Computation with Curved Shapes: Towards Freeform Shape Generation in Design

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

Shape exploration of designs in a style: toward generation of product designs

Generative specifications have been used to systematically codify established styles in several design fields including architecture and product design. We examine how designers explore new designs in the early stages of product development as they manipulate and interpret shape representations. A model of exploration is proposed with four types of shape descriptions (contour, decomposition, structure, and design) and the results of the exploration are presented. Generative rules are used to provide consistent stylistic changes first within a given decomposition and second through changing the structure. Style expresses both the analytical order of explanation and the synthetic complexity of exploration. The model of exploration is consistent with observations of design practice. The application of generative design methods demonstrates a logical pattern for early stage design exploration. The model provides the basis for tools to assist designers in exploring families of designs in a style and for following new interpretations that move the exploration from one family to another

The construction of curved shapes

Application of a shape grammar involves the repetitive task of matching and replacing subshapes of a design under transformation, and as such is well suited for computer implementation. As a result, ever since the conception of the shape grammar formalism, efforts have been made to develop computer programs that automate shape grammar applications. Much of this effort has been directed towards the problem of subshape detection, which involves recognising subshapes embedded in a design. Solutions to this problem have been presented for shapes composed of rectilinear geometric elements, such as straight lines, and algorithms based on these solutions have been implemented in a variety of shape grammar interpreters. However, there has been less research concerning the solution of the subshape detection problem for shapes composed of nonrectilinear geometric elements, such as curve segments. In this paper a method of intrinsic matching is presented, which enables comparison of the embedding properties of parametric curves. This method has been employed in order to develop shape algorithms which can be implemented in shape grammar interpreters for shapes composed of parametric curve segments, arranged in two-dimensional or three-dimensional space

Computer-aided design synthesis: an application of shape grammars

Computer-aided design systems enable the creation of digital product definitions that are widely used throughout the design process. Typically, such product definitions are created after the bulk of [shape] designing has been completed because their creation requires a detailed knowledge of the shape that is to be defined. Shape grammars have been applied in a range of domains to generate design shapes that conform to a given style early in design processes. A key challenge that restricts their implementation lies in the detection of embedded shapes, sub-shapes, which are manipulated according to shape rules to create new shapes. The automatic detection of sub-shapes is an open research question within the shape grammar community. The research reported in this paper explored the use of computer vision techniques to address this problem; the results achieved to date show real promise. An early prototype is presented and demonstrated on a designer's sketches

Computer aided design: an early shape synthesis system

Today’s computer aided design systems enable the creation of digital product definitions that are widely used throughout the design process, for example in analysis or manufacturing. Typically, such product definitions are created after the bulk of [shape] designing has been completed because their creation requires a detailed knowledge of the shape that is to be defined. Consequently, there is a gulf between the exploration processes that result in the selection of a design concept and the creation of its definition. In order to address this distinction, between design exploration and product definition, understanding of how designers create and manipulate shapes is necessary. The research outlined in this paper results from work concerned with addressing these issues, with the long term goal of informing a new generation of computer aided design systems which support design exploration as well as the production of product definitions. This research is based on the shape grammar formalism. Shape grammars have been applied in a range of domains, commonly to generate shapes or designs that conform to a given style. However, a key challenge that restricts the implementation of shape grammar systems lies in the detection of embedded parts, or sub-shapes, which are manipulated according to shape rules to create new shapes. The automatic detection of sub-shapes is an open research question within the shape grammar community and has been actively explored for over thirty years. The research reported in this paper explores the use of computer vision techniques to address this problem; the results achieved to date show real promise. An early prototype is presented and demonstrated on design sketches of martini glasses taken from a student research project

Shape detection with vision: implementing shape grammars in conceptual design

Despite more than 30 years of research, shape grammar implementations have limited functionality. This is largely due to the difficult problem of subshape detection. Previous research has addressed this problem analytically and has proposed solutions that directly compare geometric representations of shapes. Typically, such work has concentrated on shapes composed of limited geometry, for example straight lines or parametric curves, and as a result, their application has been restricted. The problem of general subshape detection has not been resolved. In this paper, an alternative approach is proposed, in which subshape detection is viewed as a problem of object recognition, a sub-domain of computer vision. In particular, a general method of subshape detection is introduced based on the Hausdorff distance. The approach is not limited in terms of geometry, and any shapes that can be represented in an image can be compared according to the subshape relation. Based on this approach, a prototype shape grammar system has been built in which the geometry of two-dimensional shapes is not restricted. The system automates the discovery of subshapes in a shape, enabling the implementation of shape rules in a shape grammar. Application of the system is illustrated via consideration of shape exploration in conceptual design. The manipulations of sketched design concepts are formalised by shape rules that reflect the types of shape transformations employed by designers when sketching