The error of matrix in the "Unity3d actual combat core Technology detailed" book

I've been learning real-time rendering recently, and it's hard to touch linear algebra. And in the rendering, will be used to the matrix, when I went to review the book I read before, found that "unity3d actual combat core technical details" on the matrix there are several errors, special marked out.

The first chapter of the book, 3D Mathematics and unity, 1.3.2 The matrix scaling, 1.3.3-speaking matrix rotation. Scaling is a matrix, followed by a rotation matrix (x, Y, z) around three different axes, a total of 4 matrices, 3 of which are wrong, and only one rotation around the y axis is correct. I am not sure is the printing problem, or the author itself on the Matrix and grasp of the not in-depth, but the emergence of such a low-level error is not.

I direct film, or accreditations.

As shown in the first figure, if the scaled matrix is as indicated in the book, then x ' = x Sx + y rather than the desired x.sx, in the same way around the x-axis rotation, then the x-axis coordinates should be fixed, that is, except the first column of the first 1, the rest should be 0, and the second row actually appeared 1, that x ' = x + y, which is not rotated ah, rotation around the z axis is even more outrageous ...

Well, the matrix is really troublesome, but it is an essential knowledge of understanding and learning 3D. What if a matrix is judged to be correct? Here I recommend a method in the book "Programmer's Mathematical 3--linear algebra", as shown in.

Pay attention to the part of the line, I just mastered the book in this simple method, and then to see the "wrong" of the book's Matrix, one eye found that the matrix is wrong. Hopefully this little trick and method will help you:

The input column vectors are inverted, and the corresponding elements are multiplied separately.

In addition, I also read the Meng Yan on the csdn of the three "Understanding Matrix", which mentioned in the book is:

Mathematics: Its contents, methods and meanings

The five-lecture on linear algebra

An Overview of mathematics

"Mathematics Supplements"

"Relive calculus"

"Computer Graphics--A detailed explanation of geometric tool algorithms"

Because the author is a non-math professional, so its description may be inaccurate, but that is his own understanding, can help people who do not understand the matrix, I think it is very valuable. After all, most people just need to understand what the matrix is, why use matrices, and the deeper study of matrices may not be so concerned. Popular science has the role of popular science, professional has a professional need.

In fact, I think about the matrix, see Wikipedia on the definition has been written very clear, clear, carefully study thoroughly, there is a general understanding. Link Address https://zh.wikipedia.org/wiki/Matrix

What is the matrix exactly, with my current understanding and cognition, matrix is mapping, matrix is mapping, matrix is mapping (important thing to say three times!). ).

Here are recommended a few I think very good video to everyone, more intuitive, further reduce the learning threshold.

The essence of "official bilingual/Collection" Linear Algebra-Series collection (use intuitive animations, concise language to tell linear code, you are worth watching !) ）

Https://www.bilibili.com/video/av6731067/index_1.html

MIT Open Class: Linear algebra
Http://open.163.com/special/opencourse/daishu.html

Introduction to Linear Algebra, fifth Edition (2016)--linear algebra tutorial evaluation of the highest book, not one
http://math.mit.edu/~gs/linearalgebra/

Linear Algebra done Wrong (Sergei Treil)
Https://www.math.brown.edu/~treil/papers/LADW/LADW.html

The error of matrix in the "Unity3d actual combat core Technology detailed" book