结合隐式曲面的网格融合
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摘要
为用户提供强大易用的造型工具,满足他们创造复杂几何形体的需要一直是计算机图形学界所致力追求的目标之一。现有商业造型系统的复杂性使得它们的使用都局限于一些专业人员。基于草图的造型工具允许用户通过一些简单的线条勾画进行三维创作,操作简洁,迎合了一般爱好者的需求,但功能有限,只支持简单几何形体的构造。
许多图像处理软件如Photoshop都支持图像之间的粘贴和混合,这些操作已成为人们由已有的图像片断生成复杂图像的习惯方式。对于三维造型来说,如果可以从已有模型的部件中“粘贴”组合出新的几何模型,一方面可降低造型的难度以满足一般业余爱好者的需要,另一方面又能大大提高动画师创作新模型的效率。
近年来,国内外研究学者在三维网格模型的融合领域做了很多开创性的工作,提出了一些切实可行的技术。但是这些现有的算法在进行网格融合时物体时都采用将待融合物体的边界直接贴在一起的策略,无法处理多个边界同时融合的情况。事实上在融合物体时,既可以直接把待融合物体的边界相接,也可以在两物体之间加入一个与原物体光滑相连的中间过渡物体。本文基于这样一种思路提出了两种新的融合算法,并对这种融合框架下的其他相关算法进行了深入的探讨。本文的主要贡献如下:
■基于函数混合的网格融合。我们提出了一种新的函数混合曲面的定义,并将之用于描述中间过渡物体。该方法能够有效的混合分别位于两个平行平面上的多个边界并保持边界连续过渡,用户只需要简单输入若干参数就可以调整过渡曲面的形状。对于非平行情况,我们提供了基于微分变形的后处理方法。
■基于草图接口的融合方法。我们采用变分隐式曲面来定义中间过渡物体,但是当约束点比较稀少时,变分隐式曲面难以生成令人满意的中间过渡物体。我们设计了一个草图接口让用户指定过渡物体的轮廓,然后将轮廓线转化为对变分隐式曲面的约束条件以生成符合给定轮廓的中间过渡物体。该草图接口也成为用户进行过渡曲面形状控制的一种直观方式。
■隐式曲面多边形化方法。我们提出了两种局部化的隐式曲面多边形化算法以满足本文应用的需要:复合粒子系统支持交互操作过程中隐式曲面的快速显示并可以在操作结束后迅速转化为三角网格;局部化Marching Cubes算法提供了一种鲁棒的等值面抽取方法。两个算法都能自动抽取出所定义隐式曲面与融合相关的部分而舍弃其余部分并与待融合部件的边界无缝连接。
■相关交互技术以及几何细节处理算法。模型分割是网格融合系统的一个基本操作,我们实现了两种分割方法以满足了应用的需求。模型定位则能进一步降低用户交互的难度,我们设计了一种基于过渡基元的方法。对于包含丰富细节的模型之间的融合,我们提供了如何在过渡曲面上延续待融合模型边界周围的细节,并达到渐变混合的效果的解决方案。
Providing powerful and easy-to-use tools for users to create complex geometric object is one of the most challenging tasks for computer graphics community. Most commercial modeling systems are difficult to use for non-professional users, which limits their applications. Conversely, 3D sketching programs are good for novices, but the limited function make them only suitable for prototype design. How to achieve the balance between easy-to-use interfaces and powerful functions has confused researchers in geometric modeling area for a long time.
Pasting and blending are two commonly used operations in image editing systems such as Photoshop. It has been a natural way to create complex images by applying the above two operations on several images coming from different sources. With the developments of data acquisition techniques, there have been lots of geometric models. If we can construct new models by compositing components from existing ones, the modeling efficiency for complex 3D objects will be improved greatly. However, it is difficult to perform pasting and blending between surfaces when they are represented by triangular meshes. In recent years, researchers have proposed various techniques for mesh fusion, however, most of them have compatible limitations.
We present a new mesh composition paradigm based on the analysis of existing methods. We choose to composite objects together by constructing a transient part which smoothly connects these objects at their boundaries other than stitching them around the boundaries directly. In our new scheme, it becomes very easy to fuse multiple boundaries together in a session which is difficult for other mesh fusion frameworks. We propose two different fusion methods under this paradigm. We also proposed feasible solutions for the other related problems such as object segmentation, part placement and detail transition. Specifically, this dissertation has the following contributions:
Mesh fusion using functional blending. We propose a new functional blending approach to specify the transient surface. A user can adjust the shape of the transient surface easily by specifying some parameters.
Sketch based mesh fusion. We adopt the variational implicit surface as the transient surface. We present a sketch interface for users to specify the shape of the transient surface, and the sketch interface also improves the stability of the variational interpolation under sparse constraints.
Implicit surface tessellation. We present two localized implicit surface tessellation algorithms to extract the part of the transient surface to be reserved automatically: Compound particle system provides a fast implicit surface visualization method meeting the requirements of interactive operations; Localized marching cubes method extracts the iso-surface with correct topology.
Other algorithms related to mesh fusion. Mesh segmentation is a basic operation in mesh fusion system, we perform two segmentation tools allowing users to cut out the part of interest from models easily. When pasting a part onto a model, the first challenge is to find the transformation that tansfroms it into the appropriate coordinate frame with respect to the rest of the model. We provide a simple-interface for the user to position and orient parts when they are added to the new model. For the mesh fusion with highly detailed models, we provide a scheme to cover these details from the boundary to the whole transient area, and make the details coming from different sources blending together.
许多图像处理软件如Photoshop都支持图像之间的粘贴和混合,这些操作已成为人们由已有的图像片断生成复杂图像的习惯方式。对于三维造型来说,如果可以从已有模型的部件中“粘贴”组合出新的几何模型,一方面可降低造型的难度以满足一般业余爱好者的需要,另一方面又能大大提高动画师创作新模型的效率。
近年来,国内外研究学者在三维网格模型的融合领域做了很多开创性的工作,提出了一些切实可行的技术。但是这些现有的算法在进行网格融合时物体时都采用将待融合物体的边界直接贴在一起的策略,无法处理多个边界同时融合的情况。事实上在融合物体时,既可以直接把待融合物体的边界相接,也可以在两物体之间加入一个与原物体光滑相连的中间过渡物体。本文基于这样一种思路提出了两种新的融合算法,并对这种融合框架下的其他相关算法进行了深入的探讨。本文的主要贡献如下:
■基于函数混合的网格融合。我们提出了一种新的函数混合曲面的定义,并将之用于描述中间过渡物体。该方法能够有效的混合分别位于两个平行平面上的多个边界并保持边界连续过渡,用户只需要简单输入若干参数就可以调整过渡曲面的形状。对于非平行情况,我们提供了基于微分变形的后处理方法。
■基于草图接口的融合方法。我们采用变分隐式曲面来定义中间过渡物体,但是当约束点比较稀少时,变分隐式曲面难以生成令人满意的中间过渡物体。我们设计了一个草图接口让用户指定过渡物体的轮廓,然后将轮廓线转化为对变分隐式曲面的约束条件以生成符合给定轮廓的中间过渡物体。该草图接口也成为用户进行过渡曲面形状控制的一种直观方式。
■隐式曲面多边形化方法。我们提出了两种局部化的隐式曲面多边形化算法以满足本文应用的需要:复合粒子系统支持交互操作过程中隐式曲面的快速显示并可以在操作结束后迅速转化为三角网格;局部化Marching Cubes算法提供了一种鲁棒的等值面抽取方法。两个算法都能自动抽取出所定义隐式曲面与融合相关的部分而舍弃其余部分并与待融合部件的边界无缝连接。
■相关交互技术以及几何细节处理算法。模型分割是网格融合系统的一个基本操作,我们实现了两种分割方法以满足了应用的需求。模型定位则能进一步降低用户交互的难度,我们设计了一种基于过渡基元的方法。对于包含丰富细节的模型之间的融合,我们提供了如何在过渡曲面上延续待融合模型边界周围的细节,并达到渐变混合的效果的解决方案。
Providing powerful and easy-to-use tools for users to create complex geometric object is one of the most challenging tasks for computer graphics community. Most commercial modeling systems are difficult to use for non-professional users, which limits their applications. Conversely, 3D sketching programs are good for novices, but the limited function make them only suitable for prototype design. How to achieve the balance between easy-to-use interfaces and powerful functions has confused researchers in geometric modeling area for a long time.
Pasting and blending are two commonly used operations in image editing systems such as Photoshop. It has been a natural way to create complex images by applying the above two operations on several images coming from different sources. With the developments of data acquisition techniques, there have been lots of geometric models. If we can construct new models by compositing components from existing ones, the modeling efficiency for complex 3D objects will be improved greatly. However, it is difficult to perform pasting and blending between surfaces when they are represented by triangular meshes. In recent years, researchers have proposed various techniques for mesh fusion, however, most of them have compatible limitations.
We present a new mesh composition paradigm based on the analysis of existing methods. We choose to composite objects together by constructing a transient part which smoothly connects these objects at their boundaries other than stitching them around the boundaries directly. In our new scheme, it becomes very easy to fuse multiple boundaries together in a session which is difficult for other mesh fusion frameworks. We propose two different fusion methods under this paradigm. We also proposed feasible solutions for the other related problems such as object segmentation, part placement and detail transition. Specifically, this dissertation has the following contributions:
Mesh fusion using functional blending. We propose a new functional blending approach to specify the transient surface. A user can adjust the shape of the transient surface easily by specifying some parameters.
Sketch based mesh fusion. We adopt the variational implicit surface as the transient surface. We present a sketch interface for users to specify the shape of the transient surface, and the sketch interface also improves the stability of the variational interpolation under sparse constraints.
Implicit surface tessellation. We present two localized implicit surface tessellation algorithms to extract the part of the transient surface to be reserved automatically: Compound particle system provides a fast implicit surface visualization method meeting the requirements of interactive operations; Localized marching cubes method extracts the iso-surface with correct topology.
Other algorithms related to mesh fusion. Mesh segmentation is a basic operation in mesh fusion system, we perform two segmentation tools allowing users to cut out the part of interest from models easily. When pasting a part onto a model, the first challenge is to find the transformation that tansfroms it into the appropriate coordinate frame with respect to the rest of the model. We provide a simple-interface for the user to position and orient parts when they are added to the new model. For the mesh fusion with highly detailed models, we provide a scheme to cover these details from the boundary to the whole transient area, and make the details coming from different sources blending together.
引文
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