1、 What is tangent space ？

Tangent Space In fact, there is an origin + A local space determined by three coordinate axes , It's just a coordinate system

• Coordinate origin ： Is the position of the vertex
  - N Axis ： Is the normal direction defined by the vertex
  
• T Axis （Tangent）： Vector perpendicular to normal . But there are many such tangents , The standard approach is to combine the tangent direction and texture space (u or v Axis ) alignment , Generally choose u

• B Axis （Bitangent）： adopt N Axis and T Cross product of axes
  

Tangent space is for any vertex of the model , How many points does the model have , How many independent tangent spaces are there

The normal texture we usually see ( Normal map ) It is constructed based on the original normal information . Each texture element stores the normal direction in the tangent space of each vertex . If the normal direction of a vertex remains the same , Or the normal direction of the original model ( The normal of a position on the surface is the vertical line of the tangent plane ), Then the normal in its tangent space is (0, 0, 1) , But this is not the value stored in the normal texture , Of each tattoo element RGB The value range of color component is (0, 1), Store normals with textures , Actually store XYZ vector , The direction of the vector XYZ The value range of the component is (-1, 1), Because the value range is different , So use textured RGB To represent the normal XYZ It doesn't mean , So we need to make a mapping , namely color = (normal + 1) / 2 . such , Normal value (0, 0, 1) Store in texture RGB The value of is (0.5, 0.5, 1), The normals stored on almost the entire texture b The components are all 1 Or very close to 1, So the normal texture is visually blue . So in summary , Normal texture RGB The channel stores the direction of the normal in the tangent space of each vertex Mapping values .

2、 Why do I need a normal map

When a model has many concave convex details , The vertex mesh of the model will be dense （ Large amount of data ）, Then comes the performance problem . The bump of the model corresponds to different vertex heights , Thus, the directions of normals are different , After shading calculation , The concave convex feeling is very strong . However, in order to save space and computational performance , Do not want to increase the number of faces of the model , What do I do ？ Only the normal information of the original model can be modified （ height map or Normal map ）, Replace the original normal of this point with the modified normal , Perform shading calculations , Make the model look concave and convex

3、 With normal mapping, why do I need a normal mapping in tangent space

If the normal direction is in world coordinates (world space), That's called world space normal. If it is in the local coordinates of the object itself , That's called object space normal. It's easy to imagine ,world space normal Once extracted from the map , You can use it directly , It's very efficient . But there's a drawback , This world space normal It's fixed , If the object does not remain the same Direction and position , That originally generated normal map It's invalid . So someone saved object space normal. It decompresses from the map , It also needs to be multiplied by the same number as the model model、view Matrix conversion to world coordinates , Or convert to other coordinates, depending on the calculation process and requirements .object space normal Generated map , Objects can be rotated and displaced . Basically satisfactory . But there is still one drawback . That is, a map can only correspond to a specific model , The model cannot be deformed .

• world space normal texture： Directly save the normal direction of the points on the model surface in the world , After mapping the texture to the vertices of the model , The internal points are mapped by interpolation . If there are two as like as two peas at this time , But the location 、 Different directions , You cannot apply the same normal texture , Otherwise, the normal direction is wrong . So efficient but inflexible .
• object space normal texture： Each texture element saves the normal direction of each point in model space , Before mapping textures , The same as the model needs to be done again model-view Transformation . Poor efficiency , High flexibility , But you can't deform .

The problem is coming. , Can we find another coordinate system , So that the normal of the model can be correctly transformed into the world coordinate system when deforming ?

• When deforming , The vertex relationship has changed , That is, the shape of the face , The direction has changed . If there is a fixed coordinate system on the face , When an object deforms , Move , When rotating , This coordinate system must move with the surface , So a point or vector in this coordinate system , There is no need to change . When the whole face changes , We only need to calculate the transformation matrix from the coordinate system on the plane to the world coordinate system , Then the point or coordinate defined on this surface ( Constant oh ), Multiply this matrix to get the coordinates in the world . How this coordinate is constructed is not important to us at present , Please be sure to understand this concept . We're just looking for a local coordinate system , Point coordinates in local coordinate system , Multiply by the transformation matrix from local coordinate system to world coordinate system ( This matrix is based on the current transformation of the model , Dynamically calculated ), Get the coordinates of the points in the local coordinate system in the world coordinate system . This the normal direction stored in the normal map ( Fixed value ) Can be used for meaningful shading calculations .
• It's obvious to see here , This requires thousands of different coordinate systems defined on the face . How many faces are there on the low die , How many such coordinate systems do you have to have . The calculation amount of this method is naturally higher than object space normal map A bigger one . On each side of the low die , To construct this coordinate system . This coordinate system is called... In terminology tangent space.

4、TBN Matrix computing , Well, No .. I'll make it up later

For reference only , For details, please see the following
https://blog.csdn.net/damenhanter/article/details/22481563
https://www.zhihu.com/question/23706933/answer/161968056
http://www.opengl-tutorial.org/cn/intermediate-tutorials/tutorial-13-normal-mapping/#%E9%A1%B6%E7%82%B9%E7%9D%80%E8%89%B2%E5%99%A8
https://blog.csdn.net/weixin_46525412/article/details/120278159