# OpenGL OpenGL: last column of matrix multiplication

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It seems OpenGL concatenates matrices like this:

void Matrix::postmult( const Matrix& matrix )
{
float newMatrix[16];

const float *a = m_matrix, *b = matrix.m_matrix;

newMatrix[0]  = a[0] * b[0]  + a[4] * b[1]  + a[8] * b[2]   + a[12] * b[3];
newMatrix[1]  = a[1] * b[0]  + a[5] * b[1]  + a[9] * b[2]   + a[13] * b[3];
newMatrix[2]  = a[2] * b[0]  + a[6] * b[1]  + a[10] * b[2]  + a[14] * b[3];
newMatrix[3]  = a[3] * b[0]  + a[7] * b[1]  + a[11] * b[2]  + a[15] * b[3];

newMatrix[4]  = a[0] * b[4]  + a[4] * b[5]  + a[8] * b[6]   + a[12] * b[7];
newMatrix[5]  = a[1] * b[4]  + a[5] * b[5]  + a[9] * b[6]   + a[13] * b[7];
newMatrix[6]  = a[2] * b[4]  + a[6] * b[5]  + a[10] * b[6]  + a[14] * b[7];
newMatrix[7]  = a[3] * b[4]  + a[7] * b[5]  + a[11] * b[6]  + a[15] * b[7];

newMatrix[8]  = a[0] * b[8]  + a[4] * b[9]  + a[8] * b[10]  + a[12] * b[11];
newMatrix[9]  = a[1] * b[8]  + a[5] * b[9]  + a[9] * b[10]  + a[13] * b[11];
newMatrix[10] = a[2] * b[8]  + a[6] * b[9]  + a[10] * b[10] + a[14] * b[11];
newMatrix[11] = a[3] * b[8]  + a[7] * b[9]  + a[11] * b[10] + a[15] * b[11];

newMatrix[12] = a[0] * b[12] + a[4] * b[13] + a[8] * b[14]  + a[12] * b[15];
newMatrix[13] = a[1] * b[12] + a[5] * b[13] + a[9] * b[14]  + a[13] * b[15];
newMatrix[14] = a[2] * b[12] + a[6] * b[13] + a[10] * b[14] + a[14] * b[15];
newMatrix[15] = a[3] * b[12] + a[7] * b[13] + a[11] * b[14] + a[15] * b[15];

set( newMatrix );
}


However, this doesn't give me a .w equal to 1 in orthographic projection.

My directional light matrix (that maps to texture space) ends up looking like a perspective projection. This also gives me wrong results when getting the screen position of 3D objects. To get pixel-perfect orthographic results I must either manually set the transformed vector's w component to 1 or use this multiplication:

void Matrix::postmult2( const Matrix& matrix )	//gives correct results, use this
{
float newMatrix[16];

const float *m1 = m_matrix, *m2 = matrix.m_matrix;

newMatrix[0] = m1[0]*m2[0] + m1[4]*m2[1] + m1[8]*m2[2];
newMatrix[1] = m1[1]*m2[0] + m1[5]*m2[1] + m1[9]*m2[2];
newMatrix[2] = m1[2]*m2[0] + m1[6]*m2[1] + m1[10]*m2[2];
newMatrix[3] = 0;

newMatrix[4] = m1[0]*m2[4] + m1[4]*m2[5] + m1[8]*m2[6];
newMatrix[5] = m1[1]*m2[4] + m1[5]*m2[5] + m1[9]*m2[6];
newMatrix[6] = m1[2]*m2[4] + m1[6]*m2[5] + m1[10]*m2[6];
newMatrix[7] = 0;

newMatrix[8] = m1[0]*m2[8] + m1[4]*m2[9] + m1[8]*m2[10];
newMatrix[9] = m1[1]*m2[8] + m1[5]*m2[9] + m1[9]*m2[10];
newMatrix[10] = m1[2]*m2[8] + m1[6]*m2[9] + m1[10]*m2[10];
newMatrix[11] = 0;

newMatrix[12] = m1[0]*m2[12] + m1[4]*m2[13] + m1[8]*m2[14] + m1[12];
newMatrix[13] = m1[1]*m2[12] + m1[5]*m2[13] + m1[9]*m2[14] + m1[13];
newMatrix[14] = m1[2]*m2[12] + m1[6]*m2[13] + m1[10]*m2[14] + m1[14];
newMatrix[15] = 1;

set( newMatrix );
}


Notice that it leaves the last row (0,0,0,1) and doesn't add the last term.

Is this because I am constructing my ortho projection incorrectly?

Matrix OrthoProj(float l, float r, float t, float b, float n, float f)
{
float m[16];

#define M(row,col)  m[col*4+row]
M(0, 0) = 2 / (r - l);
M(0, 1) = 0;
M(0, 2) = 0;
M(0, 3) = 0;

M(1, 0) = 0;
M(1, 1) = 2 / (t - b);
M(1, 2) = 0;
M(1, 3) = 0;

M(2, 0) = 0;
M(2, 1) = 0;
M(2, 2) = -1 / (f - n);
//M(2, 2) = -2 / (f - n);
M(2, 3) = 0;

M(3, 0) = -(r + l) / (r - l);
M(3, 1) = -(t + b) / (t - b);
M(3, 2) = -n / (f - n);
//M(3, 2) = -(f + n) / (f - n);
M(3, 3) = 1;
#undef M

Matrix mat;
mat.set(m);

return mat;
}


Notice that there's some commented out lines because I got different answers for that reading

void setothographicmat(float l, float r, float t, float b, float n, float f, Matrix4<T> &mat)
{
mat[0][0] = 2 / (r - l);
mat[0][1] = 0;
mat[0][2] = 0;
mat[0][3] = 0;

mat[1][0] = 0;
mat[1][1] = 2 / (t - b);
mat[1][2] = 0;
mat[1][3] = 0;

mat[2][0] = 0;
mat[2][1] = 0;
mat[2][2] = -1 / (f - n);
mat[2][3] = 0;

mat[3][0] = -(r + l) / (r - l);
mat[3][1] = -(t + b) / (t - b);
mat[3][2] = -n / (f - n);
mat[3][3] = 1;
}


and

http://www.songho.ca/opengl/gl_projectionmatrix.html

Edited by polyfrag

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Im not sure about your matrix concatenation or row column ordering, but my code and the opengl red book use the two lines you have commented out,

M(2, 2) = -2 / (f - n);
M(3, 2) = -(f + n) / (f - n);

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Concatenated affine transformations will result in an affine transformation (and an ortho is one), so the last row stays (0,0,0,1), (Edit: or column if row vectors are used) and w of a transformed vector should stay 1 as well. My bet is some row/column mixup in the construction: The first link is confusing in this regard (mixing row/column vector convention with row/column-major layout). Edited by unbird

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Concatenated affine transformations will result in an affine transformation (and an ortho is one), so the last row stays (0,0,0,1), (Edit: or column if row vectors are used) and w of a transformed vector should stay 1 as well. My bet is some row/column mixup in the construction: The first link is confusing in this regard (mixing row/column vector convention with row/column-major layout).

+1

http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-4-geometry/conventions-again-row-major-vs-column-major-vector/

I've screwed up every Matix class i have EVER written from scratch.  And every time I say to myself "OK.  This time I'll get the row/column major stuff right!"

##### Share on other sites
In adition to what NumberXaero said, your matrix is also transposed. Try switching rows and cols.

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I literally can't find what is wrong. If you need more code, ask me to post it. I will also attach all the source files.
Brain.cpp
Error.cpp
IndexBuffer.cpp
Input.cpp
Renderer.cpp
Scene.cpp
Sprite.cpp
Texture.cpp
VertexArray.cpp
VertexBuffer.cpp
VertexBufferLayout.cpp
Window.cpp
Brain.h
Error.h
IndexBuffer.h
Input.h
Renderer.h
Scene.h
SpaceShooterEngine.h
Sprite.h
Texture.h
VertexArray.h
VertexBuffer.h
VertexBufferLayout.h
Window.h

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For a couple of days now i've decided to build my own planet renderer just to see how floating point precision issues
can be tackled. As you probably imagine, i've quickly faced FPP issues when trying to render absurdly large planets.

I have used the classical quadtree LOD approach;
I've generated my grids with 33 vertices, (x: -1 to 1, y: -1 to 1, z = 0).
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The same technique is applied for the rest of the faces (obviously, with the proper rotations / translations).
The matrix that result from the multiplication of R and T (in that particular order) is send to my vertex shader as r_Grid'.
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I've read that if i could render each grid relative to the camera i could get better precision on the surface, effectively
getting rid of those rounding errors.

My question is how can i achieve this relative to camera rendering in my scenario here?
I know that i have to do most of the work on the CPU with double, and that's exactly what i'm doing.
I only use double on the CPU side where i also do most of the matrix multiplications.
As you can see from my vertex shader i only do the usual r_ModelViewProjection * (some vertex coords).