Reference Frames

Abstract

In all aspects of perception and action, the generation of shape involves reference objects - points, axes, and Cartesian frames - with respect to which the other objects are judged and constructed. For example, in human perception, reference frames strongly determine the visual organization of a stimulus set: The same stimulus set can have different perceptual representations depending on how the frames are oriented with respect to the set; see Mach [102], Goldmeier [45], Leyton [96]. In categorization, Rosch [130], has shown that cognitive categories have reference points with respect to which the remaining stimulus members are judged, e.g., diagonal orientations are seen in terms of vertical or horizontal orientations, the number 99 in terms of 100. In animal motor control and navigation, Gallistel [37] [38] has put forward substantial neurophysiological and behavioral evidence demonstrating the significant role of reference frames in determining the animal’s computation of directed action. In computer-aided design, the design process moves fowards by the successive use of reference objects, starting with the construction plane. In mechanical design, several types of reference objects are explicitly available and are usually called datum objects. These are employed for every phase of the design - from initial sketching, to full part design, to assembly planning. They are crucial in establishing constraints, which are required in all aspects of design. In 3D solid modeling, systems of reference objects are continually used; e.g., in free-form deformation, a shape is framed by a reference scaffold which is distorted, thereby distorting the embedded shape.