Why does my translation matrix needs to be transposed?

Question

I'm working on a small graphics engine using OpenGL and I'm having some issues with my translation matrix. I'm using OpenGL 3.3, GLSL and C++. The situation is this: I have defined a small cube which I want to render on screen. The cube uses it's own coordinate system, so I created a model matrix to be able to transform the cube. To make it myself a bit easier I started out with just a translation matrix as the cube's model matrix and after a bit of coding I've managed to make everything work and the cube appears on the screen. Nothing all to special, but there is one thing about my translation matrix that I find a bit odd.

Now as far as I know, a translation matrix is defined as follows:

1, 0, 0, x
0, 1, 0, y
0, 0, 1, z
0, 0, 0, 1

However, this does not work for me. When I define my translation matrix this way, nothing appears on the screen. It only works when I define my translation matrix like this:

1, 0, 0, 0
0, 1, 0, 0
0, 0, 1, 0
x, y, z, 1

Now I've been over my code several times to find out why this is the case, but I can't seem to find out why or am I just wrong and does a translation matrix needs to be defined like the transposed one here above?

My matrices are defined as a one-dimensional array going from left to right, top to bottom.

Here is some of my code that might help:

//this is called just before cube is being rendered
void DisplayObject::updateMatrices()
{
    modelMatrix = identityMatrix();
    modelMatrix = modelMatrix * translateMatrix( xPos, yPos, zPos );

    /* update modelview-projection matrix */
    mvpMatrix = modelMatrix * (*projMatrix);
}

//this creates my translation matrix which causes the cube to disappear
const Matrix4 translateMatrix( float x, float y, float z )
{
    Matrix4 tranMatrix = identityMatrix();

    tranMatrix.data[3]  = x;
    tranMatrix.data[7]  = y;
    tranMatrix.data[11] = z;

    return Matrix4(tranMatrix);
}

This is my simple test vertex shader:

#version 150 core

in vec3 vPos;

uniform mat4 mvpMatrix;

void main()
{
    gl_Position = mvpMatrix * vec4(vPos, 1.0);
}

I've also did tests to check if my matrix multiplication works and it does. I * randomMatrix is still just randomMatrix

I hope you guys can help. Thanks

EDIT:

This is how I send the matrix data to OpenGL:

void DisplayObject::render()
{
    updateMatrices();

    glBindVertexArray(vaoID);
    glUseProgram(progID);
    glUniformMatrix4fv( glGetUniformLocation(progID, "mvpMatrix"), 1, GL_FALSE, &mvpMatrix.data[0] );
    glDrawElements(GL_TRIANGLES, bufferSize[index], GL_UNSIGNED_INT, 0);
}

mvpMatrix.data is a std::vector:

Answer 1

For OpenGL

1, 0, 0, 0
0, 1, 0, 0
0, 0, 1, 0
x, y, z, 1

Is the correct Translation Matrix. Why? Opengl Uses column-major matrix ordering. Which is the Transpose of the Matrix you initially presented, which is in row-major ordering. Row major is used in most math text-books and also DirectX, so it is a common point of confusion for those new to OpenGL.

See: http://www.mindcontrol.org/~hplus/graphics/matrix-layout.html

Answer 2

You cannot swap matrices in a matrix multiplication, so A*B is different from B*A. You have to transpose B before swapping the matrices.

A * B = t(B) * A

try

void DisplayObject::updateMatrices()
{
    modelMatrix = identityMatrix();
    modelMatrix = translateMatrix( xPos, yPos, zPos ) * modelMatrix;

    /* update modelview-projection matrix */
    mvpMatrix = modelMatrix * (*projMatrix);
}