Confusion between C and OpenGL matrix order (main and column main)

float matrixA[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
float matrixB[4][4] = {{0, 1, 2, 3 }, {4, 5, 6, 7 }, {8, 9, 10, 11 }, {12, 13, 14, 15} };

matrixA[0] == matrixB[0][0];
matrixA[3] == matrixB[ 0][3];
matrixA[4] == matrixB[1][0];
matrixA[7] == matrixB[1][3];

1, 0, 0, transX
0, 1, 0, transY
0, 0, 1, transZ< br />0, 0, 0, 1

xx xy xz 0
yx yy yz 0
zx zy zz 0
px py pz 1

{ xx xy xz 0 yx yy yz 0 zx zy zz 0 px py pz 1 }

 {1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, transX, transY, transZ, 1 }.

I am very confused about the matrix definition. I have a matrix class, which stores a floating point number based on the following observations [16], I assume it is the main line:

< /p>

float matrixA[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
float matrixB[4][4] = {{0, 1, 2, 3 }, {4, 5, 6, 7 }, {8, 9, 10, 11 }, {12, 13, 14, 15} };

MatrixA and matrixB have the same linear distribution in the memory Bureau (that is, all numbers are arranged in order). According to http://en.wikipedia.org/wiki/Row-major_order, this indicates the main layout of the row.

matrixA[ 0] == matrixB[0][0];
matrixA[3] == matrixB[0][3];
matrixA[4] == matrixB[1][0];
matrixA[7] == matrixB[1][3];

Therefore, matrixB[0] = row 0, matrixB[1] = row 1, etc. Again, this means that the row is mainly Layout.

When I created a translation matrix as shown below, my question/confusion appeared:

1, 0, 0, transX
0, 1, 0, transY
0, 0, 1, transZ
0, 0, 0, 1

It is arranged in the memory as, {1 ,0,0,transX,0,1,0,transY,0,0,1,transZ,0,0,0,1}.

Then, when I call glUniformMatrix4fv, I need to change The transpose flag is set to GL_FALSE, indicating that it is a column major, otherwise the transformations such as translation/zooming etc. are not applied correctly:

If transpose is GL_FALSE, each matrix is ​​assumed to be supplied in
column major order. If transpose is GL_TRUE, each matrix is ​​assumed to
be supplied in row major order.

Why my matrix seems to be row major Yes, need to be passed to OpenGL as a column?

The matrix notation used in the OpenGL document does not describe the in-memory layout of the OpenGL matrix

If you think you give up/forget The whole “row/column main” thing will be easier. This is because in addition to the row/column profession, the programmer can also decide how he arranges the matrix in memory (whether adjacent elements form a row or column), as well as symbols, This will increase confusion.

OpenGL matrix has the same memory layout as directx matrices.

xx xy xz 0
yx yy yz 0
zx zy zz 0
px py pz 1

or

{ xx xy xz 0 yx yy yz 0 zx zy zz 0 px py pz 1 }

> x, y, z are the 3-component vectors describing the matrix coordinate system (relative to the local coordinate system of the global coordinate system).
> p is the origin of the matrix coordinate system 3-component vector.

This means that the translation matrix should be laid out in memory like this:

{ 1, 0, 0, 0, 0, 1 , 0, 0, 0, 0, 1, 0, transX, transY, transZ, 1 }.

Leave it there, the rest should be easy.

—quote Old opengl faq–

9.005 Are OpenGL matrices column-major or row-major?

For programming purposes, OpenGL matrices are 16- value arrays with base vectors laid out contiguously in memory. The translation components occupy the 13th, 14th, and 15th elements of the 16-element matrix, where indices are numbered from 1 to 16 as described in section 2.11.2 of the OpenGL 2.1 Specification.

Column-major versus row-major is purely a notational convention. Note that post-multiplying with column-major matrices produces the same result as pre-multiplying with row-major matrices. The OpenGL Specification and the OpenGL Reference Manual both use column-major notation. You can use any notation, as long as it’s clearly stated.

Sadly, the use of column-major format in the spec and blue book has resulted in endless confusion in the OpenGL programming community. Column-major notation suggests that matrices are not laid out in memory as a programmer would expect.