Recurrent Modeling

目前的分形工具缺乏对特定自然结构进行建模所需的控制级别。例如，已经建立了许多树木的分形模型，但给定一棵特定的树木，使用现有的分形建模模型很难表示该树木的特定形状。递归建模项目确定了这个问题的三个方面，并试图用几个新的分形建模工具来解决每个方面。目标一：递归模型表征。递归建模致力于将分形表示提升到光滑表面在计算机辅助几何设计中所享有的复杂程度，方法是将其经典的自参考表示转换为标准的隐式和参数形式。递归建模还尝试了“程序几何实例化”，并增强了经典的对象实例化范例，使其能够更有效地表示L系统当前指定的发展的分形模型。目标二：交互式递归建模。递归建模将计算机辅助几何设计的工具扩展到了分形几何。直接操作界面在分形建模过程中提供实时反馈。来自前一个目标的隐含配方允许应用专门为自然建模设计的标准混合配方。将构造性实体几何扩展到包括分形模型，支持从基本体构建复杂形状。目标三：自动递归建模。递归建模从基于模型的计算机视觉领域出发，攻击了分形几何的逆问题：找出与给定形状近似的分形模型的参数。第二个PI是NSF支持的基于模型的计算机视觉研究人员。他在这个问题上的独特观点导致了一种新的解决方案，称为相似散列。相似性散列算法在初始测试中成功地检测到了自相似，并返回了自相似模型参数。递归建模继续这项研究，以开发一种自动系统来发现自然结构中的自亲性。循环建模提出的新工具将对计算机图形学和森林科学领域产生影响。新工具将代表非常详细的几何图形，例如森林和庄稼。这种模型将在图像合成中得到应用，特别是在动画、虚拟环境、基于物理的建模和遥感方面。由于计算机辅助几何设计的流畅表示有助于制造商，由递归建模表示提出的细节的高效表示将有助于环境的研究。***

Current fractal tools lack the level of control necessary to model specific natural structures. For example, many fractal models of trees have been constructed, but given a particular tree, it would be difficult to represent the tree's specific shape using current models of fractal modeling. The recurrent modeling project identifies three aspects to this problem, and attempts to solve each with several new fractal modeling tools. Objective I: Recurrent Model Representation. Recurrent modeling strives to elevate fractal representation to the level of sophistication that smooth surfaces enjoy in computer-aided geometric design by translating their classical self-referential representation into standard implicit and parametric forms. Recurrent modeling also attempts "procedural geometric instancing," and enhancement of the classic object instancing paradigm that enables it to more efficiently represent the development fractal models currently specified by L-systems. Objective II: Interactive Recurrent Modeling. Recurrent modeling extends the tools of computer-aided geometric design to fractal geometry. A direct manipulation interface provides real time feedback in the fractal modeling process. The implicit formulation from the previous objective allows the application of standard blending formulations specifically designed for natural modeling. Extending constructive solid geometry to include fractal models supports the construction of complex shapes from primitives. Objective III: Automatic Recurrent Modeling. Recurrent modeling attacks the inverse problem of fractal geometry: "find the parameters of a fractal model that approximates a given shape" from the domain of model-based computer vision. The second PI is an NSF-supported model-based computer vision researcher. His unique perspective on this problem resulted in a new solution, called "similarity hashing". Similarity hashing successfully detects self-similarity and returns the paramete rs of the selfsimilar model in initial tests. Recurrent modeling continues this research to develop an automated system for discovering selfaffinity in natural structures. The new tools recurrent modeling proposes would impact the fields of computer graphics and forest science. The new tools would represent highly detailed geometrics, such as a forest and crops. Such models would have applications in image synthesis, particularly in animation, virtual environments, physically- based modeling and remote sensing. As the smooth representations of computer-aided geometric design aid manufacturers, the efficient representations of detail proposed by recurrent modeling representations would aid the study of the environment. ***