1. Topics in Computer Graphics Spring 2010

2. Application

3. Shading

4. Maps Base texture (RGB) Height map (Grey scale) Normal map (normal encoded RGB)

5. Normal Map & Height Field

6. Normal Map Normal vector encoded as rgb [-1,1] 3  [0,1] 3 : rgb = n*0.5 + 0.5 RGB 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 color Normals are then used for shading computation Diffuse: nl Specular: (nh) shininess Computations done in tangent space

7. 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

8. Suppose a point p i in world coordinate system for whose texture coordinates are (u i, v i ) Writing this equation for the points p1, p2 and p3, defining the triangle : p 1 = u 1.T + v 1.B p 2 = u 2.T + v 2.B p 3 = u 3.T + v 3.B

9. Tangent Space p 2 - p 1 = (u 2 - u 1 ).T + (v 2 - v 1 ).B p 3 - p 1 = (u 3 - u 1 ).T + (v 3 - v 1 ).B (v 3 - v 1 ).(p 2 - p 1 ) = (v 3 - v 1 ).(u 2 - u 1 ).T + (v 3 - v 1 ).(v 2 - v 1 ).B - (v 2 - v 1 ).(p 3 - p 1 ) - (v 2 - v 1 ).(u 3 - u 1 ).T - (v 2 - v 1 ).(v 3 - v 1 ).B (u 3 - u 1 ).(p 2 - p 1 ) = (u 3 - u 1 ).(u 2 - u 1 ).T + (u 3 - u 1 ).(v 2 - v 1 ).B - (u 2 - u 1 ).(p 3 - p 1 ) - (u 2 - u 1 ).(u 3 - u 1 ).T - (u 2 - u 1 ).(v 3 - v 1 ).B (v 3 - v 1 ).(p 2 - p 1 ) - (v 2 - v 1 ).(p 3 - p 1 ) T = --------------------------------------- (u 2 - u 1 ).(v 3 - v 1 ) - (v 2 - v 1 ).(u 3 - u 1 ) (u 3 - u 1 ).(p 2 - p 1 ) - (u 2 - u 1 ).(p 3 - p 1 ) B = --------------------------------------- (v 2 - v 1 ).(u 3 - u 1 ) - (u 2 - u 1 ).(v 3 - v 1 ) 6 eqns, 6 unknowns T,B: (unit) vectors in object space

10. TBN Matrix Per Vertex Use the averaged face normal as the vertex normal Do the same for tangent and bitangent vectors Note that the T, B vectors might not be orthogonal to the normal vector Use Gram-Schmidt to make sure they are orthonormal

11. Coordinate Transformation Tangent space to object space Object space to tangent space This reference (http://jerome.jouvie.free.fr/OpenGl/Lessons/Lesson8.php) is correcthttp://jerome.jouvie.free.fr/OpenGl/Lessons/Lesson8.php TyphoonLabs is not right.

12. What is mat3 (v1,v2,v3)?! It turns out to be “blue” This is the matrix that converts object space to tangent space

13. Reference http://www.opengl.org/sdk/docs/tutorials/TyphoonLabs/Chapt er_4.pdf http://www.opengl.org/sdk/docs/tutorials/TyphoonLabs/Chapt er_4.pdf http://www.ozone3d.net/tutorials/bump_mapping.php http://www.paulsprojects.net/tutorials/simplebump/simplebum p.html http://www.paulsprojects.net/tutorials/simplebump/simplebum p.html http://www.terathon.com/code/tangent.html http://www.blacksmith- studios.dk/projects/downloads/tangent_matrix_derivation.php http://www.blacksmith- studios.dk/projects/downloads/tangent_matrix_derivation.php http://jerome.jouvie.free.fr/OpenGl/Lessons/Lesson8.php