diff --git a/main/include/glga.hpp b/main/include/glga.hpp
new file mode 100644
index 0000000..2aea9be
--- /dev/null
+++ b/main/include/glga.hpp
@@ -0,0 +1,121 @@
+#include <math.h>
+
+namespace ga {
+    struct Vec;
+    struct Bivec;
+    struct Mat;
+
+    struct Vec {
+        float x, y, z, w;
+
+        Vec(float x, float y, float z, float w) :
+            x(x), y(y), z(z), w(w) {}
+
+    };
+
+    struct Bivec {
+        float xy, yz, zw, wx, xz, yw;
+
+        Bivec(float xy, float yz, float zw, float wx, float xz, float yw) :
+            xy(xy), yz(yz), zw(zw), wx(wx), xz(xz), yw(yw) {}
+    };
+
+    struct Mat {
+        Vec x, y, z, w;
+
+        Mat(Vec x, Vec y, Vec z, Vec w) : x(x), y(y), z(z), w(w) {}
+    };
+
+    namespace unit {
+        Vec x() { return Vec(1, 0, 0, 0); };
+
+        Vec y() { return Vec(1, 0, 0, 0); };
+
+        Vec z() { return Vec(1, 0, 0, 0); };
+
+        Vec w() { return Vec(1, 0, 0, 0); };
+
+        Bivec xy() { return Bivec(1, 0, 0, 0, 0, 0); }
+
+        Bivec yz() { return Bivec(0, 1, 0, 0, 0, 0); }
+
+        Bivec zw() { return Bivec(0, 0, 1, 0, 0, 0); }
+
+        Bivec wx() { return Bivec(0, 0, 0, 1, 0, 0); }
+
+        Bivec xz() { return Bivec(0, 0, 0, 0, 1, 0); }
+
+        Bivec yw() { return Bivec(0, 0, 0, 0, 0, 1); }
+    }
+
+    float length2(Vec v) {
+        return v.x * v.x + v.y * v.y + v.z * v.z + v.w * v.w;
+    }
+
+    float length2(Bivec v) {
+        return v.xy * v.xy + v.yz * v.yz + v.zw * v.zw
+            + v.wx * v.wx + v.xz * v.xz + v.yw * v.yw;
+    }
+
+    float length(Vec v) { return sqrt(length2(v)); }
+
+    float length(Bivec v) { return sqrt(length2(v)); }
+
+    Vec add(Vec u, Vec v) {
+        return Vec(u.x + v.x,
+            u.y + v.y,
+            u.z + v.z,
+            u.w + v.w);
+    }
+
+    Bivec add(Bivec u, Bivec v) {
+        Bivec(u.xy + v.xy,
+            u.yz + v.yz,
+            u.zw + v.zw,
+            u.wx + v.wx,
+            u.xz + v.xz,
+            u.yw + v.yw);
+    }
+
+    Vec mul(float c, Vec v) {
+        return Vec(c * v.x,
+            c * v.y,
+            c * v.z,
+            c * v.w);
+    }
+
+    Bivec mul(float c, Bivec v) {
+        Bivec(c * v.xy,
+            c * v.yz,
+            c * v.zw,
+            c * v.wx,
+            c * v.xz,
+            c * v.yw);
+    }
+
+    Vec normalize(Vec v) {
+        return mul(1 / length(v), v);
+    }
+
+    Bivec normalize(Bivec v) {
+        return mul(1 / length(v), v);
+    }
+
+    Mat matrix(float c) {
+        // c as a transformation
+        // scale by c
+        return Mat(Vec(c, 0, 0, 0), Vec(0, c, 0, 0), Vec(0, 0, c, 0), Vec(0, 0, 0, c));
+    }
+
+    Mat matrix(Vec v) {
+        // v as a transformation
+        // reflect along v
+        return matrix(1); // todo reflection
+    }
+
+    Mat rotor(Bivec v) {
+        // v as a transformation
+        // rotate along v
+        return matrix(1);
+    }
+}
\ No newline at end of file
diff --git a/main/src/main.cpp b/main/src/main.cpp
index 6a3562d..e735b61 100644
--- a/main/src/main.cpp
+++ b/main/src/main.cpp
@@ -7,6 +7,8 @@
 #include <vector>
 #include <cmath>
 
+#include "glga.hpp"
+
 #define PI 3.14159f
 
 namespace util {
@@ -200,16 +202,19 @@ struct State {
         float s_ = std::sin(3.f / 8);
 
         glBindBuffer(GL_UNIFORM_BUFFER, ubo);
-        util::bufferData<float>(GL_UNIFORM_BUFFER, {
-            1.f / 4 / ar, 0, 0, 0,
-            0, 0, 1.f / 10, 0,
-            0, 1.f / 4, 0, 0,
-            0, 0, 0, 1,
+        util::bufferData<ga::Mat>(GL_UNIFORM_BUFFER, {
+            ga::Mat(
+                ga::Vec(1.f / 4 / ar, 0, 0, 0),
+                ga::Vec(0, 0, 1.f / 10, 0),
+                ga::Vec(0, 1.f / 4, 0, 0),
+                ga::Vec(0, 0, 0, 1.f)),
 
-            c, 0, 0, s,
-            0, c_, s_, 0,
-            0, -s_, c_, 0,
-            -s, 0, 0, c
+            ga::Mat(
+                ga::Vec(c, 0, 0, s),
+                ga::Vec(0, c_, s_, 0),
+                ga::Vec(0, -s_, c_, 0),
+                ga::Vec(-s, 0, 0, c)
+            )
         }, GL_STREAM_DRAW);
         glBindBuffer(GL_UNIFORM_BUFFER, 0);
     }