8720995
On the derivatives of second and third degree rational Bézier curves
In this note, an estimate of Floater on the derivatives of rational Bezier curves is improved when the degree of the curve is 2 or 3.
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.
39286473
Proof of the nonintersection conjecture of Hoffmann and Peters
A theorem on the nonintersection of convex curve families is proved. A corresponding conjecture of Hoffmann and Peters concerning the nonintersection of a T-cubic family is verified.
23819859
Curve and surface design: H. Hagen (Ed.) SIAM, USA (1992), 219 pp, ISBN 089871-281-5
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.
42092183
Degree elevation for generalized Poisson functions
In this note a common generalization is given for the Bezier and Poisson functions. Further it is proved that the degree elevated control polygon converges to the function.
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.
7792659
Model-based sonification revisited---authors' comments on Hermann and Ritter, ICAD 2002
We discuss the framework of Model-Based Sonification (MBS) and its contribution to a principled design of mediators between high-dimensional data spaces and perceptual spaces, particularly sound spaces. Data Crystallization Sonification, discussed in the reprinted paper, exemplifies the design of sonification models according to this framework. Finally, promising lines of development in this area are pointed out, concerning generalizations, applications, and open research directions.
39788442
Best Fit Surface Curvature at Vertices of Topologically Irregular Curve Networks
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.
9492137
Interacting with sonification systems: closing the loop
This paper stresses the importance of the human user being tightly embedded within an interactive control loop for exploring data sets using sound. We consider the quality of interaction, and how this can be improved in computer systems by learning from real-world acoustic interactions. We describe how different sonification methods can utilise the human feedback loop to enhance the perception and analysis of the data under investigation. Some considerations are given regarding systems and applications.