FIELD [0001] The present invention relates to techniques for determining a texture function for efficient and realistic modeling and rendering of objects composed of materials that exhibit variations in surface mesostructures, translucency and/or volumetric texture BACKGROUND [0002] In the context of computer graphics, the generation of realistic looking virtual objects takes into account the interaction of light both on the surface of the object and in the volume of the object Such interactions of light with the object are otherwise referred to as reflection and scattering, respectively When accounted for, reflection and scattering produce visual effects such as shadowing, masking, interreflection, translucency and fine-scale silhouettes which elevate the realism of rendered images of the object The interactions of light with the object are physically governed by the shape and material attributes of the object [0003] Previous attempts to map material attributes (e g, color, surface normal perturbations, height field displacements, and volumetric geometry) onto surfaces to model fine-scale surface geometry, referred to as mesostructure, and its interaction with illumination, fail to take into consideration various appearance effects that arise from light transport within the material of the object This deficiency is significant since many materials in the physical world are translucent to some degree Thus, the appearance of the surface of an object may not be realistic [0004] On the other hand, further attempts to map material attributes onto surfaces that do account for translucency are beset by problems regarding the computational expense required That is, detailed renderings of translucent objects by simulating radiance transfer through a participating medium require either an impractical amount of data storage or a significant amount of computation at rendering time SUMMARY [0005] Shell texture functions are descnbed herein [0006] In particular, techniques are provided for at least modeling any one of mesostructure shadowing, masking, interreflection and silhouettes on a surface, as well as subsurface scattering within a non-homogeneous volume The techniques descnbed herein include, at least, acquiring matenal parameters for a material sample, detennimng irradiance distribution values for the material sample, synthesizing the material sample onto a mesh of an object The synthesized object may then be rendered by one of a number of rendering techniques BRIEF DESCRIPTION OF THE DRAWINGS [0007] The detailed description is descnbed with reference to the accompanying figures [0008] FIG 1 shows a computing device for implementing computer graphic techniques utilizing example embodiments of texture functions as descnbed herein [0009] FIG 2A shows a matenal sample, in accordance with an example embodiment, for which a STF may be computed [0010] FIG 2B shows a sample object to be modeled and rendered in accordance with the example embodiments of STF-related techniques descnbed herein [0011] FIG 3 is an example processing flow for modeling and rendering materials in accordance with example embodiments described herein [0012] FIG 4A shows an example embodiment of a STF base volume model sample [0013] FIG 4B shows a model illustrating lighting transport in a volumetric material in accordance with an example embodiment |0014] FIG 5A-SD illustrates perspectives of the synthesis of a material shell (the subsurface layer) onto an object, in accordance with an example embodiment [0015] FIG 6A-6B show different perspectives of a shell for illustrating shell resampling, according to an example embodiment [0016] FIG 7 illustrates the geometry of radiance evaluation, as utilized by an example embodiment [0017] FIG 8 illustrates usage of an irradiance correction at the shadow boundary, in accordance with an example embodiment [0018] FIG 9 illustrates an example of a general computer network environment which can be used to implement the techniques descnbed herein DETAILED DESCRIPTION [0019] The following description describes techniques for modeling and rendenng mesostructure shadowing, masking, interreflection and silhouettes on a surface, as well as subsurface scattenng within a non-homogeneous volume In particular, an object representation includes a volumetric shell layer and an inner core The shell is created by texture synthesis using a volumetric matenal sample that may have mesostructures and matenal non-homogeneities, further, since material non- homogeneities from within the volume have a relatively subtle effect on appearance, the inner core may be modeled as a homogeneous material [0020] FIG 1 shows an example of computing device 105 having a processing component 107 to determine at least one shell texture function of a material sample of an object, and further rendering the object after forming an object shell of the object by texture synthesis of the material sample onto a mesh of the object [0021] Computing device 105 may be any of a variety of conventional computing devices such as a desktop personal computer (PC) Alternatively, computing device 105 may be a network-associated device including, but not limited to, a laptop computer, personal digital assistant (PDA), smartphone, etc, which may be in communication with network 110 by a wired and/or wireless link An example embodiment of client device 105 is described in further detail with reference to FIG 9 [0022] Either of data sources ] 15 and 120 may be a server device that provides any of a variety of data and/or functionality to computing device 105 Data sources 115 and 120 may be a server device such as a network server or an application server A network server is a server device mat delivers content to computing device 105 by way of network 110 Such content may include web content coded in hypertext markup language (HTML), which may also contain JavaScript code or other commands It is to be appreciated that either of data sources 115 and 120 may be used in other networks that are a part of The World Wide Web (e g, where network 110 includes The Internet), as well as in other networks that are not part of The World Wide Web, such as an intranet [0023] To efficiently render a detailed object model on computing device 105 using technique 107, a texture function (hereafter referred to as "STF") of the object shell is described herein STF represents the uradiance distribution of a shell voxel with respect to incident illumination direction A shell voxel, as described herein, refers to a three-dimensional ("3-D") pixel volume near the surface of the shell of the object to be modeled and/or rendered STF enables rapid determination of radiance for each voxel in a matenal sample volume of the object [0024] FIG 2A shows an example of material sample 200 for the purpose of contextualizing the discussion of STF More specifically, STF is intended to represent irradiance distributions of points in matenal sample 200 for all incident illumination directions Computationally, material sample 200 may be modeled in terms of an STF base volume Vb STF base volume Vb contains an nxx ny x nz array of voxels on a regular 3D gnd, where nx x ny is used to compute the size of a parameter space of matenal sample 200, and n2 defines the thickness of the STF Values of n are typically predetermined Mesostructure is represented in the STF base volume Vb, and therefore the voxels of Vb may he in either the subsurface layer 20S or the surrounding free space 207 of matenal sample 200 [0025] In particular, for each subsurface voxel x of material sample 200, the following matenal properties are stored extinction coefficient K(X), albedo a(x), which is a fraction of incident radiation that is reflected by the surface of material sample 200, and phase function f(x, , ), whereby  and t are the incoming and outgoing light directions, respectively The scattering coefficient s of a matenal is related to extinction and albedo as s,= αk and the absorption coefficient is defined as , = K - s The extinction coefficient K(X) and albedo α(x) describe the radiative transfer properties of a participating medium, which determine the translucency and chromatic properties of a voxel A flag for indicating surface voxels is also included, and when the flag is on, a surface nonnal and relative index of refraction are typically predetermined as well [0026] STF is a 5D function that is defined by specifying a single-scattering component Is (x, ) and a multiple-scattering component lm (x, ), where x is representative of a current position in Vb and  is an incident light direction The aforementioned STF values, single-scattenng component Is, (x, ) and a multiple-scattering component Im (x, ), allow rapid computation of the radiance Z(x, at) at any point x of Vb and in any direction  According to the light transport equation in a participating medium, the radiance L(x, ) is expressed as (Formula Removed) [0027] Le(x, ) is the radiance from the object, and L1(x, ) is the in-scattered radiance, i e. radiance scattered within the volume of the object The radiance L(x, ) may be evaluated using a known ray marching algorithm, of which the most computationally expensive calculation is the in-scattered radiance, which can be computed using volume photon mapping as (Formula Removed) Specifically, the radiance is summed over the n photons inside a differential volume AV and Φp(x, p), is the flux carried by a photon from incoming direction p The flux Φp(x, p) is divided into single-scattering and multiple-scattering terms because single scattering may be rendered by ray tracing, and multiple scattering through a homogeneous medium may be simulated using a dipole diffusion approximation According to the example embodiments described herein, the dipole approximation may not be employed since the material sample is non-homogeneous, however the determinations leverage the property that multiple scattering may be considered to be substantially isotropic For isotropic multiple scattering, the expression of Z,,(x,