The document describes a geometry shader-based approach to bump mapping that has several advantages over traditional CPU-based approaches. The geometry shader constructs an object-to-texture space mapping for each triangle, allowing lighting computations to be done efficiently in texture space in the pixel shader. It addresses issues like texture mirroring and lighting discontinuities. Examples and Cg source code are provided to illustrate the technique.

1. Geometry shader-based bump mapping setup Mark Kilgard NVIDIA Corporation February 5, 2007 Updated October 18, 2007

3. Geometry Shader in Cg TRIANGLE void md2bump_geometry( AttribArray < float4 > position : POSITION , AttribArray < float2 > texCoord : TEXCOORD0 , AttribArray < float3 > objPosition : TEXCOORD1 , AttribArray < float3 > objNormal : TEXCOORD2 , AttribArray < float3 > objView : TEXCOORD3 , AttribArray < float3 > objLight : TEXCOORD4 ) { float3 dXYZdU = objPosition[1] - objPosition[0]; float dSdU = texCoord[1].s - texCoord[0].s; float3 dXYZdV = objPosition[2] - objPosition[0]; float dSdV = texCoord[2].s - texCoord[0].s; float3 tangent = normalize (dSdV * dXYZdU - dSdU * dXYZdV); for ( int i=0; i<3; i++) { float3 normal = objNormal[i], binormal = cross (tangent,normal); float3x3 basis = float3x3 ( tangent , binormal, normal); float3 surfaceLightVector : TEXCOORD1 = mul (basis, objLight[i]); float3 surfaceViewVector : TEXCOORD2 = mul (basis, objView[i]); emitVertex (position[i], texCoord[i], surfaceLightVector, surfaceViewVector); } } warning: not tolerant of mirroring (see next version)

4. Canonical Triangle A B C A = ( u=0, v=0, x0, y0, z0, s0, t0 ) B = ( u=1, v=0, x1, y1, z1, s1, t1 ) C = ( u=0, v=1, x2, y2, z2, s2, t2 ) ∂ xyz / ∂u = (x1,y1,z1) - (x0,y0,z0) ∂ xyz / ∂v = (x2,y2,z2) - (x0,y0,z0) ∂ s / ∂u = s1 – s0 ∂ t / ∂v = t2 – t0 v u quotient rule for partial derivatives:

5. Forming an Object-to-Texture Space Basis assumes left-handed texture space provided by vertex shader

6. Transform Object-Space Vectors for Lighting to Texture-Space object-space texture-space light vector view vector

8. Compensating for Texture Mirroing If signed area in texture space “less than” zero, compute basis with negated tangent: 2x2 determinant

9. Example of Mirroring artist’s original decal derived height field RGB normal map generated from height field Visualization of 3D model’s signed area in texture space green =front-facing red =back-facing only half of face appears in decal

10. Consequence on Lighting from Accounting for Mirroring Bad: mirrored skull buckle and belt lighting wrong on left side (indents in) Correct lighting

11. Mirroring-tolerant Geometry Shader in Cg TRIANGLE void md2bump_geometry( AttribArray < float4 > position : POSITION , AttribArray < float2 > texCoord : TEXCOORD0 , AttribArray < float3 > objPosition : TEXCOORD1 , AttribArray < float3 > objNormal : TEXCOORD2 , AttribArray < float3 > objView : TEXCOORD3 , AttribArray < float3 > objLight : TEXCOORD4 ) { float3 dXYZdU = objPosition[1] - objPosition[0]; float dSdU = texCoord[1].s - texCoord[0].s; float3 dXYZdV = objPosition[2] - objPosition[0]; float dSdV = texCoord[2].s - texCoord[0].s; float3 tangent = normalize (dSdV * dXYZdU - dSdU * dXYZdV); float area = determinant ( float2x2 (dSTdV, dSTdU)); float3 orientedTangent = area >= 0 ? tangent : -tangent; for ( int i=0; i<3; i++) { float3 normal = objNormal[i], binormal = cross (tangent,normal); float3x3 basis = float3x3 (orientedTangent, binormal, normal); float3 surfaceLightVector : TEXCOORD1 = mul (basis, objLight[i]); float3 surfaceViewVector : TEXCOORD2 = mul (basis, objView[i]); emitVertex (position[i], texCoord[i], surfaceLightVector, surfaceViewVector); } } additional & changed code for mirroring

12. Discarding Triangles Significantly Back Facing w.r.t. the Light TRIANGLE void md2bump_geometry( AttribArray < float4 > position : POSITION , AttribArray < float2 > texCoord : TEXCOORD0 , AttribArray < float3 > objPosition : TEXCOORD1 , AttribArray < float3 > objNormal : TEXCOORD2 , AttribArray < float3 > objView : TEXCOORD3 , AttribArray < float3 > objLight : TEXCOORD4 ) { float3 dXYZdU = objPosition[1] - objPosition[0]; float dSdU = texCoord[1].s - texCoord[0].s; float3 dXYZdV = objPosition[2] - objPosition[0]; float dSdV = texCoord[2].s - texCoord[0].s; float3 tangent = normalize (dSdV * dXYZdU - dSdU * dXYZdV); float maxLightZ, maxLightThreshold = -0.3; for ( int i=0; i<3; i++) { float3 normal = objNormal[i], binormal = cross (tangent,normal); float3x3 basis = float3x3 ( tangent , binormal, normal); float3 surfaceLightVector : TEXCOORD1 = mul (basis, objLight[i]); maxLightZ = i==0 ? normalize(surfaceLightVector).z : max(maxLightZ, normalize(surfaceLightVector).z); float3 surfaceViewVector : TEXCOORD2 = mul (basis, objView[i]); if (i < 2 || maxLightZ > maxLightThreshold) emitVertex (position[i], texCoord[i], surfaceLightVector, surfaceViewVector); } }

14. Sans Per-vertex Normals

15. Geometry Shader in Cg Sans Normals TRIANGLE void md2bump_geometry_sans_normal( AttribArray < float4 > position : POSITION , AttribArray < float2 > texCoord : TEXCOORD0 , AttribArray < float3 > objPosition : TEXCOORD1 , // IGNORE per-vertex normal! AttribArray < float3 > objView : TEXCOORD3 , AttribArray < float3 > objLight : TEXCOORD4 ) { float3 dXYZdU = objPosition[1] - objPosition[0]; float2 dSTdU = texCoord[1] - texCoord[0]; float3 dXYZdV = objPosition[2] - objPosition[0]; float2 dSTdV = texCoord[2] - texCoord[0]; float3 tangent = normalize (dSTdV.s * dXYZdU - dSTdU.s * dXYZdV); float3 tangent2 = normalize (dSTdV.t * dXYZdU - dSTdU.t * dXYZdV); float area = determinant (float2x2(dSTdV, dSTdU)); tangent = area >= 0 ? tangent : -tangent; float3 normal = cross(tangent2,tangent); tangent2 = area >= 0 ? tangent2 : -tangent2; for ( int i=0; i<3; i++) { float3x3 basis = float3x3 (tangent, tangent2, normal); float3 surfaceLightVector : TEXCOORD1 = mul(basis, objLight[i]); float3 surfaceViewVector : TEXCOORD2 = mul(basis, objView[i]); emitVertex (position[i], texCoord[i], surfaceLightVector, surfaceViewVector); } }

16. Geometry shader setup with and without per-vertex normals Setup without per-vertex normals, relying on normalized gradients only; faceted look Setup with per-vertex normals; smoother lighting appearance

22. Supplemental Slides

23. Authored 3D Model Inputs Key frame blended 3D model Decal skin Bump skin Gloss skin GPU Rendering

24. Animation via Key Frames or Vertex Skinning GPU Rendering Frame A Frame B Other possible key frames