Computation with Curved Shapes: Towards Freeform Shape Generation in Design
Computation with Curved Shapes: Towards Freeform Shape Generation in Design
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弯曲形状计算：在设计中实现自由形状生成
DOI：
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发表时间：
2007
期刊：
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通讯作者：
I. Jowers
中科院分区：
文献类型：
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作者：
I. Jowers
形状计算是一种形式化表示，它参考形式指定设计过程的特定方面。它们是根据形状语法定义的，其中设计的图形表示的操作通过形状和应用于这些形状的规则来形式化。它们经常被应用于建筑中，以便形式化给定设计集的风格属性，并在这些风格中生成新的设计。然而，在更一般的设计领域的应用受到限制。这主要是由于形状语法形式主义的最初定义仅限于由线、平面或实体组成的直线形状。在建筑中，这种形状很常见，但在许多设计领域，例如工业设计，更自由的形状也很普遍。因此，本论文描述的研究涉及扩展形状语法形式主义的适用性，使其能够进行自由形状的计算。
形状计算利用规则来操纵形式代数中设计的子形状。这些代数是根据嵌入属性指定的，并且之前已针对直线形状进行了定义。在本文中，探讨了自由形状的嵌入特性，并扩展了代数，以便形式化此类形状的计算。基于这些代数，指定了形状运算并引入了算法，使规则能够应用于由自由形式 B´ezier 曲线组成的形状。算法的实现使得形状语法能够应用到比以前更自由的形状。在本论文中，介绍了形状语法的实现，以便探索考虑自由形状计算时出现的理论问题，以及形状计算作为设计模型和生成自由形状的模式的应用的实际问题。
Shape computations are a formal representation that specify particular aspects of the design process with reference to form. They are defined according to shape grammars, where manipulations of pictorial representations of designs are formalised by shapes and rules applied to those shapes. They have frequently been applied in architecture in order to formalise the stylistic properties of a given corpus of designs, and also to generate new designs within those styles. However, applications in more general design fields have been limited. This is largely due to the initial definitions of the shape grammar formalism which are restricted to rectilinear shapes composed of lines, planes or solids. In architecture such shapes are common but in many design fields, for example industrial design, shapes of a more freeform nature are prevalent. Accordingly, the research described in this thesis is concerned with extending the applicability of the shape grammar formalism such that it enables computation with freeform shapes.
Shape computations utilise rules in order to manipulate subshapes of a design within formal algebras. These algebras are specified according to embedding properties and have previously been defined for rectilinear shapes. In this thesis the embedding properties of freeform shapes are explored and the algebras are extended in order to formalise computations with such shapes. Based on these algebras, shape operations are specified and algorithms are introduced that enable the application of rules to shapes composed of freeform B´ezier curves. Implementation of the algorithms enables the application of shape grammars to shapes of a more freeform nature than was previously possible. Within this thesis shape grammar implementations are introduced in order to explore both theoretical issues that arise when considering computation with freeform shapes and practical issues concerning the application of shape computation as a model for design and as a mode for generating freeform shapes.