contain structure with varying form, thus they can not be described in a simple model. We analyse paper-cut pattern features and extract them to comstruct the model with rules of variation. The models are stored in the format of vector graphics for the purpose of reuse.
(2) A layer based mesh surface editing method is proposed to simplify the mesh surface editing with different vector graphics, we construct a mapping between vector graphics and local layers which is a sub mesh of original mesh. Layer based mesh surface editing modifies both geometric and topological information of whole mesh. Our method preserve the consistence of topological information during re-meshing phase. Our method can be also used as layer based texture mapping and generating mesh model decorated with both texture and vector graphics.
(3) We proposed a hybrid parameterization optimization method utilizing the gradient field manipulation which combines features generated by different parameterization methods. Traditional parameterization methods minimize a single target metric in parametric domain, and get different results. Based on differential theory, we choose the parameterization method for each vertex with less distortion in different methods, and calculate differential coordinates in correspondence parametric domain. Those differential coordinates make a new gradient field which is then used to reconstruct a new mesh model in parametric domain to get the final optimized parameterization result .
(4) We present an 3D paper-cut generating system by which we create expressive 3D mesh models with paper-cut effect. These models are build with the layer based mesh surface editing algorithms. Besides we improve a triming algorithm to preview cut out effect in traditional paper cut crafts. We also provide a semiautomatic editing method to accelerate the generation of 3D paper-cut models. The resultant system can be used by artists to make paper-cut animations with ease.
本文的面向特征的传统艺术图案建模方法,是针对剪纸这一类艺术图案做研究,率先提出了三维剪纸图形这一艺术形式并完成了一个三维剪纸图形的编辑系统。三维剪纸图形是用二维剪纸图案装饰的具备二维剪纸特征的三维几何模型,其建模是指用参数控制的矢量几何图案来表示剪纸特征图案,并通过网格模型的表面编辑方法解决二维剪纸图案在三维网格模型表面映射问题。本文的贡献如下;
(1)本文率先提出了一种面向特征的剪纸艺术图案的矢量几何图案构造方法。剪纸图案包含不同变化特征的纹样和结构信息,因此很难用简单的模型来表示。我们用面向特征的建模方法对样本艺术图案做分析,根据图案的差异与相似关系能够准确的抽取其特征,并建立特征模型,来表示图案之间异同以及变化关系,并用矢量几何图案来表示剪纸图案。这些矢量几何图案作为基本的单元构成组件库,在组件库中用户可以选择基本单元并组合生成新剪纸图案。
(2)本文提出了面向矢量几何图案的分层网格模型表面编辑算法,它将层次定义为模型表面可重叠的面片区域,与不同层次对应的矢量几何图案可以互相重叠的在模型表面编辑。而传统的模型分片方法得到的是无交叠的区域,它引入的边界约束限制了表面编辑时矢量几何图案在模型表面的排布。分层的网格模型表面编辑方法消除了这个限制,能够准确的映射矢量几何图案到网格模型表面并实现矢量几何图案快速的移动、修改、复制、粘贴和删除功能。此外现有的分层网格模型表面编辑方法只修改模型的几何信息,而没有修改模型的拓扑结构。本文的方法将矢量几何图案在各自对应层次上分别进行几何信息与拓扑结构的融合,同时更新和保持层次与结果模型拓扑关系的对应,在合并所有的层次后得到正确拓扑结构的结果模型。
(3)在参数化方法这一领域,本文提出了一种基于网格模型微分属性控制的参数化优化方法,可以结合不同参数化方法的优点,综合得到优化的参数化映射结果。传统的参数化方法将问题都定义为针对特定变形函数最小化的约束求解问题。然而对于顶点曲率变化比较大的曲面,现有参数化方法很难保证参数域上顶点扭曲变形程度以及映射前后顶点分布密度的一致性。我们首先定义了顶点的变形度量,用于衡量不同参数化方法结果在参数平面上由顶点引起变形扭曲,然后在微分几何理论基础上,计算每个顶点在扭曲变形最小的参数平面上的微分坐标,并以此来构造梯度场,最后在新的参数域上重建网格模型,得到扭曲变形和顶点分布密度经过优化的参数化结果。
(4)本文提出了三维剪纸图形生成算法,使用分层的网格模型表面编辑的方法将剪纸图案映射到三维网格模型表面,从而得到具有剪纸艺术特征和丰富表现力的三维网格模型-三维剪纸图形。此外本文对现有的剖面图绘制算法做了改进,能够准确的绘制剪纸图案所特有的镂空效果,同时提供了半自动的编辑方法以方便用户快速的生成三维剪纸图形。
The importance of traditional culture heritage protection is growing rapidly world wide, researchers are paying more attention on the modeling of traditional culture heritage. As part of traditional culture heritage, traditional artistic designs are of big values both aesthetically and practically. The modeling process of traditional artistic design includes analyzing the shape as well as artistic characteristics, implementing storing them in computer and showing them to users if necessary. Such modeling research prompots the research how those designs are organized and transform them into methmatical expressions. Potential applications of the resultant models are advertisement, computer animation and entertainment industry. In this dissertation
we present a novel artistic effect named 3D paper-cut, on which 3D mesh models are decorated with 2D paper-cut patterns. We model the paper-cut pattern with feature-oriented modeling paradigm and store them with vector graphics form. We solve the mapping problem that may arise between paper-cut patterns and mesh model during mesh surface editing phase. Specifically we make the following contributions:
(1) We present a feature oriented paper-cut pattern modeling pardigm. The paper-cut patterns contain structure with varying form, thus they can not be described in a simple model. We analyse paper-cut pattern features and extract them to comstruct the model with rules of variation. The models are stored in the format of vector graphics for the purpose of reuse.
(2) A layer based mesh surface editing method is proposed to simplify the mesh surface editing with different vector graphics, we construct a mapping between vector graphics and local layers which is a sub mesh of original mesh. Layer based mesh surface editing modifies both geometric and topological information of whole mesh. Our method preserve the consistence of topological information during re-meshing phase. Our method can be also used as layer based texture mapping and generating mesh model decorated with both texture and vector graphics.
(3) We proposed a hybrid parameterization optimization method utilizing the gradient field manipulation which combines features generated by different parameterization methods. Traditional parameterization methods minimize a single target metric in parametric domain, and get different results. Based on differential theory, we choose the parameterization method for each vertex with less distortion in different methods, and calculate differential coordinates in correspondence parametric domain. Those differential coordinates make a new gradient field which is then used to reconstruct a new mesh model in parametric domain to get the final optimized parameterization result .
(4) We present an 3D paper-cut generating system by which we create expressive 3D mesh models with paper-cut effect. These models are build with the layer based mesh surface editing algorithms. Besides we improve a triming algorithm to preview cut out effect in traditional paper cut crafts. We also provide a semiautomatic editing method to accelerate the generation of 3D paper-cut models. The resultant system can be used by artists to make paper-cut animations with ease.
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