42941157
On a tolerance problem of parametric curves and surfaces
Abstract This paper gives bounds for the moduli of continuity of parametric curves and surfaces.
128210111
NURBS for curve and surface design: G. Farin(Ed.) SIAM, 1991, 161 pp, ISBN 0-89871-286-6
23819859
Curve and surface design: H. Hagen (Ed.) SIAM, USA (1992), 219 pp, ISBN 089871-281-5
46596104
On the smoothness of offset surfaces
It is proved that the geometric continuity of the offset of a composite base surface is the same as that of the base surface.
43499978
On higher order derivatives of blending functions
It is well-known that the derivatives of the Bezier curves can be expressed as Bezier curves where the control points are the differences of the original control points. This phenomenon is characterized for finite and infinite function systems.
15389938
Geometrical criteria on the higher order smoothness of composite surfaces
Abstract A generalization of a theorem by Pegna and Wolter—called Linkage Curve Theorem—is presented. The new theorem provides a condition for joining two surfaces with high order geometric continuity of arbitrary degree n. It will be shown that the Linkage Curve Theorem can be generalized even for the case when the common boundary curve is only G1.
10467921
Gesture Desk - An Integrated Multi-modal Gestural Workplace for Sonification
This paper presents the gesture desk, a new platform for a human-computer interface at a regular computer workplace. It extends classical input devices like keyboard and mouse by arm and hand gestures, without the need to use any inconvenient accessories like data gloves or markers. A central element is a “gesture box” containing two infrared cameras and a color camera which is positioned under a glass desk. Arm and hand motions are tracked in three dimensions. A synchronizer board has been developed to provide an active glare-free IR-illumination for robust body and hand tracking. As a first application, we demonstrate interactive real-time browsing and querying of auditory self-organizing maps (AuSOMs). An AuSOM is a combined visual and auditory presentation of high-dimensional data sets. Moving the hand above the desk surface allows to select neurons on the map and to manipulate how they contribute to data sonification. Each neuron is associated with a prototype vector in high-dimensional space, so that a set of 2D-topologically ordered feature maps is queried simultaneously. The level of detail is selected by hand altitude over the table surface, allowing to emphasize or deemphasize neurons on the map.
5100483
The Importance of Interaction in Sonification
This paper argues for a special focus on the use of dynamic human interaction to explore datasets while they are being transformed into sound. We describe why this is a special case of both human computer interaction (HCI) techniques and sonification methods. Humans are adapted for interacting with their physical environment and making continuous use of all their senses. When this exploratory interaction is applied to a dataset (by continuously controlling its transformation into sound) new insights are gained into the data’s macro and micro-structure, which are not obvious in a visual rendering. This paper reviews the importance of interaction in sonification, describes how a certain quality of interaction is required, provides examples of the techniques being applied interactively, and outlines a plan of future work to develop interaction techniques to aid sonification.
2180531
Crystallization sonification of high-dimensional datasets
This paper introduces Crystallization Sonification, a sonification model for exploratory analysis of high-dimensional datasets. The model is designed to provide information about the intrinsic data dimensionality (which is a local feature) and the global data dimensionality, as well as the transitions between a local and global view on a dataset. Furthermore the sound allows to display the clustering in high-dimensional datasets. The model defines a crystal growth process in the high-dimensional data-space which starts at a user selected “condensation nucleus” and incrementally includes neighboring data according to some growth criterion. The sound summarizes the temporal evolution of this crystal growth process. For introducing the model, a simple growth law is used. Other growth laws which are used in the context of hierarchical clustering are also suited and their application in crystallization sonification offers new ways to inspect the results of data clustering as an alternative to dendrogram plots. In this paper, the sonification model is described and example sonifications are presented for some synthetic high-dimensional datasets.
19159245
Improving and Extending the Lim/Lee Exponentiation Algorithm
. In [5] Lim and Lee present an algorithm for fast exponentiation in a given group which is optimized for a limited amount of storage. The algorithm uses one precomputation for several computations in order to minimize the average time needed for one exponentiation. This paper generalizes the previous work proposing several improvements and a method for fast precomputation. The basic Lim/Lee algorithm is improved by determining the optimal segmentation of the exponent. Finally, it is shown that the improved Lim/Lee algorithm is faster than the previous one in average case.
12168310
Hand Postures for Sonification Control
Sonification is a rather new technique in human-computer interaction which addresses auditory perception. In contrast to speech interfaces, sonification uses non-verbal sounds to present information. The most common sonification technique is parameter mapping where for each data point a sonic event is generated whose acoustic attributes are determined from data values by a mapping function. For acoustic data exploration, this mapping must be adjusted or manipulated by the user. We propose the use of hand postures as a particularly natural and intuitive means of parameter manipulation for this data exploration task. As a demonstration prototype we developed a hand posture recognition system for gestural controlling of sound. The presented implementation applies artificial neural networks for the identification of continuous hand postures from camera images and uses a real-time sound synthesis engine. In this paper, we present our system and first applications of the gestural control of sounds. Techniques to apply gestures to control sonification are proposed and sound examples are given.