Fast character modeling with sketch-based PDE surfaces

© 2020, The Author(s). Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly

The Rise-Time Distribution of Nearby Type Ia Supernovae

We present an analysis of the B-band and V-band rise-time distributions of nearby Type Ia supernovae (SNe Ia). We use a two-stretch template-fitting method to measure the rise and decline of BV light curves. Our analysis of 61 SNe with high-quality light curves indicates that the longer the time between explosion and maximum light (i.e., the rise time), the slower the decline of the light curve after maximum. However, SNe with slower post-maximum decline rates have a faster rise than would be expected from a single-parameter family of light curves, indicating that SN Ia light curves are not a single-parameter family of varying widths. Comparison of the B-band rise-time distribution for spectroscopically normal SNe Ia to those exhibiting high-velocity spectral features indicates that high-velocity (HV) SNe Ia have shorter B-band rise times compared to their spectroscopically normal counterparts. After normalising the B-band light curves to Dm15(B)= 1.1 mag (i.e., correcting the post-maximum decline to have the same shape as our template), we find that spectroscopically normal SNe Ia have a rise time of 18.03 +/- 0.24 d, while HV SNe have a faster B-band rise time of 16.63 +/- 0.29 d. Despite differences in the B band, we find that HV and normal SNe Ia have similar rise times in the V band. The initial rise of a SN Ia B-band light curve follows a power law with index 2.20 +0.27 -0.19, consistent with a parabolic rise in flux predicted by an expanding fireball toy model. We compare our early-time B-band data to models for the predicted signature of companion interaction arising from the single-degenerate progenitor scenario. There is a substantial degree of degeneracy between the adopted power-law index of the SN light-curve template, the rise time, and the amount of shock emission required to match the data.Comment: 17 pages, 9 figures, MNRAS accepte

Probing Extragalactic Dust through Nearby Gamma-ray Burst Afterglows

doi: 10.1088/0004-637X/710/1/648The quantities and wavelength dependencies of the dust extinction along the lines of sight toward 33 nearby gamma-ray bursts (GRBs) with redshifts z < 2 are derived from fitting their afterglow spectral energy distributions. Unlike previous studies which often assume a specific extinction law like that of the Milky Way (MW) and the Large and Small Magellanic Clouds (LMC/SMC), our approach—we call it the "Drude" approach—is more flexible in determining the true wavelength dependence of the extinction (while the shape of the extinction curve inferred from that relying on a priori assumption of a template extinction law is, of course, fixed). The extinction curves deduced from the Drude approach display a wide diversity of shapes, ranging from relatively flat curves to curves which are featureless and steeply rise toward the far-ultraviolet, and from curves just like that of the MW, LMC, and SMC to curves resembling that of the MW and LMC but lacking the 2175 Å bump. The visual extinction AV derived from the Drude approach is generally larger by a factor of ~2-5 than that inferred by assuming a SMC-type template extinction law. Consistent with previous studies, the extinction-to-gas ratio is mostly smaller than that of the MW, and does not seem to correlate with the shape of the extinction curve. It is shown that the standard silicate-graphite interstellar grain model closely reproduces the extinction curves of all 33 GRBs host galaxies. For these 33 bursts at z < 2, we find no evidence for the evolution of the dust extinction, dust sizes, and relative abundances of silicate to graphite on redshifts.We are supported in part by a NASA/Swift Theory Program, a NASA/Chandra Theory Program, and the NSFC Outstanding Oversea Young Scholarship

A Systematic Analysis of Supernova Light in Gamma-Ray Burst Afterglows

We systematically reanalyzed all Gamma-Ray Burst (GRB) afterglow data published through the end of 2002, in an attempt to detect the predicted supernova light component and to gain statistical insight on its phenomenological properties. We fit the observed photometric light curves as the sum of an afterglow, an underlying host galaxy, and a supernova component. The latter is modeled using published multi-color light curves of SN 1998bw as a template. The total sample of afterglows with established redshifts contains 21 bursts (GRB 970228 - GRB 021211). For nine of these GRBs a weak supernova excess (scaled to SN 1998bw) was found, what makes this to one of the first samples of high-z core collapse supernovae. Among this sample are all bursts with redshifts less than ~0.7. These results strongly support the notion that in fact all afterglows of long-duration GRBs contain light from an associated supernova. A statistics of the physical parameters of these GRB-supernovae shows that SN 1998bw was at the bright end of its class, while it was not special with respect to its light curve shape. Finally, we have searched for a potential correlation of the supernova luminosities with the properties of the corresponding bursts and optical afterglows, but we have not found such a relation.Comment: 25 pages, 7 figures, accepted by ApJ; revised, shortened and updated compared to version 1; Title slightly changed; all figures showing individual afterglow light curves removed, as advised by the referee; conclusions unchange

Geometric analysis of planar shapes with applications to cell deformations

Shape analysis is of great importance in many fields such as computer vision, medical imaging, and computational biology. In this paper we focus on a shape space in which shapes are represented by means of planar closed curves. In this shape space a new metric was recently introduced with the result that this shape space has the property of being isometric to an infinite-dimensional Grassmann manifold of 2-dimensional subspaces. Using this isometry it is possible, from Younes et al. (2008), to explicitly describe geodesics, a task that previously was not at all easy. Our aim is twofold, namely: to use this general theory in order to show some applications to the study of erythrocytes, using digital images of peripheral blood smears, in the treatment of sickle cell disease; and, since normal erythrocytes are almost circular and many Sickle cells have elliptical shape, to particularize the computation of geodesics and distances between shapes using this metric to planar objects considered as deformations of a template (circle or ellipse). The applications considered include: shape interpolation, shape classification, and shape clustering

Template Shape Estimation: Correcting an Asymptotic Bias

International audienceWe use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter σ describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data

The VANDELS survey: Dust attenuation in star-forming galaxies at z=3−4\mathbf{z=3-4}

We present the results of a new study of dust attenuation at redshifts $3 < z < 4$ based on a sample of $236$ star-forming galaxies from the VANDELS spectroscopic survey. Motivated by results from the First Billion Years (FiBY) simulation project, we argue that the intrinsic spectral energy distributions (SEDs) of star-forming galaxies at these redshifts have a self-similar shape across the mass range $8.2 \leq$ log$(M_{\star}/M_{\odot}) \leq 10.6$ probed by our sample. Using FiBY data, we construct a set of intrinsic SED templates which incorporate both detailed star formation and chemical abundance histories, and a variety of stellar population synthesis (SPS) model assumptions. With this set of intrinsic SEDs, we present a novel approach for directly recovering the shape and normalization of the dust attenuation curve. We find, across all of the intrinsic templates considered, that the average attenuation curve for star-forming galaxies at $z\simeq3.5$ is similar in shape to the commonly-adopted Calzetti starburst law, with an average total-to-selective attenuation ratio of $R_{V}=4.18\pm0.29$. We show that the optical attenuation ($A_V$) versus stellar mass ($M_{\star}$) relation predicted using our method is consistent with recent ALMA observations of galaxies at $2<z<3$ in the \emph{Hubble} \emph{Ultra} \emph{Deep} \emph{Field} (HUDF), as well as empirical $A_V - M_{\star}$ relations predicted by a Calzetti-like law. Our results, combined with other literature data, suggest that the $A_V - M_{\star}$ relation does not evolve over the redshift range $0<z<5$, at least for galaxies with log$(M_{\star}/M_{\odot}) \gtrsim 9.5$. Finally, we present tentative evidence which suggests that the attenuation curve may become steeper at log$(M_{\star}/M_{\odot}) \lesssim 9.0$.Comment: 16 pages, 12 figures, accepted for publication in MNRA

A Panoply of Cepheid Light Curve Templates

We have generated accurate V and I template light curves using a combination of Fourier decomposition and principal component analysis for a large sample of Cepheid light curves. Unlike previous studies, we include short period Cepheids and stars pulsating in the first overtone mode in our analysis. Extensive Monte Carlo simulations show that our templates can be used to precisely measure Cepheid magnitudes and periods, even in cases where there are few observational epochs. These templates are ideal for characterizing serendipitously discovered Cepheids and can be used in conjunction with surveys such as Pan-Starrs and LSST where the observational sampling may not be optimized for Cepheids.Comment: 12 pages, 14 figures. Accepted for publication in AJ fixed embarrassing typo

Fuzzy Supernova Templates I: Classification

Modern supernova (SN) surveys are now uncovering stellar explosions at rates that far surpass what the world's spectroscopic resources can handle. In order to make full use of these SN datasets, it is necessary to use analysis methods that depend only on the survey photometry. This paper presents two methods for utilizing a set of SN light curve templates to classify SN objects. In the first case we present an updated version of the Bayesian Adaptive Template Matching program (BATM). To address some shortcomings of that strictly Bayesian approach, we introduce a method for Supernova Ontology with Fuzzy Templates (SOFT), which utilizes Fuzzy Set Theory for the definition and combination of SN light curve models. For well-sampled light curves with a modest signal to noise ratio (S/N>10), the SOFT method can correctly separate thermonuclear (Type Ia) SNe from core collapse SNe with 98% accuracy. In addition, the SOFT method has the potential to classify supernovae into sub-types, providing photometric identification of very rare or peculiar explosions. The accuracy and precision of the SOFT method is verified using Monte Carlo simulations as well as real SN light curves from the Sloan Digital Sky Survey and the SuperNova Legacy Survey. In a subsequent paper the SOFT method is extended to address the problem of parameter estimation, providing estimates of redshift, distance, and host galaxy extinction without any spectroscopy.Comment: 26 pages, 12 figures. Accepted to Ap

The VANDELS survey: Dust attenuation in star-forming galaxies at z=3−4\mathbf{z=3-4}

We present the results of a new study of dust attenuation at redshifts $3 < z < 4$ based on a sample of $236$ star-forming galaxies from the VANDELS spectroscopic survey. Motivated by results from the First Billion Years (FiBY) simulation project, we argue that the intrinsic spectral energy distributions (SEDs) of star-forming galaxies at these redshifts have a self-similar shape across the mass range $8.2 \leq$ log$(M_{\star}/M_{\odot}) \leq 10.6$ probed by our sample. Using FiBY data, we construct a set of intrinsic SED templates which incorporate both detailed star formation and chemical abundance histories, and a variety of stellar population synthesis (SPS) model assumptions. With this set of intrinsic SEDs, we present a novel approach for directly recovering the shape and normalization of the dust attenuation curve. We find, across all of the intrinsic templates considered, that the average attenuation curve for star-forming galaxies at $z\simeq3.5$ is similar in shape to the commonly-adopted Calzetti starburst law, with an average total-to-selective attenuation ratio of $R_{V}=4.18\pm0.29$. We show that the optical attenuation ($A_V$) versus stellar mass ($M_{\star}$) relation predicted using our method is consistent with recent ALMA observations of galaxies at $2<z<3$ in the \emph{Hubble} \emph{Ultra} \emph{Deep} \emph{Field} (HUDF), as well as empirical $A_V - M_{\star}$ relations predicted by a Calzetti-like law. Our results, combined with other literature data, suggest that the $A_V - M_{\star}$ relation does not evolve over the redshift range $0<z<5$, at least for galaxies with log$(M_{\star}/M_{\odot}) \gtrsim 9.5$. Finally, we present tentative evidence which suggests that the attenuation curve may become steeper at log$(M_{\star}/M_{\odot}) \lesssim 9.0$.Comment: 16 pages, 12 figures, accepted for publication in MNRA