1. Normal Map Compression with ATI 3Dc™
Jonathan Zarge
ATI Research Inc.

2. Overview Normal mapping Normal map compression techniques
DXT compression
ATI 3Dc™
Swizzled DXT5 compression

3. Normal Mapping Increase visual realism Reduce geometric size of models
Create detail by simulating geometry
More efficient than dense geometry
Textures provide lighting (normal) information
Used in Half-Life 2, Doom 3, and Far Cry

4. Car Paint Demo

5. Traditional Lighting Model
Normals interpolated across triangle and
lighting values calculated at each pixel
Lighting values calculated at vertices and
then interpolated across triangle n0

6. Normal Map Lighting nx nx nz (nx,nx,nz) 3 component normal
Lighting values calculated at each
pixel using normal read from normal map
(nx,nx,nz)
nx nx nz
3 component normal
map texture

7. World Space vs. Tangent Space
Triangle normal = (-0.6,-0.3,0.74) z y x
Triangle normal can be
any normalized vector x y z
Triangle normal = (0,0,1)
Coordinate space of normal
defined by triangle orientation
z component of normal map
texel must be positive

8. Example Tangent Space Normal Maps
Tangent space normal maps are blue because a “Z” vector, (0,0,1) is represented as (127,127,255) as a color and the normals within a triangle are usually close to the normal of the “flat” triangle.
Tangent space normal maps can be
efficiently compressed

9. Generating Normal Maps

10. Normal Mapping Drawbacks
Low angle views distorted
Silhouette edges do not have detail
High texture bandwidth required
Large amount of texture memory
DXT compression not optimal for normal maps

11. Benefits of Normal Map Compression
More detailed normal maps
More normal maps
Memory and bandwidth can be diverted to other resources
Smaller media size

12. Normal Map Compression Techniques
Lower precision texture formats
Texture formats with fewer channels
Denormalization
Palletization
Direct DXT compression
ATI 3Dc™
Swizzled DXT5

13. DXT Compression Designed to compress color data
No suited for arbitrary data
One channel dependent on another
Lossy format
Image divided into 4x4 pixel blocks
16 possible colors in block
Only 3 or 4 colors in compressed data
Local similarity in small region enables high quality color compression
Each 4x4 block has a mini-palette of 3 or 4 colors
For normals, high frequency changes are the desired use

14. DXT Compression Color Block
Image divided into 4x4 blocks
Two 16-bit colors stored representing endpoints of linear color-ramp
One or two interpolated colors calculated
16 two-bit indices stored representing index into color ramp
Effective bit-rate:
64 (2*16 +16*2) / 16 = 4 bits per pixel

15. DXTC Color Compression
CYAN
WHITE
BLUE
MAGENTA
Interpolated Colors
GREEN
YELLOW
BLACK
RED

16. DXTC Color Decompression
For the four color case, given color[0], color[1], and index[1..15]:
// calculating interpolated colors
color[2] = (2*color[0] + color[1] + 1)/3
color[3] = (color[0] + 2*color[1] + 1)/3
// decompressed texel values
for n = 0 to 15
texel[n] = color[index[n]]

17. DXT5 Compression Alpha Block
Like color, image divided into 4x4 blocks
Two 8-bit scalars stored representing endpoints of linear alpha-ramp
4 or 6 intermediate alpha values calculated
16 three-bit indices stored representing index into alpha ramp
Effective bit-rate:
64 (2*8 +16*3) / 16 = 4 bits per pixel

18. DXTC Alpha Decompression
For the 8 alpha value case, given alpha[0], alpha[1], and index[1..15]:
// calculating interpolated alpha values
alpha[2] = (6*alpha[0] + 1*alpha[1] + 3)/7
alpha[3] = (5*alpha[0] + 2*alpha[1] + 3)/7 ..
alpha[7] = (1*alpha[0] + 6*alpha[1] + 3)/7
// decompressed texel values
for n = 0 to 15
texel[n] = alpha[index[n]]

19. Using DXT Compression for Normal Maps
Not a good idea!
Block artifacts
Normals describe curved surfaces, not lines
Especially visible in diagonal gradients
Colors stored in format
Fine detail lost
Errors are amplified for specular lighting
Storage is inefficient because normalized vectors can be stored in two values

20. ATI 3Dc™ Texture Format Two independent channel texture format
Exposed in D3D via the FOURCC code “ATI2”
Composed of 2 DXT5 alpha blocks
Extremely useful for normal textures
Compression:
4:1 for 32 bit textures
2:1 for 16 bit textures

21. Ruby Demo

22. ATI 3Dc™ Texture Format Decompression accomplished in hardware
Almost no impact on performance
Can be used for two unrelated scalars
e.g. shininess, refractive index, transparency
Library for compressing to 3Dc™ available from ati.com/developer
Available in OpenGL using the GL_ATI_texture_compression_3dc extension

23. ATI 3Dc™ Texture Format

24. Using ATI 3Dc™ with Normal Maps
x and y (of normal) stored in the texture
z value calculated by x2 + y2 + z2 = 1
z = ±sqrt(1 – x2 – y2)
Only positive root used because normal is in tangent space
Calculation done in pixel shader
Can also be derived by a texture lookup
Single channel z component texture

25. Using ATI 3Dc™ Pixel shader 2.0 code: ; scale, bias, half, one
def c0, 2.0f, -1.0f, 0.5f, 1.0f .
texld r1, t1, s1 ;normal map
mad r1, r1, c0.x, c0.y ; scale/bias to -1,1
; Compute third component
dp2add r1.z, r1, -r1, c0.w ; 1-x*x-y*y
rsq r1.z, r1.z ; 1 / sqrt(1-x*x-y*y)
rcp r1.z, r1.z ; sqrt(1-x*x-y*y)

26. Using ATI 3Dc™ Pixel shader code (HLSL): sampler bump_map;
float4 ps_main( PS_INPUT_STRUCT psInStruct ) :COLOR0 {
// Unpack two component bump map
float3 bump = tex2D( bump_map, psInStruct.bump_map );
// Put x and y in range and compute z
bump = ( bump * 2.0f ) - 1.0f;
bump.z = sqrt(1 - dot(bump.xy, bump.xy)); .

27. ATI 3Dc™ Compression Comparison

28. ATI 3Dc™ Normal Compression Sample

29. Drawbacks of ATI 3Dc™ Can only represent tangent space normal maps
Cannot represent high precision normal maps
Large areas of low curvature (car hood) may require 16 bits per component
More pixel shader instructions required
Not available on all hardware

30. Normal Map Compression Using Swizzled DXT5
For any hardware with at least ps 1.4 support
Store x and y in alpha and green channels of the texture map
Shader similar to 3Dc™ with one extra pixel shader instruction
Results better than using DXTC directly but not as good as 3Dc™

31. Using DXT5 Compression Pixel shader 2.0 code: ;scale, bias, half, one
def c0, 2.0f, -1.0f, 0.5f, 1.0f .
texld r1, t1, s1 ;normal map
mov r1.x, r1.a ; restore x from alpha
mad r1, r1, c0.x, c0.y ; scale/bias to -1,1
; Compute third component
dp2add r1.z, r1, -r1, c0.w ; 1-x*x-y*y
rsq r1.z, r1.z ; 1 / sqrt(1-x*x-y*y)
rcp r1.z, r1.z ; sqrt(1-x*x-y*y)

32. DXT5 Normal Map Compression RenderMonkey Example

33. Summary Normal Mapping great feature
Directly using DXT compression not great for normal textures
Compression with 3Dc™ lowers the cost normal mapping
3Dc™ available in D3D and OpenGL
Swizzled DXT5 compression reasonable alternative for older hardware

34. QUESTIONS? Email me jzarge@ati.com or devrel@ati.com
More information available at ati.com/developer
Please go see Chris Oat’s talk on “Advanced Character Rendering” Saturday, 10:25am