McLaren's Improved Snub Cube and Other New Spherical Designs in Three Dimensions

Evidence is presented to suggest that, in three dimensions, spherical 6-designs with N points exist for N=24, 26, >= 28; 7-designs for N=24, 30, 32, 34, >= 36; 8-designs for N=36, 40, 42, >= 44; 9-designs for N=48, 50, 52, >= 54; 10-designs for N=60, 62, >= 64; 11-designs for N=70, 72, >= 74; and 12-designs for N=84, >= 86. The existence of some of these designs is established analytically, while others are given by very accurate numerical coordinates. The 24-point 7-design was first found by McLaren in 1963, and -- although not identified as such by McLaren -- consists of the vertices of an "improved" snub cube, obtained from Archimedes' regular snub cube (which is only a 3-design) by slightly shrinking each square face and expanding each triangular face. 5-designs with 23 and 25 points are presented which, taken together with earlier work of Reznick, show that 5-designs exist for N=12, 16, 18, 20, >= 22. It is conjectured, albeit with decreasing confidence for t >= 9, that these lists of t-designs are complete and that no others exist. One of the constructions gives a sequence of putative spherical t-designs with N= 12m points (m >= 2) where N = t^2/2 (1+o(1)) as t -> infinity.Comment: 16 pages, 1 figur

Metrics for Evaluating the Spatial Accuracy of Microphone Arrays

The interest in 3D audio is constantly growing, thus leading to the appearance on the market of many microphone arrays for recording spatial audio, having a variety of sizes, number of channels and shapes, mostly spherical. Among the various characteristics that may have an influence on the quality of these systems, the presented work will deal with the spatial accuracy. The availability of robust methods for evaluating the spatial performance of the microphone arrays allows to compare the systems and to study the effect of different geometries, or beamforming algorithms. On one side, the design of new solutions can be optimized, on the other side a user can identify an optimal system depending on his needs. In this paper, two metrics for evaluating the spatial performance of microphone arrays are described, and two common formats for spatial audio are employed, Ambisonics and Spatial PCM Sampling (SPS). In the first part, the parameters Spatial Correlation and Level Difference are used for assessing the accuracy of the Ambisonics format, which is based on Spherical Harmonics functions. In the second part two classic metrics for loudspeakers, i.e., directivity factor and half power beam width, are employed for evaluating the accuracy of unidirectional virtual microphones, which constitute the base of the SPS format. In the last section, four well-known spherical microphone arrays are analyzed and compared through the described metrics and spatial audio formats

Low Frequency Simulations for Ambisonics Auralization of a Car Sound System

In this paper, a technique is described for obtaining the High Order Ambisonics (HOA) Impulse Responses (IRs) of an automotive infotainment system, relying on Finite Elements Method (FEM) simulations performed in COMSOL Multiphysics. The resulting HOA IRs are employed for auralizing the car sound system, either inside an Ambisonics listening room with a loudspeaker rig or with binaural rendering on a Head Mounted Display (HMD), benefiting from head-tracking and personalized Head Related Transfer Functions (HRTFs). This allows performing subjective tests before the prototype is built and preserving the auditory experience with a degree of realism unattainable with the static binaural approach. Measurements performed in a prototype vehicle with a spherical microphone array are compared to FEM simulations. A good agreement between numerical and experimental methods have been demonstrated

Recording, Analysis and Playback of Spatial Sound Field using Novel Design Methods of Transducer Arrays

Nowadays, a growing interest in the recording and reproduction of spatial audio has been observed. With virtual and augmented reality technologies spreading fast thanks to entertainment and video game industries, also the professional opportunities in the field of engineering are evolving. However, despite many microphone arrays are reaching the market, most of them is not optimized for engineering or diagnostic use and remains mainly confined to voice and music recordings. In this thesis, the design of two new systems for recording and analysing the spatial distribution of sound energy, employing arrays of transducers and cameras, is discussed. Both acoustic and visual spatial information is recorded and combined together to produce static and dynamic colour maps, with a specially designed software and employing Ambisonics and Spatial PCM Sampling (SPS), two common spatial audio formats, for signals processing. The first solution consists in a microphone array made of 32 capsules and a circular array of eight cameras, optimized for low frequencies. The size of the array is designed accordingly to the frequency range of interest for automotive Noise, Vibration & Harshness (NVH) applications. The second system is an underwater probe with four hydrophones and a panoramic camera, with which it is possible to monitor the effects of underwater noise produced by human activities on marine species. Finite Elements Method (FEM) simulations have been used to calculate the array response, thus deriving the filtering matrix and performing theoretical evaluation of the spatial performance. Field tests of the proposed solutions are presented in comparison with the current state-of-the-art equipment. The faithful reproduction of the spatial sound field arouses equally interest. Hence, a method to playback panoramic video with spatial audio is presented, making use of Virtual Reality (VR) technology, spatial audio, individualized Head Related Transfer Functions (HRTFs) and personalized headphones equalization. The work in its entirety presents a complete methodology for recording, analysing and reproducing the spatial information of soundscapes

Impiego di tecniche di misura DIC per lo studio di sistemi di sintesi ortopedici

Nel presente lavoro si esamina la possibilità di impiego di tecniche di correlazione digitale di immagini in configurazione stereoscopica per la valutazione sperimentale in-vitro del campo tridimensionale di spostamento e deformazione generato sottocarico sull’osso trattato con un impianto di sintesi intramidollare. L’inserimento di una rima di frattura praticata sulla diafisi media dell’osso sintetico, ha consentito di studiare il differente comportamento nelle due condizioni limite del decorso clinico a seguito del trattamento chirurgico di impianto. I risultati preliminari riportati nel lavoro dimostrano l’efficacia dell’approccio proposto, che consente di valutare sperimentalmente lo stato tenso-deformativo indotto dalla protesi sull’osso a campo intero e con elevata risoluzione spaziale