Games101 Lesson 9 shading 3 Notes

One 、 The coordinates of the center of gravity （Barycentric Coordinates）

（1） Why do we want to do interpolation ？
① The properties of the three vertices of a triangle are known , Want to get the attribute of smooth change inside the triangle （ Such as texture coordinates , Color , Normals, etc ）.
② Interpolation can be achieved by using barycentric coordinates .
（2） The barycentric coordinates are for a triangle （α,β,γ） In terms of the .

① Different triangles correspond to different barycentric coordinate systems .
②α,β,γ Both are nonnegative and the sum is 1 when , The point is in the triangle .
③ Any point in the triangle can be represented by barycentric coordinates . Just like A The coordinate of the center of gravity is （1,0,0）, spot B The coordinate of the center of gravity is （0,1,0）.
④ After projection , The triangle may become deformed , Then the center of gravity coordinates may change .
（3） From a geometric point of view

① With α For example ,α And A relevant ,α The value is A The area of the triangle opposite the vertex AA With triangles ABC The area ratio of .
（4） The calculation formula of the center of gravity coordinate is as follows ：

（5） Use of barycentric coordinates

① We know the attributes of three vertices and the barycentric coordinates of a point , Then the attribute of the point can be calculated .
② Attributes in three-dimensional space should be obtained in three-dimensional space .

Two 、 Texture mapping

（1） Take diffuse reflection as an example to map texture
① For each pixel （ Usually the pixel center ） Coordinates of , Calculate the corresponding texture coordinates .
② Apply to the texture coordinates to calculate the corresponding color .
③ Set the color .

3、 ... and 、 Texture magnification （Texture Magnification）

（1） Texture magnification （ Case study 1）
① If the texture is small , Then the image may appear jagged .
② This is because pixels in a small area may be mapped to the same texture element .
③ Use bilinear interpolation to get more accurate attributes .

（2） Bilinear interpolation （Bilinear Interpolation）
① Find four pixels around the target location .
② to s Interpolation in direction , get u1 and u2 Properties of .

② Then on u1 and u2 Conduct t Interpolation in direction , You can get the attribute of the target location .

（3） Texture magnification （ Case study 2）
① If the texture is large , Then the image may appear moire and jagged .
② Pixels in different positions cover different texture elements , Pixels in the distance may cover a large area of texture .

（4） Texture magnification （ Case study 2） Solutions for
① Oversampling can be used , But this scheme costs a lot .
② Use average range query （Range Query） Methods .

Four 、Mipmap

（1）Mipmap： Reduce the picture to scale

① Allow range queries .
② Fast query speed , But you can only do approximate and square queries .
③ Only more 1/3 Storage space .
（2） Find the corresponding mipmap The layer number

① Map pixels to texture coordinates , It can be found that the original square pixel area will be mapped into an irregular texture .

② Find the mapping to the texture coordinate system , The current pixel and the surrounding two （ It can also be more ） The maximum distance between pixels L.
③ Use a side length of L To approximate this irregular region , To get the texture .

④ According to the side length L It can be calculated that the corresponding is mipmap Which floor in , To get the texture .
（3）mipmap The effect of

① It has preliminary effect , But it can be seen that some places are discontinuous . This is because only number 0、1、2 Properties of equal layers , There is no calculation in the middle, such as 1.5 Layer properties .
② Trilinear interpolation can be used to solve , It's on the second floor mipmap Third interpolation between , To get more continuous properties .

③ The result of using trilinear interpolation is as follows .

（4）mipmap The problem is

① Distant images will become blurred .
② Anisotropic filtering can be used to improve .

5、 ... and 、 Anisotropic filtering （Anisotropic Filtering）

（1）ripmap

① Zoom out in both directions .
② Allow range query of rectangular area .
③ There is not much improvement for oblique area range query .

④ Too much storage overhead 3 times .
（2）EWA filtering

① Query the range of circular areas .
② Multiple queries are required .

reference

Course video link : GAMES101 Lecture09 Shading 3