The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic Bézier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of Bézier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible.

One challenge in building collaborative design tools that use speech and sketch input is distinguishing gesture pen strokes from those representing device structure, that is, object strokes. In previous work, we developed a gesture/object classifier that uses features computed from the pen strokes and the speech aligned with them. Experiments indicated that the speech features were the most important for distinguishing gestures, thus indicating the critical importance of the speech–sketch alignment. Consequently, we have developed a new alignment technique that employs a two-step process: the speech is first explicitly segmented (primarily into clauses), then the segments are aligned with the pen strokes. Our speech segmentation step is unique in that it uses sketch features for locating segment boundaries in multimodal dialog. In addition, it uses a single classifier to directly combine word-based, prosodic (pause), and sketch-based features. In the second step, segments are initially aligned with strokes based on temporal correlation, and then classifiers are used to detect and correct two common alignment errors. Our two-step technique has proven to be substantially more accurate at alignment than the existing technique that lacked explicit segmentation. It is more important that, for nearly all cases, our new technique results in greater gesture classification accuracy than the existing technique, and performed nearly as well as the benchmark manual speech–sketch alignment.