Upload
halie-bickerton
View
226
Download
3
Tags:
Embed Size (px)
Citation preview
Spectacular Specular-LEAN and CLEAN specular highlights
Dan BakerFiraxis Games
MotivationObservations from Movie folks
• “The most important aspect of rendering for a movie is anti-aliasing”
• “Games today still don’t look as good as animated movies 12 years ago.”
• “Why in video games does everything look so shiny?”
Reality Check• Have a habit of comparing ourselves against
other games• Therefore miss the obvious: Some of our
materials don’t look anything like they should• And they alias• And they sparkle
Shiny things• Water, Metal, commonly seen in games• Used for water in Civilization V, but metals
suffer from similar problems• Will tour two common lighting models, Phong
and Blinn Phong• Both have huge problems
Phong• Simple to implement• Since L is constant for environments, can turn
specular part into a preconvolved environment
Psp LRKNLKLRF )()(),(
Sometimes accurate
Good for perfect reflectors,like still water. But, perfect reflectors = high power
Problems with Phong• Aliases• Can’t get elongated reflections• Pretty inaccurate – very plastic look to it• No good way to add normals maps together• Anisotropic (grooved) materials will lose there
anisotropy at zoom• Can’t use high powers or else!
Problems with Phong
Classic Scene, sunset. Can’t get this with Phong lighting
Blinn Phong• Much more accurate if we have real lights in
our scene• Can get elongated shapes• Cheap to evaluate
psd HNKpLNK )()(
Blinn Phong problems• Aliases• Shading becomes very wrong with roughness• Highlights change based on pixel coverage, and become• Anisotropic (groved) materials will lose there
anisotropy at zoom• Can’t do environments easily• Can’t use high powers or else!
Spectacular Specular fail
A very rough wave filters to a perfectly flat standing water,An example
Down sampled of the final render
What Blinn-Phong gives us
Bump Filtering
Exactly the same substance, but one side is wrinkled. This completely changes the reflections. (Thanks to Chipotle for the foil)
Overviews problems• “The shimmies”, “The speckles” Lots and lots of talks about
this problem• The more substantial the normal map, the higher the power,
the more noise we get. Lots of artist tweaking, limits to our data
• Reflections are just plan wrong at distant scale, makes objects way over-shiny
• Can’t add normal maps together easily to get detail maps
Why this happens • The integral of a function over a range of
inputs isn’t the same as function with inputs integrated over a range
i iii
RR
IwFIFw
drRFdrRF
)()(
)()(
Where R is a region of a texture, F is our shader (in this case, a Phong or Blinn Phong shader) . The second version is a discrete version, where W is the sample weights from our hardware filtering.
How do Movies solve this?• Typically use REYES, or more
advanced techniques• Roughly equivalent of shading
every relevant texel and averaging the results
• Very expensive, potentially thousands of shader evals per pixel
Dreaming the dream• Ideal lighting model:
– Can use any power we want– Will deal with zooming in and out correctly– Won’t alias– Easy to use: compatible with our current pipeline– Relatively inexpensive– Can add normals together– Can use all of our MIP hardware
Formal definition• What we really want is to build a replacement
for Blinn Phong that has this property (where F is basically our shader):
i i
ii IwFIFw )()(
LEAN Mapping• Linear Efficient Antialiased Normal Mapping• Considered Fast Antialiased Reflectance Texture Mapping• Fast and flexible solution for bump filtering
– Shiny bumps won’t alias– Distant bumps will change surface shading– Directional bumps will become anisotropic highlight
• Allows blending layers of bumps• Works with existing Blinn-Phong pipeline
Scale problem solved
LEAN MapNormal Map
Prior Work• Posed by Kajiya 1985• Monte-Carlo
– Cabral et al. 1987, Westin et al. 1992, Becker & Max 1993• Multi-lobed distributions
– Fournier 1992, Han et al. 2007• Single Gaussian/Beckmann distribution
– Olano & North 1997, Schilling 1997, Toksvig 2005• Diffuse [Kilgard 2000]
Beckman Shading Model
2tan2
2
1 s
e
b
tb hh
e
1
2
1
2
1
The math is simpler then it looks. We are raising the power based on the distance of the half angle from the normal. This second formulation rolls the power into a covariance matrix, thereby giving us anisotropic power (e.g. two powers, one for X and one for Y).
Probability Distributions in Shading• Distribution of microfacet normals
– Perfectly reflective facets– Only facets oriented with reflect to – Look up probability of in distribution
• Beckmann distribution– Gaussian of facet tangents = projection
Filtering• Filter is linear combination over kernel• Linear representation → any linear filter
– Summed Area, EWA, …– MIP map, Hardware Anisotropic
• We need a BRDF that is linear
Filtering: Gaussians• Gaussian described by mean and variance
– –
• Mean combines linearly• Variance does not, but second moment does
Blinn-Phong ↔ Beckmann• Blinn-Phong approximates Gaussian [Lyon 1993]
• Better fit as increases• Variance , normalize
with
Blinn-Phong ↔ Beckmann
Blinn-Phong Beckmann
LEAN mapping• Blinn-Phong ↔ Beckmann• Filtering Bumps• Sub-facet shading• Layers of bumps
Distributions & Bumps• If the normal is changing our surface
orientation, is there any way to add them together?
• Does that even • meaning?
LEAN Mapping• Beckman distribution can be broken into pieces
that filter, but doesn’t deal with the normals.• Key insight: We think of the normal instead as a
shift of the distribution of microfacets
)()(2
1 1
2
1 nnt
nn bhbhe
Distributions
Beckman distribution works on a 2d plane. The blue discs represent the distribution of normals. Rather then change the orientation of the surface, we simply shift the center location of the distribution of normals by the x,y component of the normals. Thus, we interpret the normal as a shift in distribution, rather then a change in surface orientation
Filtering Bumps• Rather than bump-
local frame• Use surface
tangent frame– Bump normal =
mean of off-center distribution
Bumps vs. Surface Frame
Surface-frame BeckmannBump-frame Beckmann
LEAN Data• Normal (for diffuse)
• Bump center in tangent frame
• Second moments
LEAN Use• Pre-process
– Seed textures with , and – Build MIP chain
• Render-time– Look up with HW filtering– Reconstruct 2D covariance– Compute diffuse & specular per light
Sub-facet Shading• What about base specularity?
– Given base Blinn-Phong exponent,– Base Beckmann distribution
• One of these at each facet = convolution– Gaussians convolve by adding ’s– Fold into , or add when reconstructing
LEAN Map features• Seamless replacement for Blinn-Phong• Specular bump antialiasing• Turns directional bumps into anisotropic
microfacets
Bump Layers• Uses
– Bump motion (ocean waves)– Detail texture– Decals
• Our approach– Conceptually a linear combination of heights– Equivalent to linear combination of
• Even from normal maps
Bump Layers: The Tricky Part• What about ?
– – – Expands out to , , and terms– terms are in , terms are in – terms are new:
– Total of four new cross terms
Layering Options1. Generate single combined LEAN map
– Mix actual heights, or use mixing equations– Time varying: need to generate per-frame– Decal or detail: need high-res LEAN map
2. Generate mixing texture– One per pair of layers– Decal or detail: need high-res LEAN mixture maps
3. Approximate cross terms– Use rather than a filtered mixing texture
Single LEAN MapMixture TextureApproximationSource 2Source 2Source 1
Layer Options
Source 1
MIP Biased
Mixed
PerformanceSingle Layer Two Layers
Blinn-Phong LEAN Per-frame Mix texture Approx
ATI Radeon HD 5870
1570 FPS 1540 FPS 917 FPS 1450 FPS 1458 FPS
D3D Instructions 30 ALU1 TEX
42 ALU2 TEX
50 ALU3 TEX
54 ALU5 TEX
54 ALU4 TEX
1600 x 1200, single full screen object
Converting Blinn-Phong Data • So fast could be done at load time
float3 tn = tex2D(normalMap, coord);
float3 N = float3(2*tn.xy-1, tn.z);
float2 B = N.xy/(ScaleFactor&N.z);
float3 M = float3(B.x*B.x + 1/s, B.y*B.y + 1/s, B.x*B.y)
Output.lean1 = float4(tn, .5*M.z + .5)
Output.lean2 = float4(.5*B + .5, M.xy)
Texture Compression and Precision• Normal maps get big, painful to compress• Lean MAPs require 5 fields• x,y, x^2, xy, y^2• Caveat: The precision matters. Unlike other
techniques, we are using the normal filtering hardware
Obligatory Shader Codefloat4 f4BaseMeshColor = tex2D(BaseMeshColor, f2BaseTexCoord);
float4 f4BaseColor = tex2D(LeanTextureMap1, f2BaseTexCoord);
float Var = tex2D(LeanTextureMap2,f2BaseTexCoord).x;
float GradientScale = g_fLeanMapScale;
float VarianceScale = GradientScale*GradientScale;
float2 Gradient = float2(f4BaseColor.x*2-1,f4BaseColor.y*2-1) *GradientScale;
float3 Covar = float3(f4BaseColor.zw , Var*2 - 1) * VarianceScale;
// turn moments into elements of covariance matrix, matrix is
mat4(Covar.x,Covar.z,Covar,z,Covar.y)
Covar -= float3(Gradient.xy*Gradient.xy, Gradient.x*Gradient.y);
float3 Half = normalize(ViewDir + LightDir);
//Transform half angle back into tangent spaceHalf = mul(mTS, Half);
float2 HalfCenter = Half.xy/Half.z - Gradient.xy;
//Now calculate the specfloat Cxx = Covar.x + 1/g_fExp, Cyy = Covar.y + 1/g_fExp, Cxy = Covar.z;float Cdet = Cxx*Cyy - Cxy*Cxy;float e = (Cyy*HalfCenter.x*HalfCenter.x + (Cyy*HalfCenter.y - 2*Cxy*HalfCenter.x)*HalfCenter.y)*.5/Cdet;
fExp = (Cdet<=0 || e>=10 | Half.z < 0) ? 0 : exp(-e)/sqrt(Cdet);
Typical strategy• Remember that our is stored power is 1/s• Simple normalized texture, pow 32 = 4 bits
precision, pow 128 = 2 bits!• Can renormalize range, to capture some bits• If we want to use very high powers, e.g.
10,000+, really need 16 bits precision
Water For Civilization V• Lots of background, but why did we do this?• Needed to make water that worked at a
distance, not a smooth reflection• And, wanted a realistic wave combing effect• Does not use a reflection map, high powers let
us use an analytic model istead
Civ 5’s water• Linear combination of 4
moving bump maps• Allows us to accurate
wave directions
Can we make a cheaper version?• CLEAN Mapping
– An extension to LEAN mapping developed after paper published
– Common art problem: Went to 5 values, hard to drop into most pipelines, and need more precision
– Can we make it use less values• CLEAN mapping Cheap Linear Efficient Antialiased Normal
Mapping.
Dropping Anisotropy• Cool feature of LEAN maps, but efficiency might be
more important• Let’s examine the Beckmann distribution again
• Be really nice if we could make only 1 value instead of 3
)()(2
1 1nn
tnn bhbh
e
Dropping Terms• Can just approximate the covariance matrix
with a diagonal matrix
• Then store just X^2 + Y^2 in addition to X,Y
)var(0
0)var(22
22
YX
YX
)var(
)()(
2
122 YX
bhbh nnt
nn
e
CLEAN Mapping• Now we have only 3 terms to store. X, Y, X^2 +
Y^2, can store in 3 values• Then, calculating the variance:
)( 22yxz MMMV
),,( zyx MMM
V
MHMH yyxx
e
22 )()(
2
1
Combining CLEAN Maps
2122)1(1
21
21
))1(2,2(2
))1(1,1(1
BBMttMM
BBM
BBM
tMtMB
tMtMB
zzz
yyy
xxx
yx
yx
Coming CLEAN• Most of the high level benefits of LEAN
mapping• About half the data costs• Does not support anisotropy
Conclusions• Normal map filtering = solved problem• Cheap, easy to make art for• Huge Visual Impact• NO EXCUSE to have messy specular!
Thanks• Marc Olano – can find I3D paper on his
website• Firaxis Games