42414181
G2 interpolation of free form curve networks by biquintic Gregory patches
Abstract The problem of interpolating a free form curve network with irregular topology is investigated in order to create a curvature continuous surface. The spanning curve segments are parametric quintic polynomials, the interpolating surface elements are biquintic Gregory patches. A necessary compatibility condition is formulated and proved which need to be satisfied at each node of the curve network. Constraints are derived for assuring G 2 continuity between biquintic Gregory patches, which share a common side or a common corner point. The above conditions still leave certain geometric freedom for defining the entire G 2 surface, so following some analysis a particular construction is presented, by which after computing the principle curvatures at each node the free parameters are locally set for each interpolating Gregory patch.
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.
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.
23819859
Curve and surface design: H. Hagen (Ed.) SIAM, USA (1992), 219 pp, ISBN 089871-281-5
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.
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.
944953
The Sonification of Rhythms in Human Electroencephalogram
We use sonification of temporal information extracted from scalp EEG to characterize the dynamic properties of rhythms in certain frequency bands. Sonification proves particularly useful in the simultaneous monitoring of several EEG channels. Our results suggest sonification as an important tool in the analysis of multivariate data with subtle correlation differences.
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.
1385818
Gestural Interactions for Multi-parameter Audio Control and Audification
This paper presents an interactive multi-modal system for real-time multi-parametric gestural control of audio processing applications. We claim that this can ease the use / control of different tasks and for this we present the following as a demonstration: (1) A musical application, i.e. the multi-parametric control of digital audio effects, and (2) a scientific application, i.e. the interactive navigation of audifications. In the first application we discuss the use of PCA-based control axes and clustering to obtain dimensionality reduced control variables. In the second application we show how the tightly closed human-computer loop actively supports the detection and discovery of features in data under analysis.
13115995
Neural gas sonification - growing adaptive interfaces for interacting with data
In This work we present an approach using incrementally constructed neural gas networks to 'grow' an intuitive interface for interactive exploratory sonification of high-dimensional data. The sonifications portray information about the intrinsic data dimensionality and its variation within the data space. The interface follows the paradigm of model-based sonification and consists of a graph of nodes that can be acoustically 'excited' with simple mouse actions. The sound generation process is defined in terms of the node parameters and the graph topology, following a physically motivated model of energy flow through the graph structure. The resulting sonification model is tied to the given data set by constructing both graph topology and node parameters by an adaptive, fully data-driven learning process, using a growing neural gas network. We report several examples of applying this method to static data sets and point out a generalization to the task of process analysis.
39788442
Best Fit Surface Curvature at Vertices of Topologically Irregular Curve Networks