Outdoor Light Scattering Sample Update

Transcription

1 Intoduction Outdoo Light Scatteing Sample Update Ego Yusov This document descibes an update to the peviously published Outdoo Light Scatteing sample 1. The following new featues wee implemented: Multiple scatteing of sun light in the atmosphee. o Multiple scatteing has subtle effect duing the day time, but makes the sky look much moe natual. o Duing the twilight, multiple scatteing has highe impotance add impoves ealism significantly (Figue 1). o Light adiance due to multiple scatteing is pe-computed fo all possible locations and diections duing initialization and stoed in a 4-dimensional look-up table. Faste method fo endeing light shafts using pe-computed look-up table. o Since light adiance is pe-computed, this new method do not pefom numeical integation of ai light integal, but only computes total length of the illuminated ay faction and distance to the fist lit point. Two look-ups into the scatteing look-up table ae then pefomed. o This method is faste than numeical integation, but causes some atifacts due to significant non-lineaity of the data stoed in the look-up table. Physically-based shades fo endeing Eath suface using coect sun light extinction and pecomputed ambient skylight look-up table. o The sun light extinction due to the atmosphee is evaluated fo each vetex of the Eath mesh; pe-computed ambient skylight textue is used to estimate ambient light. Vaious tone mapping opeatos. o The sample implements a numbe of diffeent tone mapping opeatos that pefom HDR to LDR convesion. 1

2 Figue 1. Twilight sky endeed with single scatteing (left) and multiple scatteing (ight). Multiple Scatteing Multiple scatteing is the most impotant new featue implemented in the sample update. The implementation follows the method descibed in [Buneton and Neyet 08]. The main idea of this method is that the light adiance due to multiple scatteing ( C, v, l ) at point C when looking in diection v and sun is in diection l can be pe-computed and stoed in a 4-dimensional look-up table. In ou implementation, we use simplified pe-computation algoithm which ignoes Eath suface eflection. It can be summaized as follows: (1) 1. Compute single scatteing ( C, v, l ) with tapezoidal integation, fo all possible C v l,,. L In 2. Fo evey highe ode scatteing n fom 2 to N: ( ) a. Compute ode n scatteed light adiance J n ( C, v, l ) at evey point of space C and all diections v and l by integating pevious ode scatteing L M In L ove the whole set of diections ω: ( n) s h / H s h / H ( n 1) R M J ( C, v, l ) = β e p ( ω l ) + β e p ( ω l ) L ( C, ω, l ) dω, (1) 4π ( ) R whee h is the height of point C above sea level. R b. Compute ode n in-scatteing adiance fo evey point of space, view diection and light M (n) diection by integating scatteed adiance J along the view ay: X T ( n) T ( P( s) C ) ( n) L ( C, v, l ) e J ( P( s), v, l ) ds, (2) In = C M ( n 1) In whee P( s) = C+ v s, and X T is the point whee the ay C+ v s teminates, i.e. hits the top of the atmosphee o the Eath suface. c. Add ode n in-scatteing to the total highe ode-scatteing look-up table: L = L + L. H In H In (n) In In

3 3. Compute multiple scatteing look-up table as the sum of single and highe ode scatteing: LMIn = LHIn + L(In1). In ou implementation we suppot thee look-up tables: tex3dsinglescatteing stoes single scatteing only ( LIn ); tex3dhighodescatteing stoes highe ode scatteing only ( LIn ); tex3dmultiplescatteing stoes multiple scatteing ( LIn ). (1) H M Afte multiple scatteing look-up table LMIn is eady, we compute one-dimensional ambient sky light look-up table accoding to the following equation: E Sky (ϕ ) = LMIn (C, ω, l (ϕ )) (ω N Eath ) dω, (3) 2π whee integation is pefomed ove the uppe hemisphee, and ϕ is the angle between light diection l and the Eath nomal N Eath (note that any vecto l which makes angle ϕ with N Eath can be used in the equation). The camea C is assumed to be located on the gound. Look-up table paameteization As shown by Buneton and Neyet [Buneton and Neyet 08], the look-up table can be paameteized by 4 vaiables: height of the point above sea level (altitude), and cosine of thee angles: the angle between the view diection ( v ) and zenith ( N Eath ), the diection on sun ( l ) and zenith, and the angle between view and sun diections. We will denote these paametes by h, cα = cosα = ( v N Eath ), cϕ = cos ϕ = (l N Eath ) and cθ = cosθ = ( v l ). Unfotunately, simple linea scaling of these paametes esults in sevee atifacts nea hoizon (Figue 2, left). Buneton and Neyet [Buneton and Neyet 08] poposed a moe efficient non-linea paameteization which eliminates most of the atifacts. We howeve found that some issues still emain when sun is close to hoizon (Figue 2, ight). Figue 2. Atifacts nea hoizon when using linea paameteization (left) and Buneton and Neyet s non-linea paameteization (ight).

4 We thus use a diffeent paameteization ( u h, u α, u ϕ, u θ ) descibed below: 0.5 h u h =, (4) HAtm whee H = is the height of the top of the atmosphee. Atm u α 0.2 c α ch , cα > c 1 ch = 0.2 c h cα 0.5, cα ch ch ( 1) h (5) whee c h = h (2R R Eath Eath + h + h) is the cosine of the hoizon angle fo altitude h. We use the same paameteization fo c ϕ as in Buneton s implementation: (, ) tan( )) /1.1+ ( ) ) u ϕ 0.5 actan(max( c = ϕ Finally, paameteization fo c θ is as follows: ( 2 ( γ 0.5) ) ( 2 (0.5 γ )). (6) , γ 0.5 u θ = (7) , γ < 0.5 accos(cθ ) θ whee γ = =. π π Figue 3 depicts the above non-linea paameteization ( u α is given fo h = 20000).

5 Figue 3. Non-linea paameteization. This paameteization helps eliminate atifacts at the hoizon, as shown in Figue 4. Figue 4. Ou paameteization does not exhibit appaent atifacts. It must be noted that due to substantial non-lineaity of the adiance data stoed in the look-up table, all the atifacts can be fixed only by impactical incease of the look-up table esolution. In ou implementation, we use 32x128x64x16 16-bit float look-up tables equiing 32 MB of video memoy. Lowe esolution tables can be used to tead mino quality degadation fo educed memoy consumption.

6 Pefoming Look-ups into the Table Since 4D textues ae not natively suppoted by the cuent gaphics hadwae, ou 4D look-up table is packed into a 3D textue. Consequently, manual linea intepolation fo the fouth coodinate is equied. The souce code of the function that pefoms one look-up into the povided table is given in Listing 1. float3 LookUpPecomputedScatteing(float3 f3statpoint, float3 f3viewdi, float3 f3eathcente, float3 f3dionlight, in Textue3D<float3> tex3dscatteinglut, inout float4 f4uvwq) { float3 f3eathcentetopointdi = f3statpoint - f3eathcente; float fdisttoeathcente = length(f3eathcentetopointdi); f3eathcentetopointdi /= fdisttoeathcente; float fheightabovesuface = fdisttoeathcente - EARTH_RADIUS; float fcosviewzenithangle = dot( f3eathcentetopointdi, f3viewdi ); float fcossunzenithangle = dot( f3eathcentetopointdi, f3dionlight ); float fcossunviewangle = dot( f3viewdi, f3dionlight ); // Povide pevious look-up coodinates f4uvwq = WoldPaams2InsctLUTCoods(fHeightAboveSuface, fcosviewzenithangle, fcossunzenithangle, fcossunviewangle, f4uvwq); float3 f3uvw0; f3uvw0.xy = f4uvwq.xy; float fq0slice = floo(f4uvwq.w * PRECOMPUTED_SCTR_LUT_DIM.w - 0.5); fq0slice = clamp(fq0slice, 0, PRECOMPUTED_SCTR_LUT_DIM.w-1); float fqweight = (f4uvwq.w * PRECOMPUTED_SCTR_LUT_DIM.w - 0.5) - fq0slice; fqweight = max(fqweight, 0); float2 f2sliceminmaxz = float2(fq0slice, fq0slice+1)/precomputed_sctr_lut_dim.w + float2(0.5,-0.5) / (PRECOMPUTED_SCTR_LUT_DIM.z*PRECOMPUTED_SCTR_LUT_DIM.w); f3uvw0.z = (fq0slice + f4uvwq.z) / PRECOMPUTED_SCTR_LUT_DIM.w; f3uvw0.z = clamp(f3uvw0.z, f2sliceminmaxz.x, f2sliceminmaxz.y); float fq1slice = min(fq0slice+1, PRECOMPUTED_SCTR_LUT_DIM.w-1); float fnextsliceoffset = (fq1slice - fq0slice) / PRECOMPUTED_SCTR_LUT_DIM.w; float3 f3uvw1 = f3uvw0 + float3(0,0,fnextsliceoffset); float3 f3insct0 = tex3dscatteinglut.samplelevel(samlineaclamp, f3uvw0, 0); float3 f3insct1 = tex3dscatteinglut.samplelevel(samlineaclamp, f3uvw1, 0); float3 f3inscatteing = lep(f3insct0, f3insct1, fqweight); etun f3inscatteing; } Listing 1. Souce code of the function pefoming one look-up into the pe-computed scatteing textue. The function fist computes wold space attibutes of the cuent point, namely fheightabovesuface (h), fcosviewzenithangle ( c α ), fcossunzenithangle ( c ϕ ), and fcossunviewangle ( c θ). It then calls WoldPaams2InsctLUTCoods() function (which implements equations (4)-(7)) to tansfom these attibutes into the look-up table coodinates f4uvwq ( u h, u α, u ϕ, u θ ). Afte that the function computes

7 intepolation weight fo the fouth coodinate, pefoms two linea fetches fom the 3D textue and intepolates the esulting values accodingly. Handling of the u α coodinate equies special cae, because it has discontinuity at the hoizon. Thus when pefoming look-ups into the scatteing textue, it is vey impotant that all the look-ups ae consistent with espect to the hoizon, othewise atifacts will appea (Figue 5). Figue 5. Atifacts at the hoizon due to inconsistent look-ups. To avoid the above poblem, we must guaantee that that if the fist look-up fo the view ay is above (below) hoizon, then all subsequent look-ups ae also above (below) hoizon. We use the pevious textue coodinate to find out if the pevious look-up was above o below hoizon. Fo the fist look-up, the textue coodinate is negative. The function given in Listing 2 computes u α accounting fo the pevious look-up. float ZenithAngle2TexCood(float fcoszenithangle, float fheight, float ftexdim, float powe, float fpevtexcood) { fcoszenithangle = fcoszenithangle; float ftexcood; float fcoshozangle = GetCosHoizonAnlge(fHeight); // We use pevious textue coodinate, if it is povided, to find out if pevious look-up // was above o below hoizon. If textue coodinate is negative, then this is the fist // look-up bool bisabovehoizon = fpevtexcood >= 0.5; bool bisbelowhoizon = 0 <= fpevtexcood && fpevtexcood < 0.5; if( bisabovehoizon!bisbelowhoizon && (fcoszenithangle > fcoshozangle) ) { // Scale to [0,1] ftexcood = satuate( (fcoszenithangle - fcoshozangle) / (1 - fcoshozangle) ); ftexcood = pow(ftexcood, powe); // Now emap textue coodinate to the uppe half of the textue. // To avoid filteing acoss discontinuity at 0.5, we must map // the textue coodinate to [ /fTexDim, 1-0.5/fTexDim] ftexcood = 0.5f + 0.5f / ftexdim + ftexcood * (ftexdim/2-1) / ftexdim; } else

8 { } ftexcood = satuate( (fcoshozangle - fcoszenithangle) / (fcoshozangle - (-1)) ); ftexcood = pow(ftexcood, powe); // Now emap textue coodinate to the lowe half of the textue. // To avoid filteing acoss discontinuity at 0.5, we must map // the textue coodinate to [0.5, /fTexDim] ftexcood = 0.5f / ftexdim + ftexcood * (ftexdim/2-1) / ftexdim; etun ftexcood; } Listing 2. Computing textue coodinate u α. Computing Single Scatteing (1) Pe-computation of single scatteing adiance ( C, v, l ) L In fo all possible positions C, view diections v and diections on sun l is implemented by a pixel shade given in Listing 3. float3 PecomputeSingleScatteingPS(SSceenSizeQuadVSOutput In) : SV_Taget { // Get attibutes fo the cuent point float2 f2uv = PojToUV(In.m_f2PosPS); float fheight, fcosviewzenithangle, fcossunzenithangle, fcossunviewangle; InsctLUTCoods2WoldPaams(float4(f2UV, g_miscpaams.f2wq), fheight, fcosviewzenithangle, fcossunzenithangle, fcossunviewangle ); float3 f3eathcente = - float3(0,1,0) * EARTH_RADIUS; float3 f3raystat = float3(0, fheight, 0); float3 f3viewdi = ComputeViewDi(fCosViewZenithAngle); float3 f3dionlight = ComputeLightDi(f3ViewDi, fcossunzenithangle, fcossunviewangle); // Intesect view ay with the top of the atmosphee and the Eath float4 f4isecs; GetRaySpheeIntesection2( f3raystat, f3viewdi, f3eathcente, float2(earth_radius, ATM_TOP_RADIUS), f4isecs); float2 f2rayeathisecs = f4isecs.xy; float2 f2rayatmtopisecs = f4isecs.zw; if(f2rayatmtopisecs.y <= 0) etun 0; // This is just a sanity check and should neve happen // as the stat point is always unde the top of the // atmosphee (look at InsctLUTCoods2WoldPaams()) // Set the ay length to the distance to the top of the atmosphee float fraylength = f2rayatmtopisecs.y; // If ay hits Eath, limit the length by the distance to the suface if(f2rayeathisecs.x > 0) fraylength = min(fraylength, f2rayeathisecs.x); float3 f3rayend = f3raystat + f3viewdi * fraylength; // Integate single-scatteing float3 f3inscatteing, f3extinction; float fnumsteps = 100; IntegateUnshadowedInscatteing(f3RayStat, f3rayend, f3viewdi,

9 f3eathcente, f3dionlight, fnumsteps, f3inscatteing, f3extinction); etun f3inscatteing; } Listing 3. Shade implementation of single-scatteing adiance pe-computation. The shade fist tansfoms input coodinates uvwq ( u h, u α, u ϕ, u θ ) into the wold space attibutes fheight (h), fcosviewzenithangle ( c α ), fcossunzenithangle ( c ϕ ), and fcossunviewangle ( c θ) by inveting equations (4)-(7). It then intesects the view ay with the top of the atmosphee o the Eath suface and computes the closest intesection point. Finally, it pefoms numeical integation of the single scatteing along the ay. Computing Scatteed Light Radiance Evaluation of equation (1) is pefomed by a pixel shade shown in Listing 4. float3 ComputeSctRadiancePS(SSceenSizeQuadVSOutput In) : SV_Taget { // Get attibutes fo the cuent point float2 f2uv = PojToUV(In.m_f2PosPS); float fheight, fcosviewzenithangle, fcossunzenithangle, fcossunviewangle; InsctLUTCoods2WoldPaams( float4(f2uv, g_miscpaams.f2wq), fheight, fcosviewzenithangle, fcossunzenithangle, fcossunviewangle ); float3 f3eathcente = - float3(0,1,0) * EARTH_RADIUS; float3 f3raystat = float3(0, fheight, 0); float3 f3viewdi = ComputeViewDi(fCosViewZenithAngle); float3 f3dionlight = ComputeLightDi(f3ViewDi, fcossunzenithangle, fcossunviewangle); // Compute paticle density scale facto float2 f2paticledensity = exp( -fheight / PARTICLE_SCALE_HEIGHT ); float3 f3sctradiance = 0; // Go though a numbe of samples andomly distibuted ove the sphee fo(int isample = 0; isample < NUM_RANDOM_SPHERE_SAMPLES; ++isample) { // Get andom diection float3 f3randomdi = nomalize( g_tex2dspheerandomsampling.load(int3(isample,0,0)) ); // Get the pevious ode in-scatteed light when looking in diection f3randomdi // (the light thus goes in diection -f3randomdi) float4 f4uvwq = -1; float3 f3pevodesct = LookUpPecomputedScatteing(f3RayStat, f3randomdi, f3eathcente, f3dionlight.xyz, g_tex3dpevioussctode, f4uvwq); // Apply phase functions fo each type of paticles // Note that total scatteing coefficients ae baked into the angula // scatteing coeffs float3 f3drlghinsct = f2paticledensity.x * f3pevodesct; float3 f3dmieinsct = f2paticledensity.y * f3pevodesct; float fcostheta = dot(f3viewdi, f3randomdi); ApplyPhaseFunctions(f3DRlghInsct, f3dmieinsct, fcostheta); f3sctradiance += f3drlghinsct + f3dmieinsct;

10 } // Since we tested N andom samples, each sample coveed 4*Pi / N solid angle // Note that ou phase function is nomalized to 1 ove the sphee. Fo instance, // unifom phase function would be p(theta) = 1 / (4*Pi). // Notice that fo unifom intensity I if we get N samples, we must obtain exactly I afte // numeic integation etun f3sctradiance * 4*PI / NUM_RANDOM_SPHERE_SAMPLES; } Listing 4. Pixel shade fo computing ode n scatteed light adiance. Like the pevious one, the shade fist tansfoms input coodinates uvwq into the wold space attibutes by inveting equations (4)-(7). It then computes Rayleigh and Mie paticle density scale factos f2paticledensity fo the cuent point. Afte that it samples NUM_RANDOM_SPHERE_SAMPLES andom diections, loads pevious ode scatteing adiance f3pevodesct fom each diection, computes integand of equation (1) and accumulates it in f3sctradiance vaiable. The esulting net adiance is then multiplied by 4π / N whee N is the numbe of samples, as each sample coves 1/N faction of the entie sphee, which is 4 π. Computing Multiple Scatteing Ode The shade given in Listing 5 implements numeical integation of equation (2). float3 ComputeScatteingOdePS(SSceenSizeQuadVSOutput In) : SV_Taget { // Get attibutes fo the cuent point float2 f2uv = PojToUV(In.m_f2PosPS); float fheight, fcosviewzenithangle, fcossunzenithangle, fcossunviewangle; InsctLUTCoods2WoldPaams(float4(f2UV, g_miscpaams.f2wq), fheight, fcosviewzenithangle, fcossunzenithangle, fcossunviewangle ); float3 f3eathcente = - float3(0,1,0) * EARTH_RADIUS; float3 f3raystat = float3(0, fheight, 0); float3 f3viewdi = ComputeViewDi(fCosViewZenithAngle); float3 f3dionlight = ComputeLightDi(f3ViewDi, fcossunzenithangle, fcossunviewangle); // Intesect the ay with the atmosphee and Eath float4 f4isecs; GetRaySpheeIntesection2( f3raystat, f3viewdi, f3eathcente, float2(earth_radius, ATM_TOP_RADIUS), f4isecs); float2 f2rayeathisecs = f4isecs.xy; float2 f2rayatmtopisecs = f4isecs.zw; if(f2rayatmtopisecs.y <= 0) etun 0; // This is just a sanity check and should neve happen // as the stat point is always unde the top of the // atmosphee (look at InsctLUTCoods2WoldPaams()) float fraylength = f2rayatmtopisecs.y; if(f2rayeathisecs.x > 0) fraylength = min(fraylength, f2rayeathisecs.x); float3 f3rayend = f3raystat + f3viewdi * fraylength; const float fnumsamples = 64; float fsteplen = fraylength / fnumsamples; float4 f4uvwq = -1;

11 float3 f3pevsctradiance = LookUpPecomputedScatteing(f3RayStat, f3viewdi, f3eathcente, f3dionlight.xyz, g_tex3dpointwisesctradiance, f4uvwq); float2 f2pevpaticledensity = exp( -fheight / PARTICLE_SCALE_HEIGHT ); float2 f2netpaticledensityfomcam = 0; float3 f3inscatteing = 0; fo(float fsample=1; fsample <= fnumsamples; ++fsample) { float3 f3pos = lep(f3raystat, f3rayend, fsample/fnumsamples); float fcuheight = length(f3pos - f3eathcente) - EARTH_RADIUS; float2 f2paticledensity = exp( -fcuheight / PARTICLE_SCALE_HEIGHT ); f2netpaticledensityfomcam += (f2pevpaticledensity + f2paticledensity) * (fsteplen / 2.f); f2pevpaticledensity = f2paticledensity; // Get optical depth float3 f3rlghopticaldepth = g_mediapaams.f4rayleighextinctioncoeff.gb * f2netpaticledensityfomcam.x; float3 f3mieopticaldepth = g_mediapaams.f4mieextinctioncoeff.gb * f2netpaticledensityfomcam.y; // Compute extinction fom the camea fo the cuent integation point: float3 f3extinctionfomcam = exp( -(f3rlghopticaldepth + f3mieopticaldepth) ); } // Get attenuated scatteed light adiance in the cuent point float4 f4uvwq = -1; float3 f3sctradiance = f3extinctionfomcam * LookUpPecomputedScatteing(f3Pos, f3viewdi, f3eathcente, f3dionlight.xyz, g_tex3dpointwisesctradiance, f4uvwq); // Update in-scatteing integal f3inscatteing += (f3sctradiance + f3pevsctradiance) * (fsteplen/2.f); f3pevsctradiance = f3sctradiance; etun f3inscatteing; } Listing 5. Pixel shade fo computing ode n in-scatteed light adiance. Like the shade given in Listing 3, this shade fist tansfoms input coodinates uvwq into the wold space attibutes and econstucts the view ay fom camea to the top of the atmosphee o intesection with the Eath, whicheve is close. It then pefoms tapezoidal integation of equation (2). At each step the shade updates extinction fom the camea f3extinctionfomcam and computes diffeential amount of light f3sctradiance in-scatteed fom the unit length ay section at cuent point. The total inscatteed light is accumulated in f3inscatteing. Computing Ambient Sky Light Pe-computation of the ambient sky light accoding to equation (3) is pefomed by the shade shown in Listing 6. float3 PecomputeAmbientSkyLightPS(SSceenSizeQuadVSOutput In) : SV_Taget { float fu = PojToUV(In.m_f2PosPS).x;

12 float3 f3raystat = float3(0,20,0); float3 f3eathcente = -float3(0,1,0) * EARTH_RADIUS; float fcoszenithangle = clamp(fu * 2-1, -1, +1); float3 f3dionlight = float3(sqt(satuate(1 - fcoszenithangle*fcoszenithangle)), fcoszenithangle, 0); float3 f3skylight = 0; // Go though a numbe of andom diections on the sphee fo(int isample = 0; isample < NUM_RANDOM_SPHERE_SAMPLES; ++isample) { // Get andom diection float3 f3randomdi = nomalize( g_tex2dspheerandomsampling.load(int3(isample,0,0)) ); // Reflect diections fom the lowe hemisphee f3randomdi.y = abs(f3randomdi.y); // Get multiple scatteed light adiance when looking in diection f3randomdi // (the light thus goes in diection -f3randomdi) float4 f4uvwq = -1; float3 f3sct = LookUpPecomputedScatteing(f3RayStat, f3randomdi, f3eathcente, f3dionlight.xyz, g_tex3dpevioussctode, f4uvwq); // Accumulate ambient iadiance though the hoizontal plane f3skylight += f3sct * dot(f3randomdi, float3(0,1,0)); } // Each sample coves 2 * PI / NUM_RANDOM_SPHERE_SAMPLES solid angle // (integation is pefomed ove uppe hemisphee) etun f3skylight * 2 * PI / NUM_RANDOM_SPHERE_SAMPLES; } Listing 6. Pe-computing ambient sky light. The shade fist computes cosine of the sun zenith angle fcoszenithangle and econstucts sun light diection. It then samples NUM_RANDOM_SPHERE_SAMPLES andom diections on the uppe hemisphee, loads multiple scatteing adiance intensity fom each diection, computes integand of equation (3) and accumulates it in f3skylight vaiable. The esulting iadiance is then multiplied by 2π / N whee N is the numbe of samples, as each sample coves 1/N faction of the uppe hemisphee, which is 2 π. Light Shafts Calculation Using Scatteing Look-up Table Since multiple scatteing adiance ( C, v, l ) is pe-computed, we can evaluate in-scatteing L M In contibution between any two points P 1 and P 2 on the view ay using the following equation: L T ( C P,, ) 1 ) M T ( C P2 ) M P P l e L ( P, v, l ) e L ( P, v, l = ). (8) In ( 1 2 In 1 In 2 Evaluating the above equation at each step of the ay maching loop would be pohibitively expensive. In oiginal method Buneton and Neyet compute total length of the ay faction which is lit by the sun and then apply equation (8) assuming that the faction is continuous and stats diectly at the camea [Buneton and Neyet 08]. When camea is located in shadow (Figue 6, left) this method gives too bight scatteing. In ou method we take advantage of the ay maching pocess not only to evaluate total lit length D Lit, but also to compute distance D Stat to the fist lit point on the view ay (Figue 6).

13 D Lit D Lit D Stat = 0 D Stat Figue 6. Total length D Lit of the illuminated ay faction and distance D Stat to the fist lit point. Afte the ay maching loop is completed, we use D Lit and D Stat to compute stat and end points of the lit ay faction and apply equation (8) as show in the code snippet below: float3 f3litsectionend = f3litsectionstat + ftotallitlength * f3viewdi; float3 f3extinctiontostat = GetExtinctionUnveified(f3RestainedCameaPos, f3litsectionstat, f3viewdi, f3eathcente); float4 f4uvwq = -1; f3multiplescatteing = f3extinctiontostat * LookUpPecomputedScatteing(f3LitSectionStat, f3viewdi, f3eathcente, g_lightattibs.f4dionlight.xyz, tex3dsctlut, f4uvwq); float3 f3extinctiontoend = GetExtinctionUnveified(f3RestainedCameaPos, f3litsectionend, f3viewdi, f3eathcente); f3multiplescatteing -= f3extinctiontoend * LookUpPecomputedScatteing(f3LitSectionEnd, f3viewdi, f3eathcente, g_lightattibs.f4dionlight.xyz, tex3dsctlut, f4uvwq); f3insctintegal += max(f3multiplescatteing, 0); In the code fagment above, GetExtinctionUnveified() function evaluates extinction between two points without checking if the points ae inside the atmosphee. f3restainedcameapos vaiable contains camea position esticted by the top of the atmosphee. Impotant aspect to notice is that textue coodinates f4uvwq etuned fom the fist call to LookUpPecomputedScatteing() function ae passed to the second call to assue consistent sampling with espect to hoizon. Occluded vs unoccluded highe ode scatteing Highe ode scatteing is vey difficult to model pecisely because the path a photon can each the camea can be vey complicated. Some simplifications ae necessay to make multiple scatteing feasible fo eal-time endeing. Buneton and Neyet in thei wok account fo multiple scatteing contibution fom the same illuminated ay faction only [Buneton and Neyet 08]. The esulting sky could look too dak when camea is located in Eath s shadow, which is especially noticeable duing the twilight (Figue 7, left top). We believe that moe plausible esults could be obtained if highe ode scatteing is consideed unoccluded and is thus always added to the esulting scatteing adiance. The easoning behind this appoach is that highe ode scatteing is caused by the adiance coming fom the whole

14 hemisphee. With the exception of some cases, usually most of the points on the ay ae not occluded fom the sky dome adiance, making significant contibution to highe ode scatteing. The image endeed with this method looks significantly moe ealistic (Figue 7, ight top). To implement this appoach, we use two look-up tables. Fist, afte completing the ay maching, we pefom two look-ups into the single scatteing look-up table (tex3dsinglescatteing) as descibed above. Afte that we do anothe two look-ups into the highe ode look-up table (tex3dhighodescatteing) to get unoccluded highe ode scatteing contibution fom the whole ay. Figue 7. Occluded highe ode scatteing (left column) vs unoccluded highe ode scatteing (ight column). Though the method descibed above impoves twilight sky damatically, it esults in some false glow in the sun diection when sun is actually occluded (Figue 7, bottom ow). We howeve believe that this mino dawback can be teaded fo the impoved twilight sky. Teain shades Teain shades compute sun light extinction due to the atmosphee and account fo the ambient sky light. Sun light extinction and ambient sky light ae evaluated in the vetex shade as shown in the following code snippet: void GetSunLightExtinctionAndSkyLight(in float3 f3posws, out float3 f3extinction, out float3 f3ambientskylight) { float3 f3eathcente = float3(0, -g_mediapaams.feathradius, 0); float3 f3difomeathcente = f3posws - f3eathcente; float fdisttocente = length(f3difomeathcente);

15 f3difomeathcente /= fdisttocente; float fheightabovesuface = fdisttocente - g_mediapaams.feathradius; float fcoszenithangle = dot(f3difomeathcente, g_lightattibs.f4dionlight.xyz); float frelativeheightabovesuface = fheightabovesuface / g_mediapaams.fatmtopheight; float2 f2paticledensitytoatmtop = g_tex2doccludednetdensitytoatmtop.samplelevel(samlineaclamp, float2(frelativeheightabovesuface, fcoszenithangle* ), 0).xy; float3 f3rlghopticaldepth = g_mediapaams.f4rayleighextinctioncoeff.gb * f2paticledensitytoatmtop.x; float3 f3mieopticaldepth = g_mediapaams.f4mieextinctioncoeff.gb * f2paticledensitytoatmtop.y; // And total extinction fo the cuent integation point: f3extinction = exp( -(f3rlghopticaldepth + f3mieopticaldepth) ); } f3ambientskylight = g_tex2dambientskylight.samplelevel( samlineaclamp, float2(fcoszenithangle* , 0.5), 0); Intepolated extinction and ambient sky light ae then passed to the pixel shade, which uses them to attenuate sun light intensity and appoximate ambient light as shown in the following code snippet: // Attenuate extateestial sun colo with the extinction facto float3 f3sunlight = g_lightattibs.f4extateestialsuncolo.gb * In.f3SunLightExtinction; // Ambient sky light is not pe-multiplied with the sun intensity float3 f3ambientskylight = g_lightattibs.f4extateestialsuncolo.gb * In.f3AmbientSkyLight; // Account fo occlusion by the gound plane f3ambientskylight *= satuate((1 + dot(eathnomal, f3nomal))/2.f); Tone mapping The sample suppots a numbe of diffeent tone mapping opeatos, namely: Exp simple exponential tone mapping opeato; Reinhad basic Reinhad tone mapping opeato [Reinhad et al 02]; Modified Reinhad modified Reinhad tone mapping opeato [Reinhad et al 02]; Unchated 2 tone mapping opeato fom Unchated 2 [Hable 10]; Filmic ALU filmic tone mapping opeato [Hable 10]; Logaithmic logaithmic tone mapping opeato [Dago et al 03]; Adaptive log adaptive logaithmic tone mapping opeato [Dago et al 03]. To estimate aveage scene luminance, we unwap the scene into the low-esolution (64x64) buffe, outputting luminance only, and geneate the whole mipmap chain. The coasest level then contains aveage value. Pefomance Results and Discussion Pefomance of diffeent stages of the algoithm on Intel HD gaphics 5000 is given in the Figue 8. Fou diffeent modes wee evaluated:

16 SS-Int single scatteing computed with the numeical integation, no highe ode scatteing; SS-Int+MS-UnO single scatteing computed with the numeical integation plus unoccluded highe ode scatteing; SS-LUT+MS-UnO single scatteing plus unoccluded highe ode scatteing both computed using two look-up tables; SS-LUT+MS-Occ single and occluded highe ode scatteing computed with the two look-ups into single table. Figue 8. Pefomance of diffeent stages of the algoithm on Intel HD gaphics 5000 (1280x720 esolution). It can be seen that most of the stages take the same time in all modes except fo the endeing coase inscatteing and the ay maching. Both stages take the most time in SS-Int+MS-UnO mode because in this case besides evaluating single scatteing integal with the numeical integation, additional look-up into the scatteing look-up table is pefomed. With this additional look-up, ay maching becomes 24% slowe (3.17 ms vs 2.55 ms). Meanwhile, oveall slowdown due adding highe-ode scatteing is modest 10.1%, ising the total time fom 11.3 to 12.4 ms. It must be noted that this mode geneates the most convincing visual esults, so additional pefomance cost seems to be justified. In the two emaining modes, SS-LUT+MS-UnO and SS-LUT+MS-Occ, numeical integation of single scatteing is not pefomed and only total lit length and distance to the fist point in light is computed. This makes ay maching loop significantly simple and faste, as Figue 8 eveals. It can be seen that the diffeence between two modes is in fact insignificant despite the fact that in SS-LUT+MS-UnO mode, fou look-ups into two tables ae pefomed, while two look-ups into one table ae pefomed in SS- LUT+MS-Occ mode. The ay maching time goes down by 36% fom 2.5 ms to 1.6 ms. Computing coase inscatteing is also much faste in this case, because instead of pefoming tapezoidal integation, only two look-ups into the table ae pefomed. The time goes down fom 1.05 ms to 0.81 ms. Oveall speedup compaed to numeical integation only (SS-Int mode) is 10% (11.3 ms vs 10.0 ms). Contols w,s,a,d,q,e - move camea

17 GUI shift acceleate left mouse button otate camea ight mouse button otate light F1 show/hide help text F8 ebuild shades (could be used to modify shades and see the effect at un time) The sample GUI has thee panels, which can be selected using the top most dop-down list: basic, additional and tone mapping. Basic contols Figue 4. Left to ight: basic, additional and tone mapping contol sets. Full sceen button toggles the full sceen mode. VSync checkbox toggles vetical synchonization at 60 fps.

18 Enable light scatteing checkbox enables o disables the light scatteing effect. Enable light shafts checkbox enables o disables endeing shafts of light. If this option is disabled, simple algoithm is used to compute scatteing integal which ignoes shadows. Scatteing technique selection dop-down list has two options: o Epipola sampling calculate scatteing effect using epipola sampling; o Bute foce ay maching calculate scatteing effect fo each sceen pixel without 1D min/max binay tee optimization. This mode can be used to geneate the efeence gound tuth image and compae the quality with the epipola sampling. Shadow map esolution dop down list enables selecting the esolution fom 512x512 up to 4096x4096. Note that the numbe of cascades can be selected on the Additional contols panel. Num integation steps slide sets the numbe of steps pefomed when computing single scatteing integal. This contol is only enabled when Enable light shafts checkbox is not maked and when Single sct: integation is selected on the Additional contols panel. Epipola slices slide selects the numbe of slices in the ange fom 32 to The moe epipola slice, the highe visual quality and the highe computational cost. Good visual esults can be obtained when numbe of slices is at least half the maximum sceen esolution (fo 1280x720 esolution, good esults ae obtained fo slices).

19 64 slices 256 slices Total samples in slice slide enables selecting the numbe of samples in the ange fom 32 to Convincing visual esults ae geneated when numbe of samples is at least half the maximum sceen esolution (fo 1280x720 esolution, good esults ae obtained fo samples). Initial sample step slide sets the step fo the initial ay maching samples. The lowe the step, the moe initial ay maching samples will be placed along each epipola line and the highe image quality will be obtained. Initial ay maching samples ae seen as ectangles/cicles going away fom the epipole at egula steps. Initial step: 16 Initial step: 64 Epipole sampling density slide contols additional incease of the initial ay maching sampling density nea the epipole, which could be equied to account fo high fequency light vaiations due to stong fowad Mie scatteing. Refinement theshold slide contols the efinement accuacy. Smalle theshold causes moe ay maching samples to be placed at discontinuities of light intensity and poduces highe quality endeing. Scatteing scale slide contols the intensity of the scatteing effect (note that this option has almost no effect when tone mapping with automatic exposue is enabled). Show sampling check box toggles visualization of the epipola sampling stuctue. Thick ed dots denote ay maching samples, thin ed dots epesent intepolation samples.

20 1D Min/Max optimization check box enables/disables using 1-D min/max binay tees to acceleate ay maching. Optimize sample locations checkbox enables an option to fix ovesampling along shot epipola lines. Optimized locations Non-optimized locations Coection at depth beaks checkbox toggles additional fix-up pass fo coecting these samples, fo which scatteed light cannot be pecisely computed by unwaping epipola scatteing image. Duing this pass, ay maching algoithm is executed fo these pixels. 1D min/max binay tee acceleation cannot be used at this time, because the pixels do not belong to any epipola line. Thus ay maching is much less efficient in this case. Fo typical teain scene, usually only a vey few pixels (if any) equie coection (see pictue below). So this option can be safely disabled without noticeable loss of visual quality. Show depth beaks checkbox enables visualizing (in geen) these pixels, fo which coection pass is pefomed. This option has effect only when Coection at depth beaks checkbox is maked.

21 Lighting only checkbox toggles showing the light scatteing effects only. Additional contols Single scatteing mode dop-down list has the following options: o Singl sct: none do not compute single scatteing. o Singl sct: integation compute single scatteing with the numeical integation duing ay maching. o Singl sct: LUT compute single scatteing using look-up table. If this option is enabled, only total length of the illuminated potion of the ay is evaluated duing ay mached and distance to the fist lit section is stoed. Afte that two look-ups ae pefomed to get single scatteing contibution along the ay. Multiple scatteing mode dop-down list has the following options: o Mult sct: none do not compute multiple scatteing. o Mult sct: occluded account fo multiple scatteing contibution only fom the illuminated pat of the ay. This is implemented by pefoming look-ups into the highe ode scatteing textue, if single scatteing mode is none o integation. If single scatteing mode is LUT, then single and highe ode scatteing ae computed by pefoming look-ups into the multiple scatteing look-up textue. o Mult sct: unoccluded add highe ode scatteing contibution fom the whole view ay. This is implemented by pefoming two look-ups into the highe ode scatteing look-up textue.

22 SS-none + MS-unoccluded SS-none + MS-occluded SS-integation + MS-none SS-LUT + MS-unoccluded Num cascades dop down enables selecting the numbe of shadow cascades in the ange fom 1 to 8. Show cascades checkbox toggles visualization of shadow map cascades. Smooth shadows checkbox enables softening shadow edges by aveaging 5 PCF samples. Best cascade seach checkbox enables impoving shadow quality by finding the smallest cascade the point pojects into instead of elying on cascade z ange. Patitioning facto slide contols the atio between linea and logaithmic cascade distibution. Cascade pocessing mode dop down contains the following options:

23 o Single pass all cascades ae pocessed by a single daw call. The shade loops though all the cascades; o Multi pass each cascade is pocessed by a sepaate daw call. The scatteing contibution fom each cascade is accumulated in a scatteing textue using alpha blending; o Multi pass inst woks in the same way as Multi pass, but single instanced daw call is issued. Fist cascade to ay mach dopdown enables selecting the smallest cascade which will be consideed duing ay maching. Usually one o two smallest cascades can be safely skipped without affecting visual quality. Extinction evaluation mode dopdown enables selecting one of the following two modes: o Epipola ende epipola extinction textue duing coase scatteing integal calculation pass and use it at the final unwaping stage to get extinction fo each pixel. o Pe pixel use analytical expession to evaluate extinction individually fo each pixel. Selecting one of these two options does not affect visual quality. Epipola mode howeve is much faste. Refinement citeion dopdown enables selecting one of the following two inscatteing efinement citeions: o Depth use diffeence in depth as a efinement citeion. o Inscatteing use diffeence in coase unshadowed inscatteing integal as the efinement citeion. This citeion is much moe appopiate than depth citeion as significant diffeences in scatteed light is what we need to find to efine sampling. The advantages of this citeion become appaent fo oute space views whee depth does not exhibit any changes while scatteed light vaies significantly. As a esult, depth citeion geneates evident banding atifacts nea epipole, while inscatteing citeion does not suffe fom this poblem.

24 Refinement citeion - depth Refinement citeion - inscatteing Min/max fomat dop down enables selecting fomat of the textue stoing 1D min/max binay tees. Two options ae available: 16-bit unom and 32-bit float. This option has no visual effect, but selecting 16-bit unom fomat impoves pefomance a bit. Use custom sct coeffs check box enables setting custom Rayleigh and Mie scatteing coefficients. This option enables Set Rayleigh colo and Set Mie Colo buttons which selects coesponding scatteing coefficients. Note that changing one of these options takes some time because all the look-up tables need to be e-computed. Aeosol density and Aeosol absoption slides contols the appopiate paametes. Note that changing eithe paamete takes some time because all the look-up tables need to be ecomputed. Animate sun checkbox toggles sun animation. Tone mapping contols Middle gay (Key) slide contols the tone of the scene. Default value is Lage values make the scene look bighte, smalle values make it look dimme. White point slide selects the white point value fo some tone mapping opeatos (Reinhad Mod, Unchated 2, Logaithmic and Adaptive log). Luminance satuation slide contols additional colo satuation fo Exp, Reinhad, Reinhad mod, Logaithmic and Adaptive log tone mapping opeatos.

25 Auto exposue enables computing logaithmic aveage luminance of the scene to automatically adjust exposue. Tone mapping opeato povides selection of one of the following modes: o Exp exponential tone mapping opeato; o Reinhad basic Reinhad tone mapping opeato; o Reinhad mod modified Reinhad tone mapping opeato; o Unchated 2 tone mapping opeato fom Unchated 2; o Filmic ALU filmic tone mapping opeato; o Logaithmic logaithmic tone mapping opeato; o Adaptive log adaptive logaithmic tone mapping opeato. Light adaptation checkbox enables simulation of tempoal light adaptation. Refeences [Buneton and Neyet 08] Eic Buneton and Fabice Neyet. Pecomputed Atmospheic Scatteing. Comput. Gaph. Foum 27:4 (2008), Special Issue: Poceedings of the 19th Euogaphics Symposium on Rendeing [Reinhad et al 02] E. Reinhad, M. Stak, P. Shiley, and J. Feweda. Photogaphic Tone Repoduction fo Digital Images. ACM Tansactions on Gaphics, 21(3): , Available online ( [Dago et al 03] F. Dago, K. Myszkowski, T. Annen, and N. Chiba. Adaptive logaithmic mapping fo displaying high contast scenes. Compute Gaphics Foum, vol. 22, no. 3, Available online ( [Hable 10] John Hable. Unchated 2: HDR Lighting" In Poceedings Game Develope Confeence, Available online ( HDR_Lighting).

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