BUMP MAPPING. Programação 3D Simulação e Jogos Prof. João A. Madeiras Pereira MEIC-A/IST

Transcription

1 UMP MAPPIG Programação 3D Simulação e Jogos Prof. João A. Madeiras Pereira MEIC-A/IS

2 Eamples

3 Shading

4 Generating ormal Map ase teture (RG) Height map (Gre scale) ormal map (normal encoded RG)

5 Displacement Mapping ump mapping can be at piel leel has no geometr/shape change Displacement Mapping Actuall modif the surface geometr (ertices) re-calculate the normals Can include bump mapping

6 Displacement Mapping ump mapped normals are inconsistent with actual geometr. o shadow. Displacement mapping affects the surface geometr

7 ump Mapping ase teture (RG) ormal map (normal encoded RG)

8 ormal Map ormal ector encoded as rgb [-1,1] 3 [0,1] 3 : rgb = n* RG decoding in fragment shaders ec3 n = teture2d(ormalmap, tecoord.st).rgb * In tangent space, the default (unit) normal points in the + direction. Hence the RG color for the straight up normal is (0.5, 0.5, 1.0). his is wh normal maps are a blueish color ormals are then used for shading computation Diffuse: n l Specular: (n h) shininess Computations done in tangent space

9 angent Space concept ( he big problem is how to conert our normal, which is epressed in the space of each indiidual triangle ( tangent space), in model space (since this is what is used in our shading equation). we need 3 ectors. We alread hae our UP ector : it s the normal, computed from the triangle b a simple cross product. It s represented in blue, just like the oerall color of the normal map

10 angent Space concept et we need a tangent, : a ector perpendicular to the surface. ut there are man such ectors :

11 angent Space concept Which one should we choose? In theor, an, but we hae to be consistent with the neighbors to aoid introducing ugl edges. he standard method is to orient the plane defined b the tangent (red color) and the other orthogonal ector (called bitangent in green color) in the same direction that our 2D teture space referential :

12 angent Space concept

13 angent () Space In order to build this angent Space, which is a 3D space, we need to define an orthonormal basis angent space is composed of 3 orthogonal ectors (,, ) angent ( angent) itangent ( angent) wrongl also called inormal ormal () - perpendicular to (,) plane o align the tangent space (3D) with teture space (2D), means: (, ) ectors correspond to (u, ) ectors. is the ector (1, 0) and is the ector (0, 1). ote that a 2D point in teture space (ui, i) corresponds to a 3D point (ui, i, 0) in angent space

14 at each Verte ighting calculations: light ector in World/Ee space; normal ector at angent space -> spaces transformation matri; First, calculate the ectors in World coordinates for each triangle of the mesh: the riangle-based hen, calculate a tangent space matri for eer single erte b aeraging the triangle-based s which share that erte: Vertebased.

15 Verte-based (per erte)

16 riangle-based angent Space Suppose a point p i in world coordinate sstem for whose teture coordinates are (u i, i ) Writing this equation for the points p1, p2 and p3, defining the triangle : p 1 = u p 2 = u p 3 = u

17 riangle-based angent Space p 2 - p 1 = (u 2 - u 1 ). + ( 2-1 ). p 3 - p 1 = (u 3 - u 1 ). + ( 3-1 ). 6 eqns, 6 unknowns ( 3-1 ).(p 2 - p 1 ) = ( 3-1 ).(u 2 - u 1 ). + ( 3-1 ).( 2-1 ). - ( 2-1 ).(p 3 - p 1 ) - ( 2-1 ).(u 3 - u 1 ). - ( 2-1 ).( 3-1 ). (u 3 - u 1 ).(p 2 - p 1 ) = (u 3 - u 1 ).(u 2 - u 1 ). + (u 3 - u 1 ).( 2-1 ). - (u 2 - u 1 ).(p 3 - p 1 ) - (u 2 - u 1 ).(u 3 - u 1 ). - (u 2 - u 1 ).( 3-1 ). ( 3-1 ).(p 2 - p 1 ) - ( 2-1 ).(p 3 - p 1 ) = (u 2 - u 1 ).( 3-1 ) - ( 2-1 ).(u 3 - u 1 ) (u 3 - u 1 ).(p 2 - p 1 ) - (u 2 - u 1 ).(p 3 - p 1 ) = ( 2-1 ).(u 3 - u 1 ) - (u 2 - u 1 ).( 3-1 ),: (unit) ectors in WCS space = cross(, ) // no need to do it since is the triangle normal

18 Verte-based Use the aeraged triangle normal as the erte normal Do the same for tangent and bitangent ectors ut, as we are going to see, it s not necessar to store an etra arra containing the per-erte bitangent; wh?

19 Spaces ransformation W W W W W W W W W 1 angent space to World space World space to angent space Onl if is also orthogonal in World space wo source of non-orthogonalit in World space: 1) riangle-based 2) Verte-based Forget the ranslation. Onl the rotation is important. Wh?

20 on-orthogonalit in World space riangle-based he transformation from the teture space into world space ma not be distance/angle conseratie. So, generall, (,, ) is not orthonormal in world space: and are not necessaril perpendicular, but the are perpendicular with. As well, possibl not unit ectors. Verte-based Use the aeraged triangle normal as the erte normal Do the same for tangent and bitangent ectors, ectors might not be orthogonal to the normal ector Use Gram-Schmidt to make sure the are orthogonal

21 Orthogonal Verte-based is the normal erte using the Gram-Schmidt technique: = ( ) = ( ) ( ) / 2 After normaliing, the matri to conert from World to angent is simpl the transposed matri: Send both and to the Verte Shader, or not necessar to store an etra arra containing the per-erte bitangent since the cross product can be used to obtain m m = ±1 represents the handedness of the tangent space. Implementation: as a four-dimensional entit whose w coordinate holds the alue of m; so = w ( ) Code for w, where t, b, n are ec3d and t is ec4d t = normalie [(t n * (Dot (n, t))] t.w = (Dot(Cross(n, t ), b) < 0.0f? -1.0f : 1.0f;

22 GS Matri operations ) normalie ( ightdir ); dot (, ); dot (, ); dot (, ector - matri product matri - ector product 1 GS makes no distinction between column and row ectors. If a ector multiplied from the left to the matri is row ector; if multiplied from the right is column ector

23 GS Verte Shader in ec4 Pos, ormal, ecoord, angent; out ec3 lightvec, halfvec; out ec2 te_coord; uniform mat4 ModelViewMatri, pmmatri; uniform light ightsource; uniform mat3 ormalmatri; oid main() } te_coord = ecoord.st; // uilding the matri Ee Space -> angent Space ec3 n = normalie (ormalmatri * ormal.); ec3 t = normalie (ormalmatri * angent.); ec3 b = angent.w * cross (n, t); ec3 ee_position = ec3(modelviewmatri * Pos); ec3 lightdir = normalie(ightsource.pos ee_position); // transform light and half angle ectors b tangent basis ec3 ;. = dot (lightdir, t);. = dot (lightdir, b);. = dot (lightdir, n); lightvec = normalie (); ec3 halfvector = normalie(lightdir - ee_position);. = dot (halfvector, t);. = dot (halfvector, b);. = dot (halfvector, n); halfvec = normalie (); } gl_position = pmmatri * Pos ;

24 GS Fragment Shader uniform sampler2d baseeture; uniform sampler2d normaleture; uniform light ightsource; uniform material Material; in ec3 lightvec, halfvec; in ec2 te_coord; oid main() { // lookup normal from normal map, moe from [0,1] to [-1, 1] range, normalie ec3 normal = 2.0 * teture(normaleture, te_coord).rgb - 1.0; normal = normalie (normal); } // compute diffuse lighting float lambertfactor= ma (dot (lightvec, normal), 0.0) ; ec4 diffusematerial = 0.0; ec4 diffuseight = 0.0; float shininess ; ec4 ambientight = ightsource.ambient; if (lambertfactor > 0.0) { diffusematerial = teture (baseeture, te_coord) * Material.diffuse; shininess = pow (ma (dot (halfvec, normal), 0.0), Material.shininess) ; gl_fragcolor = diffusematerial * ightsource.diffuse * lambertfactor ; gl_fragcolor += Material.specular * ightsource.specular * shininess ; } gl_fragcolor += ambientight;

25 References normal-mapping/) pdf

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