nml::mat4 operator*(nml::mat4 lhs, const nml::mat4& rhs)

Return a mat4 that is the product between two mat4.

The product between two mat4 is calculated this way:

\(\begin{bmatrix} lhs.x.x & lhs.y.x & lhs.z.x & lhs.w.x \\ lhs.x.y & lhs.y.y & lhs.z.y & lhs.w.y \\ lhs.x.z & lhs.y.z & lhs.z.z & lhs.w.z \\ lhs.x.w & lhs.y.w & lhs.z.w & lhs.w.w \end{bmatrix} * \begin{bmatrix} rhs.x.x & rhs.y.x & rhs.z.x & rhs.w.x \\ rhs.x.y & rhs.y.y & rhs.z.y & rhs.w.y \\ rhs.x.z & rhs.y.z & rhs.z.z & rhs.w.z \\ rhs.x.w & rhs.y.w & rhs.z.w & rhs.w.w \end{bmatrix} =\)

\(\begin{bmatrix} a & e & i & m \\ b & f & j & n \\ c & g & k & o \\ d & h & l & p \end{bmatrix}\)

\(\small a = lhs.x.x * rhs.x.x + lhs.y.x * rhs.x.y + lhs.z.x * rhs.x.z + lhs.w.x * rhs.x.w\) \(\small b = lhs.x.x * rhs.y.x + lhs.y.x * rhs.y.y + lhs.z.x * rhs.y.z + lhs.w.x * rhs.y.w\) \(\small c = lhs.x.x * rhs.z.x + lhs.y.x * rhs.z.y + lhs.z.x * rhs.z.z + lhs.w.x * rhs.z.w\) \(\small d = lhs.x.x * rhs.w.x + lhs.y.x * rhs.w.y + lhs.z.x * rhs.w.z + lhs.w.x * rhs.w.w\) \(\small e = lhs.x.y * rhs.x.x + lhs.y.y * rhs.x.y + lhs.z.y * rhs.x.z + lhs.w.y * rhs.x.w\) \(\small f = lhs.x.y * rhs.y.x + lhs.y.y * rhs.y.y + lhs.z.y * rhs.y.z + lhs.w.y * rhs.y.w\) \(\small g = lhs.x.y * rhs.z.x + lhs.y.y * rhs.z.y + lhs.z.y * rhs.z.z + lhs.w.y * rhs.z.w\) \(\small h = lhs.x.y * rhs.w.x + lhs.y.y * rhs.w.y + lhs.z.y * rhs.w.z + lhs.w.y * rhs.w.w\) \(\small i = lhs.x.z * rhs.x.x + lhs.y.z * rhs.x.y + lhs.z.z * rhs.x.z + lhs.w.z * rhs.x.w\) \(\small j = lhs.x.z * rhs.y.x + lhs.y.z * rhs.y.y + lhs.z.z * rhs.y.z + lhs.w.z * rhs.y.w\) \(\small k = lhs.x.z * rhs.z.x + lhs.y.z * rhs.z.y + lhs.z.z * rhs.z.z + lhs.w.z * rhs.z.w\) \(\small l = lhs.x.z * rhs.w.x + lhs.y.z * rhs.w.y + lhs.z.z * rhs.w.z + lhs.w.z * rhs.w.w\) \(\small m = lhs.x.w * rhs.x.x + lhs.y.w * rhs.x.y + lhs.z.w * rhs.x.z + lhs.w.w * rhs.x.w\) \(\small n = lhs.x.w * rhs.y.x + lhs.y.w * rhs.y.y + lhs.z.w * rhs.y.z + lhs.w.w * rhs.y.w\) \(\small o = lhs.x.w * rhs.z.x + lhs.y.w * rhs.z.y + lhs.z.w * rhs.z.z + lhs.w.w * rhs.z.w\) \(\small p = lhs.x.w * rhs.w.x + lhs.y.w * rhs.w.y + lhs.z.w * rhs.w.z + lhs.w.w * rhs.w.w\)

Example

#include "include/mat4.h"
#include <iostream>

int main() {
        nml::mat4 a(2.0f, 0.0f, 0.0f, 0.0f, 0.0f, 2.0f, 0.0f, 0.0f, 0.0f, 0.0f, 2.0f, 0.0f, 0.0f, 0.0f, 0.0f, 2.0f);
        nml::mat4 b = nml::inverse(a);
        nml::mat4 c = a * b;
        std::cout << nml::to_string(c) << std::endl;

        return 0;
}

Result:

[[1.000000, 0.000000, 0.000000, 0.000000], [0.000000, 1.000000, 0.000000, 0.000000], [0.000000, 0.000000, 1.000000, 0.000000], [0.000000, 0.000000, 0.000000, 1.000000]]