freevec.org

We tackle the 4x4 matrix inversion using the matrix partitioning method, as described in the "Numerical Recipes in C" book (2nd ed., though I guess it will be similar in the 3rd edition). Using the AltiVec SIMD unit, we achieve almost 300% increase in performance, making the routine the fastest -at least known to us, matrix inversion method!

Getting the translation matrix of a vector is essential to do movements of a vector in 3D space.

For the theory behind translation matrices please see [url=http://en.wikipedia.org/wiki/Translation_(geometry)]here[/url].

The nice thing about the identity matrix, is that we don't have to do any reading of the matrix. And since the form of the identity matrix is already known:

(Please see Matrix 4x4 addition/subtraction (floats) for the typedefs and definitions used.)

void Mat44MulVec(Vec3f vout, Mat44 mat, Vec4f vin)
{
        vector float vm_1, vm_2, vm_3, vm_4,
                     vec, vec_1, vec_2, vec_3, 
                     vr, vr_1, vr_2, vr_3, v0;
 
        // Load matrix and vector
        LOAD_ALIGNED_MATRIX(mat, vm_1, vm_2, vm_3, vm_4);
        LOAD_ALIGNED_VECTOR(vec, vin);
 
        v0 = (vector float) vec_splat_u32(0);
        vec = vec_ld(0, (float *)vec);
        vec_1 = vec_splat(vec, 0);
        vec_2 = vec_splat(vec, 1);
        vec_3 = vec_splat(ve0, 2);
 
        // Do the vector x matrix multiplication
        vr_1 = vec_madd(vm_1, vec_1, v0);
        vr_2 = vec_madd(vm_2, vec_2, vr_1);
        vr_3 = vec_madd(vm_3, vec_3, vr_2);
        vr   = vec_add(vr_3, vm_4);
 
        // Store back the result
        STORE_ALIGNED_VECTOR(vr, vout);
}

For the theory behind matrix transposition, please see here.

So, the 4x4 transpose would be: