Computation of spherical harmonic representations of source directivity based on the finite-distance signature

The measurement of directivity for sound sources that are not electroacoustic transducers is fundamentally limited because the source cannot be driven with arbitrary signals. A consequence is that directivity can only be measured at a sparse set of frequencies—for example, at the stable partial oscillations of a steady tone played by a musical instrument or from the human voice. This limitation prevents the data from being used in certain applications such as time-domain room acoustic simulations where the directivity needs to be available at all frequencies in the frequency range of interest. We demonstrate in this article that imposing the signature of the directivity that is obtained at a given distance on a spherical wave allows for all interpolation that is required for obtaining a complete spherical harmonic representation of the source’s directivity, i.e., a representation that is viable at any frequency, in any direction, and at any distance. Our approach is inspired by the far-field signature of exterior sound fields. It is not capable of incorporating the phase of the directivity directly. We argue based on directivity measurement data of musical instruments that the phase of such measurement data is too unreliable or too ambiguous to be useful. We incorporate numerically-derived directivity into the example application of finite difference time domain simulation of the acoustic field, which has not been possible previously

Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space

A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that no gauge invariant perturbation should become unbounded in time. A self-consistent linear response analysis of these perturbations, based upon an invariant effective action principle, necessarily involves metric fluctuations about the mean semi-classical geometry, and brings in the two-point correlation function of the quantum energy-momentum tensor in a natural way. This linear response equation contains no state dependent divergences and requires no new renormalization counterterms beyond those required in the leading order semi-classical approximation. The general linear response criterion is applied to the specific example of a scalar field with arbitrary mass and curvature coupling in the vacuum state of Minkowski spacetime. The spectral representation of the vacuum polarization function is computed in n dimensional Minkowski spacetime, and used to show that the flat space solution to the semi-classical Einstein equations for n=4 is stable to all perturbations on distance scales much larger than the Planck length.Comment: 22 pages: This is a significantly expanded version of gr-qc/0204083, with two additional sections and two new appendices giving a complete, explicit example of the semi-classical stability criterion proposed in the previous pape

DeepJoin: Learning a Joint Occupancy, Signed Distance, and Normal Field Function for Shape Repair

We introduce DeepJoin, an automated approach to generate high-resolution repairs for fractured shapes using deep neural networks. Existing approaches to perform automated shape repair operate exclusively on symmetric objects, require a complete proxy shape, or predict restoration shapes using low-resolution voxels which are too coarse for physical repair. We generate a high-resolution restoration shape by inferring a corresponding complete shape and a break surface from an input fractured shape. We present a novel implicit shape representation for fractured shape repair that combines the occupancy function, signed distance function, and normal field. We demonstrate repairs using our approach for synthetically fractured objects from ShapeNet, 3D scans from the Google Scanned Objects dataset, objects in the style of ancient Greek pottery from the QP Cultural Heritage dataset, and real fractured objects. We outperform three baseline approaches in terms of chamfer distance and normal consistency. Unlike existing approaches and restorations using subtraction, DeepJoin restorations do not exhibit surface artifacts and join closely to the fractured region of the fractured shape. Our code is available at: https://github.com/Terascale-All-sensing-Research-Studio/DeepJoin.Comment: To be published at SIGGRAPH Asia 2022 (Journal

Learning Neural Parametric Head Models

We propose a novel 3D morphable model for complete human heads based on hybrid neural fields. At the core of our model lies a neural parametric representation that disentangles identity and expressions in disjoint latent spaces. To this end, we capture a person's identity in a canonical space as a signed distance field (SDF), and model facial expressions with a neural deformation field. In addition, our representation achieves high-fidelity local detail by introducing an ensemble of local fields centered around facial anchor points. To facilitate generalization, we train our model on a newly-captured dataset of over 3700 head scans from 203 different identities using a custom high-end 3D scanning setup. Our dataset significantly exceeds comparable existing datasets, both with respect to quality and completeness of geometry, averaging around 3.5M mesh faces per scan 1 1 We will publicly release our dataset along with a public benchmark for both neural head avatar construction as well as an evaluation on a hidden test-set for inference-time fitting.. Finally, we demonstrate that our approach outperforms state-of-the-art methods in terms of fitting error and reconstruction quality

Study of Kinematic Analysis Using Python Programming Language: A Visualization Approach

Kinematics as a field of study is often referred to as the geometry of motion. To describe motion, kinematics studies the trajectories of points, lines and other geometric objects and their differential properties such as velocity and acceleration to investigate the variety of means by which the motion of objects can be described. The variety of representations that one can investigate includes verbal representations, numerical representations, and graphical representations. In planar mechanisms, kinematic analysis can be performed either analytically or graphically. In this paper we first discuss analytical kinematic analysis. In the present paper, graphical representation of kinematical equation is studied. Analytical kinematics is a systematic process that is most suitable for developing into a computer program. Plotting few points does not provide us with a complete picture of the distance traveled over time. For this we need more points. Program written in Python calculates as many points as required almost instantaneously and help to see the better perspective of the conceptual language

Artin-Schreier families and 2-D cycle codes

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational points on certain Artin-Schreier curves via the additive form of Hilbert’s Theorem 90. We use our results on Artin-Schreier families to give a minimum distance bound for a large class of 2-D cyclic codes. Then, we look at some specific classes of 2-D cyclic codes that are not covered by our general result. In one case, we obtain the complete weight enumerator and show that these types of codes have two nonzero weights. In the other cases, we again give minimum distance bounds. We present examples, in some of which our estimates are fairly effcient

NU-MCC: Multiview Compressive Coding with Neighborhood Decoder and Repulsive UDF

Remarkable progress has been made in 3D reconstruction from single-view RGB-D inputs. MCC is the current state-of-the-art method in this field, which achieves unprecedented success by combining vision Transformers with large-scale training. However, we identified two key limitations of MCC: 1) The Transformer decoder is inefficient in handling large number of query points; 2) The 3D representation struggles to recover high-fidelity details. In this paper, we propose a new approach called NU-MCC that addresses these limitations. NU-MCC includes two key innovations: a Neighborhood decoder and a Repulsive Unsigned Distance Function (Repulsive UDF). First, our Neighborhood decoder introduces center points as an efficient proxy of input visual features, allowing each query point to only attend to a small neighborhood. This design not only results in much faster inference speed but also enables the exploitation of finer-scale visual features for improved recovery of 3D textures. Second, our Repulsive UDF is a novel alternative to the occupancy field used in MCC, significantly improving the quality of 3D object reconstruction. Compared to standard UDFs that suffer from holes in results, our proposed Repulsive UDF can achieve more complete surface reconstruction. Experimental results demonstrate that NU-MCC is able to learn a strong 3D representation, significantly advancing the state of the art in single-view 3D reconstruction. Particularly, it outperforms MCC by 9.7% in terms of the F1-score on the CO3D-v2 dataset with more than 5x faster running speed.Comment: Project page: https://numcc.github.io

Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis

We introduce a data-driven approach to complete partial 3D shapes through a combination of volumetric deep neural networks and 3D shape synthesis. From a partially-scanned input shape, our method first infers a low-resolution -- but complete -- output. To this end, we introduce a 3D-Encoder-Predictor Network (3D-EPN) which is composed of 3D convolutional layers. The network is trained to predict and fill in missing data, and operates on an implicit surface representation that encodes both known and unknown space. This allows us to predict global structure in unknown areas at high accuracy. We then correlate these intermediary results with 3D geometry from a shape database at test time. In a final pass, we propose a patch-based 3D shape synthesis method that imposes the 3D geometry from these retrieved shapes as constraints on the coarsely-completed mesh. This synthesis process enables us to reconstruct fine-scale detail and generate high-resolution output while respecting the global mesh structure obtained by the 3D-EPN. Although our 3D-EPN outperforms state-of-the-art completion method, the main contribution in our work lies in the combination of a data-driven shape predictor and analytic 3D shape synthesis. In our results, we show extensive evaluations on a newly-introduced shape completion benchmark for both real-world and synthetic data