Topics in Computer Graphics

Spring 2010

Application

Shading

Maps

Base texture (RGB)

Height map (Grey scale)

Normal map (normal encoded RGB)

Normal Map & Height Field

Normal MapNormal vector encoded as rgb

[-1,1]3 [0,1]3: rgb = n*0.5 + 0.5RGB decoding in fragment shaders

vec3 n = texture2D(NormalMap, texcoord.st).xyz * 2.0 – 1.0

In tangent space, the default (unit) normal points in the +z direction. Hence the RGB color for the straight up normal is (0.5,

0.5, 1.0). This is why normal maps are a blueish colorNormals are then used for shading computation

Diffuse: n•lSpecular: (n•h)shininess

Computations done in tangent space

In order to build this Tangent Space, we need to define an orthonormal (per vertex) basis, which will define our tangent space.

Tangent space is composed of 3 orthogonal vectors (T, B, N)Tangent (S Tangent)Bitangent (T Tangent)Normal

One has to calculate a tangent space matrix for every single vertex

Tangent Space

Tangent SpaceSuppose a point pi in world coordinate

system for whose texture coordinates are (ui, vi)

Writing this equation for the points p1, p2 and p3, defining the triangle :p1 = u1.T + v1.B p2 = u2.T + v2.Bp3 = u3.T + v3.B

Tangent Space6 eqns, 6 unknowns

T,B: (unit) vectors in

object space

TBN Matrix Per VertexUse the averaged face normal as the vertex

normalDo the same for tangent and bitangent

vectorsNote that the T, B vectors might not be

orthogonal to the normal vectorUse Gram-Schmidt to make sure they are

orthonormal

Coordinate Transformation

zoy

ox

o

zyx

zyx

zyx

zoy

ox

o

zzz

yyy

xxx

zT

yT

xT

zT

yT

xT

zzz

yyy

xxx

zoy

ox

o

v

v

v

NNN

BBB

TTT

v

v

v

NBT

NBT

NBT

v

v

v

v

v

v

NBT

NBT

NBT

v

v

v

1

Tangent space to object space

Object space to tangent space

This reference (http://jerome.jouvie.free.fr/OpenGl/Lessons/Lesson8.php) is correctTyphoonLabs is not right.

What is mat3 (v1,v2,v3)?!It turns out to be “blue”

)(

)(

)(

3 deduce We

333

222

111

zyx

zyx

zyx

vvv

vvv

vvv

mat

This is the matrix that converts object space to tangent space

Referencehttp://www.opengl.org/sdk/docs/tutorials

/TyphoonLabs/Chapter_4.pdfhttp://www.ozone3d.net/tutorials/bump_mapping.phphttp://www.paulsprojects.net/tutorials/simplebump/

simplebump.htmlhttp://www.terathon.com/code/tangent.htmlhttp://www.blacksmith-studios.dk/projects/

downloads/tangent_matrix_derivation.phphttp://jerome.jouvie.free.fr/OpenGl/Lessons/

Lesson8.php