SIGGRAPH University - Introduction to "Physically Based Shading in Theory and Practice"

so first of all it's my pleasure once again to welcome nattie Hoffman so natty first organises course in a 2010 and so really always a really grateful to him for always helping us out find speakers each year so um so Natalie is the vice present technology at 2k so previously who has employed at Activision working on graphics R&D for various titles including the Call of Duty series Santi Sonjia Santa Monica studio so coding graphics technology for God of War 3 Naughty Dog and developing first ps3 first party libraries Westwood Studios leading graphics development on earth and Beyond and internal driving of Pentium pipe our modifications and assisting the SSE instruction set definitions she's got a long and illustrious history and thanks to volcán matting thanks for introduction hi so some of you may have seen this background talk before I've done quite a few modifications to it this year so hopefully won't all be old hat so but one thing that hasn't changed is that over the next 15 minutes I'll be going from the physics underlying shading to the math used to describe it so what is light from a physics standpoint it's technically an electromagnetic transverse wave which sounds very fancy but it actually means that the electromagnetic field wiggles sideways as the energy propagates forward this wiggling in the in the electromagnetic field can be seen as two coupled fields electric and magnetic wiggling at 90 degrees to each other electromagnetic waves can be characterized by frequency the number of wiggles they do in a second or wave length the distance between two wave Peaks now engineers have in various disciplines have to deal with electromagnetic wavelengths ranging from gamma waves that have wavelengths of less than one hundredth of a nanometer to extreme low frequency radio waves that those waves are tens of thousands of kilometers long and everything in between but the range that we can actually see with our eyes is own a tiny tiny subset of that range only from 402 nanometers for violet light to 700 nanometers for red light now to give you a bit of intuition for what 400 to 700 nanometers actually is because the physical size of this will become relative relevant later in the talk so on the left you can see visible light wavelengths relative to this sort of gray cylinder that's a single strand of spider silk which is one micron in width and on the right to give some extra context you see that same strand of spider silk how it would be relative to the width of a human hair so you know it's something that's very very tiny but still it's I mean you can see a strand of spider silk with your naked eye and these are fairly close to that maybe half or a third of that in width so far what I've shown you are simple sine waves that have a single unique wave length and this is the simplest possible type of light wave but it isn't at all a common type of light wave most lightweights contain many different wavelengths with a different amount of energy in each this is typically visualized as a spectral power distribution or SPD for short as you can see in the upper left the SPD for this particular wave shows that this waves energy is all the single wavelength it's all in the in a single wavelength in the green part of the spectrum and this is typically what you will see in light emitted by laser so it's sort of a Dirac Delta function in the SPD in actuality lasers actually have a little bit of bandwidth but they are extremely narrow now here we see the SPD's for red green and blue laser that h multiplied by a factor and added together to produce the SPD on the right now this kind of spectral power distribution is similar to what you would see in light for a laser projector and laser projectors are starting to show up in higher-end theaters nor theaters they offer wide contrast white gamut they have some advantages so this is an extremely spiky spectrum and very still very simple I mean it's not one sine wave it's three sine waves and if we look at the actual wave form we can see that after adding up these three simple sine waves we end up with something that maybe looks a little more complicated than a single sine wave but not that much more so I mean it's you can see some underlying frequency and there's some larger beats there however most light that you'll see in nature doesn't look like that SPD looks more like this this is the SPD 4d 65 which is a standard spectrum for white light outdoors light and you can see also the wave form that it will create which is of course very complex basically the broader the more do tell the SPD the more chaotic looking the way from forum will be in the less resemble a simple sine wave now an interesting thing is that although these two SPG's could not be more different one is extremely smooth and broad the other one is 3 Delta functions but they have the exact same color appearance to humans now the y-axis isn't the same scales obviously spikes are higher to compensate for the lack of width but the the fact that the human color vision cannot distinguish between these two signals tells us that you in color vision is incredibly lossy it it Maps the infinite dimensional SPD down to a three-dimensional perceptual space now if we look at this waveform in vacuum it will propagate forever the electric and magnetic waves will sort of reinforce each other and will just keep on going and going but for rendering what we care about is what happens when this light wave interacts with matter now what happens is when an electromagnetic wave hits a bunch of atoms or molecules it polarizes them that means that it stretches this and separates the positive and negative charges and forms dipoles this absorbs energy for the incoming wave and this energy is radiated back out you can imagine like a spring and then the dipoles sort of snap back and this energy is rear ad ated outwards and sometimes some of it is lost heat other times all of it is preserved and radiate outwards in new waves going in all kinds of directions in a thin gas the molecules are far enough apart that you can treat them individually and then there are fairly simple physical and mathematical formulations to understand what's happening but in other cases and bends gases liquids solids the combinations of the dipoles interact with each other and the waves interfere with each other and the the whole thing is in the general case much too complex to accurately simulate so the science of optics in this case physical or wave optics in order to tame this sort of chaotic situation they adopt certain abstraction simplifications and approximations for example they have the concept of a homogeneous medium through which light travels in a straight line now a homogeneous medium is an abstraction obviously because matter composed of atoms can never be truly homogeneous at all scales but in practice this abstraction works quite well for materials at uniform density and Composition the optical properties of this homogeneous medium is described by its index of refraction or IOR for short this is a complex or in other words a two part number one part of the IOR describes the speed of light through the medium and the other one describes how much light is absorbed by the medium and there are many media that are completely non absorbent and for them that number will be zero localized in homogeneities in the medium because you have to model things other than a completely homogeneous medium so the way that optics models these localized inhomogeneities is as particles so the assumption is that we have these abrupt IR discontinuities and they scatter the incoming light over various directions this is similar to individual molecule polarization that we discussed earlier but these particles can be composed of many molecules and there are some formalisms in order to handle this situation again it's it's a bit of an abstraction over what's actually happening now the overall appearance of a medium is determined by the combination of its absorption and scattering properties for example a wide appearance like the whole milk in the lower right corner is caused by high scattering and low absorption you can sort of see absorption and scattering is two independent axes here and if a liquid is colored that means it absorbs light more readily in some wavelengths than others so it's sort of spectrally selective now we've briefly touched on participating media here but actually the rest of my talk will be focused on object surfaces which is a more common and basic case in rendering now from an optical perspective the most important thing about a surface is its roughness no surface can be perfectly flat at the very least irregularities at the atomic level irregularities that are of similar size are smaller than the light wavelength we will I will call this nano geometry and these caused a phenomenon called diffraction there is something called the Huygens Fornell principle that can help understand the diffraction on a intuitive way it states that each point on a planar wave you can imagine each point on a planar light wave is the center of a new spherical wave that's being emitted and then these spherical waves will interfere with each other in order to create a new plane wave now so far this hasn't gained us anything in terms of intuition we went for a plain wave through a bunch of sea ways back to a plain wave but where this where this sort of mental picture helps is when the wave hits an obstacle and that's when you get diffraction so when the wave hits the obstacle then you imagine these spherical waves and then one side of it the spherical wave that's on the very corner of this obstacle it doesn't get canceled out because there's no other way to next to it and you see the light is kind of bending around the corner it's actually not travelling a straight line and that's an example of something you don't get with the standard geometric optics and the effect of this will be to slightly soften shadows even if you have a point light your shadows will be very slightly soft due to this effect now what's more interesting for reflectance which is what this course is about is diffraction on the surface the irregularities this nano geometry that's on a surface and at for this case I'm going to look at an optically smooth surface logically smooth surface is defined as a surface where all the irregularities are in the Nano geometry category so all the irregularities are smaller than the light wavelength it's actually not hard to polish a surface to that degree commercial glass is commonly polished far smaller than a visible light wavelength and if we look at this plane way of hitting this surface that's irregular on a scale of tens or hundreds of nanometers then we can apply the same Huygens principle and so we see that every point on the surface is emitting its own spherical wave and this looks a bit chaotic because it is some of these surface points are higher some of them are lower that's due to the Nano geometry and then all of these skier waves will sort of interfere and reinforce each other destructive and constructive interference and you'll get this kind of complexly structured wavefront this little drawing actually doesn't do adjust this and you'll end up with some amount of the light scattered in all kinds of directions now the smaller the Nano geometry the less light will be diffracted the more of it will be reflected sort of in the regular specular way that I'll talk about soon so it's really a function of the height of the bump so if you have a surface that's I think the term is super polished I don't know if that's a technical term but I've seen it used on several websites it is possible with some effort and expense to polish the surface to the of individual atoms then the scattering that happens on a surface like that will be small it will be around 1% or half a percent of incident light but it's definitely still measurable so there's no such thing as a perfect surface now we're going to take a break from wave optics and move into the more familiar geometric or ray optics which is a more simplified model and it's really the model at all of computer graphics with a handful of exceptions has been using since forever one simplification will make is to ignore nano geometry basically as far as geometric optics is concerned if it's smaller than a light wavelength it doesn't exist any optically smooth surface will treat us this mathematically perfect abstract flat surface now it can be shown from the equations governing electromagnetic waves that such a perfectly flat surface ideal surface will split light into exactly two directions reflection and refraction now most real-world surfaces aren't optically smooth but they have irregularities of the scale that's much larger than the light wavelength but still smaller than a pixel so we will call this micro geometry to differentiate from the nano geometry those smaller than light wavelength and this micro geometry variation it doesn't cause diffraction what it does it simply is tilting the surface in various directions and since as we saw here both the reflection and refraction Direction depend on the surface normal on the surface orientation then the micro geometry is simply changing the local normal at a very small scale and you end up with reflected rays even though each specific point on the surface is only reflecting then coming right into a single direction because a pixel covers a lot of bits of surface angled in different directions you end up with this sort of statistical aggregate now this is roughness on the microscopic scale if I look at these two surfaces then to our eye they seem equally smooth they seem like these nice you know smooth hemispheres one has a hole in the middle but other than that there are very similar shapes but in a microscopic scale they're different this top surface is slightly rough if you took a micro micrograph of it or micro photograph of it you would see these sort of gently undulating hills as it were and that means that incoming light rays will hit surface points that are angled slightly differently and will bounce out by the different directions and you'll end up with this sort of narrow ish cone and that's why the reflections are only slightly blurred the surface on the bottom however it is on the micro scale very rough if you looked at in a microscope it would look like the Alps or something and so every bit of surface hit by the light is angled in a very different direction and the light spreads out in a very wide cone now in the macroscopic view we don't model the microscope the micro geometry explicitly we tweeted statistically and view the surface as reflecting and refracting light in multiple directions in a cone and the rougher the surface the wider this cone will be now the questions we've talked about Fleck tonight but what happens to refracted light and this depends on what kind of material logic is made of light is since light is composed of electromagnetic waves the optical properties of a substance are closely linked to its electric properties and we can group materials into three main optical categories metals or conductors dielectrics or insulators and semiconductors and you really in games and in movies you don't see a lot of exposed semiconductors lying around so we can in most cases ignore that situation and just divide everything the metal of all metals that has the advantage of being way more intuitive to an artist and talking about dielectrics and the like now metals immediately absorb or refract the light basically there's the sea of reelect ron's it sucks up all the electromagnetic energy and it's gone never to return nonmetals however behave like those cups of liquid we saw earlier effectively you have this participating medium underneath the surface that the refracted light is participating in and the refract light is scattered or absorbed or scattered and absorbs that you have all the same variations we saw in those cups of liquid if the object is made of a completely clear substance like glass or liquid the light will just keep on going but if there's enough scattering which most objects will have some of this refracted light will be scattered back out of the surface and those are the little blue arrows that you see coming out of the surface in various directions and I've kind of tried to visualize the fact that the light internally is getting selectively absorbed so it's getting tinted blue so there was a sort of the LR was turning bluer and bluer and bluer until they get back out of the surface now this readmitted light comes out of varying distances from the entry point and you can see the yellow bars showed one way one way is coming out really close to entry point one way is coming out a bit farther and this distribution of distances depends on the density and other properties of the scattering particles now if the pixel size our shading sample area or distance between shading points a shading rate or however however you conceptualize that but just sort of the area of interest for shading if that pixel size is large like the red border green circle in image compared to the entry exit distances then we can assume distances are effectively zero for shading purposes we can't resolve the fact that the light is coming out in a different point that it's entering so in that case by going the entry tags a distance we can compute all shading locally at a single point and the shading color is only affected by light that's sitting at one point it's convenient to split these two very different light material interactions into different shading terms so we tend to call the surface reflection term specular and the term resulting from refraction absorption scattering and re refraction we call diffuse now in the other case where the pixel is very small or small compared to the enter entry exit distances so we have the red border green circle again but it's much smaller in this picture compared to the scattering distances then we can't treat the shading the as all happening at a single point we need some special subsurface scattering rendering techniques and even regular diffuse shading the physical phenomenon is the same it's it's still subsurface scattering the only difference between something we're running a subsurface scattering shader and one where you're running a regular diffuse shader is the the difference between the shading resolution and the scattering distance so it's not true to say that this material is a subsurface scattering material because all depends on the distance to the camera right if you have plastic from far away or from arms-length then it lacks like diffuse but if you're looking at a super up-close like in the lego movie then it you can see visible diffusion happening and the same thing happens in Reverse if human skin has visible scattering behavior but if you're looking at a human from far away you can just shade them with a brdf now so far we've discussed the physics of light matter interactions of course to implement them in a game or film render you have to turn these physics into a mathematical model and the first step is to quantify light as a number radiometry is the measurement of light of there are many different radiometric quantities that are integrals over direction over area but will mostly use radians and radians measures the intensity of light along a single ray and it is spectrally varying now radiance values are properly expressed like SPD's like the ones I showed earlier in the talk and later in the course you'll hear about what a digital and how they do proper spectral rendering where they're looking at the whole sort of spectral distribution of energy however for the rest of this talk I'm going to follow traditional film and game usage and that is basically to use RGB for anything that's spectrally varying like radians now the units of radians are watts press the Radian per square meter now since we are using the sumption that shading can be handled locally we're sort of taking the subsurface scattering case out of the scope of this particular talk then light responds at a surface point only depends on the light in view directions and since you can parameterize each of those with two numbers then you have this four-dimensional function which we call the bi-directional reflectance distribution function or brdf and that's a function of light Direction L and view Direction V as I said in principles of function these three or four angles it's three angles if it's isotropic but in practice there are various different ways of parameterizing the RDF and with various advantages and disadvantages time now note that the brdf is only defined for light and view vectors above the macroscopic surface and I talked a little bit more in the course notes that how to handle other cases now now we come to the actual math this is the reflectance equation and it may be somewhat scary-looking if you're not of a mathematical bent let's say you have a more artistic background but basically what it's saying is that outgoing radians from a point equals the integral of incoming radians times the PID F times the cosine factor over there my sphere of incoming directions line I'm sure that doesn't sound much more reassuring but if you're not familiar with integrals you can think of it as a sort of weighted average over incoming direction so I'm really doing is I'm taking all the light coming in I'm using this brdf to kind of average it so I'll give more importance to some directions less importance other and just just adding it all together and this X and circle notation it's not a standard notation of any kind but it's one that I used in in we use in our book real-time rendering and since we didn't find an alternative we just talked with it it means component-wise RGB multiplication as distinguished from simple scalar multiplication now we'll start by looking at the surface or specular term in this figure it's known by these orange arrows they're reflected back from the surface and we'll be looking at it through the lens of micro facet Theory micro facet theory is a way to derive brdf for surface reflection from these non optically flat surfaces and the assumption behind it is that we have a surface with detail that is small compared to scale of observation but large compared to a light wavelength which is how we defined micro geometry and in that case each point is locally a perfect mirror remember where we said that with geometric optics we're ignoring nanoscale irregularities or assuming that anything under the wavelength of light is like this mathematically perfectly flat plane locally so each point is locally a perfect mirror and as we've seen a perfect mirror will reflect each incoming ray of light ignoring refraction for the moment into one outgoing direction and that outgoing direction depends on the light direction the normal in this case depends the light direction and the micro facet normal now only those micro facets that happen to have their surface normal em oriented exactly just so in order to balance L into V only those will reflect any visible light right any micro facets aiming in even a slightly different direction will be bouncing L into some direction that's not V and we will not contribute to the brdf so this direction where is the half vector H and that vector H is very common in shading physical shading models but it's important to note that this is its actual meaning the half vector H is very simply the direction in which the micro fascist need to be pointing now not all micro facets that have m equal taste will contribute some will be blocked by other micro facets from either the light direction which we call shadowing or the view direction which we call masking in reality block lights will continue to bounce and some of it will eventually contribute to the brdf micro facet the IDF's ignore this so effectively they assume that all blocked light is lost and we know that's an error we just live with it for now now this is the form of a general micro facet specular brdf you can derive it based on the assumptions I just described and I'll go it has a sort of component structure to it which is useful I can I'm going to explain each part individually now this practical expression is the fernell reflectance it's the fraction of incoming light that is reflected as opposed to refracted from an optically flat surface of a given substance add a given lighting angle and it varies based on the light angle and on the surface normal so for number of lectins tells us basically remember I said only certain micro facets are relevant the ones with their normal equal to H and those micro facets behave is a perfect mirror so what this expression tells us is of the light hitting each of those perfect mirrors what percentage is reflected now you can graph this for a given material you can graph this as a function of the angle of incidence which is the angle between the incoming light ray and the normal and the normal in this case is M and M in this case is H we don't care about the micro fasts for which M is not H and some materials here have one line in this graph like water diamond iron and glass and some of them have three the ones that have three that the three lines are simply showing the RG and B channels and how they vary and I didn't distinguish them here but for copper the high one is R and the low one is B and for aluminum I think it's reversed now if you look at the four no reflectance then you can see that it has a very specific kind of behavior so if we look at an optically flat surface the relevant angle for final reflectance as done between the viewing normal vectors we can see here I'm visualizing the final reflectance of a teapot and we can see that it has a very dark reflectance color in the middle and it brightens to white at the edges if we look again at the graph we can see that we can divide into sort of three zones so we start out at the angle of incidence zero on the left side of the graph and then it has this sort of constant value and as Daniel vincent's increases you can see the lines within the green zone remain basically flat so the green zone is the zone over which the specular reflectance doesn't really change and then in the yellow zone it starts changing slowly and in the red zone it changes abruptly and goes to one and you can visualize those same zone colors over 3d objects you can see that the vast majority are in the areas where the reflectance either doesn't change or barely changes and there's only a very small number of pixels that are exhibiting this rapid increase to reflectance of one now since over most of the visible surface the fernell reflectance value is is similar to value that has at zero degrees then it's it's a very useful anchor to treat this value as a surf as the characteristic specular color of the surface in general so we take the value of your know reflectance at zero degrees and we just call it the specular color of the material and you know we can calculate that it has a physical meaning and it can be calculated from non physical constants as I know what it earlier it's useful to divide substances into metals dielectrics and semiconductors and here we see a bunch of metals and metals in as a general rule they have bright specular with one exception the gold blue channel surrounded by this red circle here there's no value in this table below 0.5 and or at least not much below 0.5 and most of them are much higher and besides linear values we also have a column for 8-bit srgb values which is what an artist would paint into the texture and we also visualize the color and since metals lacks subsurface scattering as we said they just swallow up all refracted light then all the visible color of the metal is the surface reflection or specular color now some metals are very strongly colored gold is a bit of an outlier in two ways it's blue channel is unusually low and it's red channel is unusually high in fact it's red channel is actually outside the srgb gama so I show the value here which is 1.0 to 2 in practice you just clamp that to one now the fact that gold is so unusually strongly colored for metals probably contributes to its unique cultural and economic significance despite its low blue value Gold is also one of the brightest metals this table is ordered by lightness CIE y coordinate of specular color and you can see that among these metals at least which are sort of a bunch of common metals elemental metals gold is like the third brightest now on the other hand dielectrics have dark specular colors and and they're on a chromatic uncoloured which is why this table I'm giving single values or ranges but I'm not giving RGB triples and delicous typically will also have a diffused color or subsurface scattering color in addition to the specular color shown in this table so unlike metals this is not the only source of surface color now in this table I'm going to group common dielectrics into categories of increasing of zero values so we start with water which at 2% is sort of the darkest specular reflectance you're likely to see outside some custom anti-reflective coating and common plastics and glass and as I'll mention later a whole bunch of other things are in this sort of forward four and a half percent range I would look at the linear column because that's the amount of light actually reflected physically and then we have decorative substances that are decorative precisely because they are very shiny and have bright reflectance like crystal ware and gems and finally we have diamonds and things that are used as replacements for diamonds from ranging from Swarovski Swarovski crystals to last night which is actually brighter than a diamond and so it goes from like 2% all the way up to you know 20% but you notice that the lower you go on this table the higher numbers get the sort of rarer the materials get and the less of them you'll see in a given scene since the vast majority of dielectrics that you'll see in practice false up into the plastic glass row of this table it's not unusual in many engines or texturing systems just set a constant electric color of 4% and call it a day now what about semiconductors as you would expect they're in between they tend to have a f0 values in between the brightest dielectrics and the darkest metals and we use silicon here as sort of a proxy for semiconductors in general typically like I said before you don't just have big blocks of silicon lying around in most game and movie scenes and practical purposes I recommend treating the range of X 0 values between 20 and 45 percent is a kind of Forbidden Zone where materials won't go into that zone unless you're trying consciously to do some kind of exotic effect now we've talked about how to get the value for zero degrees but we do need to model the angular variation in some way and everyone has been using the slick approximation pretty much forever though there are some more optimized math expressions that have gained some popular use in recent years but the nice thing about it is it's fairly accurate I don't have a graph here comparing the two but if I didn't see that it stays reasonably close and over most the range it's quite cheap to calculate and more importantly than all of those properties it's parameterised by F zero because the original Fornell math is parametrized by spectral indices of refraction and spectral indices of fraction is not the kind of thing you want your artists worrying about so if zero is a nice color it's RGB is zero to one it has a very intuitive meaning and it's much better thing to parameterize by and then depending on whether you're doing sort of a mirror reflection or micro fasten the idea if you just plug it different or Melin either N or or H now the other chunk in this - sort of Lego expression is the normal distribution function or D and we evaluate it for the direction H because as we said H is the direction that the microf assets need to point for us to care about them for them to contribute and we want to know how many of the total micro facets in on this surface are pointing in that direction so that's why we're evaluating this normal distribution function and that's a function that will just tell you for any direction you give it what's the sort of concentration of micro fast normals that point in that direction and then the F intuitively determines the size and shape of the highlight that you'll have now the course notes go into great detail and all kinds of options for NDS and there's the mostly fall into two main classes the sort of more historically used ones are the Gaussian issuance Beckman Fong they all have this sort of overall Gaussian appearance they have Lobby highlights and then G GX or more properly trowbridge rates has slightly different appearance it's more it has more kurtosis it has the spiky Center and in these sort of long tails so the appearance of the highlight is more like a sharp highlight surrounded by kind of haze or a halo now there are many surfaces are not well represented by such smooth since I'll show some images from last year's glint rendering paper by Yann at all production brdf snore mapper and filtering technique extent these smooth lobes either isotropic smooth lobes or anisotropic smooth lobes but and those are good models for surfaces where the micro geometry is much smaller than a pixel where the pixels covering tens hundreds of thousands of bumps and they all get nicely smooth the average together but there are many surfaces of interest which maybe it's covering the pixels covering dozens of bumps or and much less than tens of thousands and then you don't get this nice statistical averaging you get something that looks like this and that's obviously very different trying to model this with this bob is not is going to losing something what you lose is this characteristic glint the appearance that the paper was addressing now the solution the paper looks at least to my sort of not film expert eye as something you could use in film production it's definitely too costly for games games at the moment use more ad hoc methods if anyone attended the advances meal time rendering course Monday there was a snow sparkle talk that's a good example of the kind of things that we do in games for this sort of effect now one other thing which is also highlighted by images from a recent paper it's important to account for the effect of surface deformation and in DFS this is something that is usually ignored and not modeled the following images are from the skin micro structural deformation paper by Nagano at all and it's going to be presented at the appearance capture session this afternoon the left side of also a series of images and the left side will show a patch of skin which is undergoing varying amounts of compression and stretch and the NDF of that patch of skin is on the right and you can see that as the skin goes from compression to relaxation and enter stretch the shape of India changes quite a bit and although the paper is talking about human skin in principle that you'll have this type of behavior with any flexible surface material that has some micro structure to it so this is something that in theory we should be modeling whenever we're skinning something in practice I don't think that many people are so this is definitely an unaddressed area so finally we have the geometry or shadowing masking function that's the last part of the Brda from the rest are just dot products they're basically we projection factor and this is the geometry function or sometimes called the shadowing masking function and you know D gives us how many micro facets what concentration of micro facets do we have pointing the right direction F tells me how reflective they are and G tells me how many of them are unshadowed and unmasked so they are actually transferring light from the L direction into the V direction and it basically gives us the chance of Micra faster the given orientation is lit and visible now there are many different options in literature for the geometry function but there was a very good analysis of this function it's meaning by air kites which I strongly recommend reading for anyone's interest in this area and he showed that only the Smith function the uncorrelated form which is shown here is both mathematically valid and physically realistic now there are further details about this and there are also various other forms there is correlated or partially correlated forms of Smith that can be found at Heights as paper so this is basically the function you should use now if we put it all together we see that the brdf is proportional to the concentration of active micro facets which are the ones with normals aligned with H times the visibility times their Fornell reflectance the rest of the RDF in the denominator consists of correction factors relate to the various strains involve now all I'm running a bit late so I'll skim over the diffuse part and which is the subsurface term so people are traditionally models with Lambert which is a constant the NL is part of the reflectance equation a part of the brdf and there are very small is going beyond Lambert's some of them we've seen in this course in previous years some of the model is diffuse specular tradeoff whereas for nil is causing more light to go towards a specular that means that necessarily it's causing less light to be refracted and less light to be available for the diffuse model which Lambert does not model and there's also beer debts to take account of surface roughness that's something I really wanted to stress a particular point here that take an account of roughness for diffuse reflectance is a good thing to but you have to be very careful in how you do it it depends on this whether the surface has micro geometry that's larger or smaller than the scattering distance and that's when you pull out the models like or an IR or or distant diffuse and there's there's this common pattern I've seen where people just use this roughness base diffused on all their mouth materials and they just plug in the specular roughness into the fuse roughness and I think that's really not a good approach because it's been known for a while that the fuse responds effectively smoothes out small bumps if you're familiar with lie CTS light stage they give you separate normal Maps for specular and for diffuse so if you look at some human skin the specular nog will be very high freq i've lots of high-frequency detail and the diffuse no map will be sort of smoother and more filtered effectively the diffusion profile filters out the low map and and everybody or a lot of people know that but it seems that a lot of few people know that this applies even more so to the roughness and ideally you should have complete separate roughness for diffuse and for specular because it's not a simple factor you can't say okay my diffuser Office's 1/2 or 1/3 because it really depends on the size right you don't know how big the bumps are then DF doesn't tell you that so otherwise that recommend just use them sparingly don't have them be the default use them in cases where you know the material has this property that the roughness is very coarse compared to the scattering distance and I'm sure you thought I completely forgot about wave optics but it's back done Taunton and it is turns out that it is actually important we've all been ignoring it for around 3040 years with handful of exceptions like hey at all in 91 and we've either ignored the effects of nano geometry diffraction or we asserted there in significance but at the recent material appearance modeling symposium in June which I sadly missed all true and pecan all ski showed pretty convincing evidence that part of the visible brdf behavior the long tail of the highlights in particular was due to this phenomenon that we've been likely ignoring now for more detail I recommend looking at the talk slides that are online but I'll just go over some high-level differences between the two so it appears that in many materials reflecting is affected by roughness on both the micro nano scales the micro scales is all the stuff we've been talking about the lobes safe is determined by the surface to this things turns out that nano geometry the lobe shape is also determined by a complete different surface statistic which is the surface roughness SPD which is the same SPD we saw in the beginning but applied to 2d spatial properties other than one the time property micro geometry has no wavelength dependence nano geometry reflectance as a strong wavelength dependence in both cases incidence angle can affect the effective surface statistics due to different effects now of course all this math needs to be turned into rendering implementation which I'm not going to talk about now but basically all the other talks in this course both this year in previous years are at least partly about that and I'd like to acknowledge people of helping with this talk and to end on a note that we are hiring we have open positions at many of our studios and personally my central tech department is looking for some top-notch men doing an engine programmers thank you

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Keywords: ACM, ACM SIGGRAPH, SIGGRAPH University, Course, Naty Hoffman, Physically Based Shading

Id: j-A0mwsJRmk

Length: 38min 35sec (2315 seconds)

Published: Fri Jul 15 2016