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Bump Mapping

Bump Mapping. Topics in Computer Graphics Spring 2010. Application. Shading. Maps. Height map (Grey scale). Base texture (RGB). Normal map (normal encoded RGB). Normal Map & Height Field. Normal Map. Normal vector encoded as rgb [-1,1] 3 [0,1] 3 : rgb = n*0.5 + 0.5

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Bump Mapping

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  1. Bump Mapping Topics in Computer Graphics Spring 2010

  2. Application

  3. Shading

  4. Maps Height map (Grey scale) Base texture (RGB) 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: n•l • Specular: (n•h)shininess • Computations done in tangent space

  7. 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

  8. Tangent Space • Suppose 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

  9. Tangent Space 6 eqns, 6 unknowns • p2 - p1 = (u2 - u1).T + (v2 - v1).Bp3 - p1 = (u3 - u1).T + (v3 - v1).B • (v3 - v1).(p2 - p1)  =   (v3 - v1).(u2 - u1).T + (v3 - v1).(v2 - v1).B- (v2 - v1).(p3 - p1)    - (v2 - v1).(u3 - u1).T - (v2 - v1).(v3 - v1).B • (u3 - u1).(p2 - p1)  =  (u3 - u1).(u2 - u1).T + (u3 - u1).(v2 - v1).B- (u2 - u1).(p3 - p1)    - (u2 - u1).(u3 - u1).T - (u2 - u1).(v3 - v1).B • (v3 - v1).(p2 - p1) - (v2 - v1).(p3 - p1)T = --------------------------------------- (u2 - u1).(v3 - v1) - (v2 - v1).(u3 - u1) • (u3 - u1).(p2 - p1) - (u2 - u1).(p3 - p1)B = ---------------------------------------(v2 - v1).(u3 - u1) - (u2 - u1).(v3 - v1) 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 correct 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/Chapter_4.pdf • http://www.ozone3d.net/tutorials/bump_mapping.php • http://www.paulsprojects.net/tutorials/simplebump/simplebump.html • http://www.terathon.com/code/tangent.html • http://www.blacksmith-studios.dk/projects/downloads/tangent_matrix_derivation.php • http://jerome.jouvie.free.fr/OpenGl/Lessons/Lesson8.php

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