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

Incommensurable design descriptions

Data management is a persistent problem in design and manufacturing. This is because different processes require different descriptions of the same design concept. Descriptions can include geometry and/or topology as well as other non-spatial information, such as design intent, and over the course of a design and manufacturing process it is often necessary to convert between descriptions non-sequentially, to support development and realisation of a design concept. This paper highlights the difficulties that arise in managing different descriptions by exploring what are possibly unrealistically simple examples involving drawings of simple shapes. Although simple, the examples illustrate a fundamental truth; that the information embedded in the structures of different descriptions of a design are often incommensurable, and this can introduce challenges in the management of design data

Shape interpretation with design computing

How information is interpreted has significant impact on how it can be used. This is particularly important in design where information from a wide variety of sources is used in a wide variety of contexts and in a wide variety of ways. This paper is concerned with the information that is created, modified and analysed during design processes, specifically with the information that is represented in shapes. It investigates how design computing seeks to support these processes, and the difficulties that arise when it is necessary to consider alternative interpretations of shape. The aim is to establish the problem of shape interpretation as a general challenge for research in design computing, rather than a difficulty that is to be overcome within specific processes. Shape interpretations are common characteristics of several areas of enquiry in design computing. This paper reviews these, brings an integrated perspective and draws conclusions about how this underlying process can be supported

Implementation of curved shape grammars

Research into shape grammar implementation has been largely concerned with rectilinear shapes and there has been limited research into implementation on shapes composed of curves. This reflects developments of the shape grammar formalism which has been defined largely according to straight lines, planes, and associated volumes. In this paper, implementation of shape grammars on curved shapes is examined using algorithms for shape operations on shapes composed of para- metric curves. These algorithms have been implemented in a shape grammar interpreter for shapes composed of quadratic Bezier curves, which is illustrated via application of a shape grammar that generates Celtic knotwork patterns. Implementing shape grammars on shapes composed of Bezier curves highlights difficulties that arise when the shape grammar formalism is applied to curved shapes, and the paper concludes with a discussion that explores these difficulties and indicates potential implications for the shape grammar formalism

Exploration of multi-material surfaces as weighted shapes

The introduction of multi-material additive manufacturing makes it possible to fabricate objects with varying material properties, leading to new types of designs that exhibit interesting and complicated behaviours. But, computational design methods typically focus on the structure and geometry of designed objects, and do not incorporate material properties or behaviour. This paper explores how material properties can be included in computational design, by formally modelling them as weights in shape computations. Shape computations, such as shape grammars, formalise the description and manipulations of pictorial representation in creative design processes. The paper explores different ways that material properties can be formally modelled as weights, and presents examples in which multi-material surfaces are modelled as weighted planes, giving rise to flexible behaviours that can be considered in design exploration

Extending the algebras of design

Algebras of design have previously been investigated for shapes composed of rectilinear geometric elements, such as lines and planes, and the properties of these algebras have been found to be beneficial for formalising designs, as well as the visual processes used by designers as they manipulate shapes in their design explorations. In this paper, an overview is presented of the application of these algebras in formalising design processes, and this is followed by a discussion concerning issues that arise when the algebras are extended to accommodate non-rectilinear designs, represented by shapes composed of curves, surfaces and solids. Consideration of non-rectilinear shapes introduces new problems not previously identified in the established formalism, resulting from the geometries and topologies of the shapes. These give rise to significant questions about the relationships between shapes and the property of embedding, which is fundamental to the construction of algebras of design

Formalising flexible multi-material surfaces as weighted shapes

The introduction of multi-material additive manufacturing makes it possible to fabricate objects with varying material properties, leading to new types of designs that exhibit interesting and complicated behaviours. But, computational design methods typically focus on the structure and geometry of designed objects, and do not incorporate material properties or behaviour. This paper explores how material properties can be included in computational design, by formally modelling them as weights in shape computations. Shape computations, such as shape grammars, formalise the description and manipulations of pictorial representation in creative design processes. The paper explores different ways that material properties can be formally modelled as weights, and presents examples in which multimaterial surfaces are modelled as weighted planes, giving rise to flexible behaviours

Towards product platform introduction: optimising commonality of components

Companies that design and manufacture products for a wide range of related applications need to offer the right product for each use. A platform design strategy allows designing the product range based on product platforms, where some of the components and systems are common across the range whereas other components are individual for each product variant. This paper presents the problems that a company faces when trying to introduce a platform strategy and outlines a method to find suitable components to be made common. The method is shown with a simple case. The approach uses fuzzy logic to obtain a suitable criterion to assess the overall value of the product line and a genetic algorithm for finding the set of components to be made commo

Pinwheel patterns: from 2D to 3D schemas

Pinwheels are generic configurations in architectural layout planning. Planar pinwheels provide familiar schemes for layouts which present design ‘in the round’ with a cyclic symmetry. The paper examines the 3-D versions of 2-D pinwheels where a ‘locked’ joint with three rectangular volume elements aligned along orthogonal axes is a characteristic feature. Pairing handed versions of these locked joints yields a candidate for a 3-D pinwheel schema with six repeated volume elements and threefold cyclic symmetry. Shape rules, based on spatial relations between volumes, generate this and other examples of 3-D pinwheel schemas. These schemas are set in a wider analysis of the numbers and types of joints in 3-rectangulations in terms of maximal bounding planes. The bounding-plane views of the arrangements is set alongside more functional volume descriptions which enables the elements and relations in architectural form to be (re)generated and (re)interpreted both ‘in view’ and ‘in use’

Supporting shape reinterpretation with eye tracking

It has been argued that reinterpretation is an essential process in design generation and idea exploration. However, computational design tools, such as computer-aided design systems, offer poor support for shape reinterpretation, and as such are not well suited to ideation in conceptual design. One of the key difficulties in implementing computational systems that support shape reinterpretation is the issue of interface – how can a user intuitively guide a system with respect to their interpretation of a designed shape? In this paper, a software prototype is presented that uses an eye tracking interface to support reinterpretation of shapes according to recognised subshapes. The prototype is based on eye tracking studies, and uses gaze data and user input to restructure designed shapes so that they afford manipulation according to users’ interpretations