LibGfx: Make Matrix class consistently row-major

Matrix elements were interpreted in different ways.
This makes it definitely row-major, allowing initialization via
initializer list in a standard scientific order. Also matrix
multiplication now happens in the correct order and accessing
elements happens as m_elements[row][column].

Userland/Demos/GLTeapot/main.cpp

@@ -87,6 +87,10 @@ void GLContextWidget::timer_event(Core::TimerEvent&)
         * FloatMatrix4x4::rotate(FloatVector3(0, 1, 0), 0.0f)
         * FloatMatrix4x4::rotate(FloatVector3(0, 0, 1), angle);
 
+    // We need to transpose here because OpenGL expects matrices in column major order
+    // but our matrix class stores elements in row major order.
+    matrix = matrix.transpose();
+
     glMatrixMode(GL_MODELVIEW);
     glLoadMatrixf((float*)matrix.elements());
 

Userland/Libraries/LibGL/GLMat.cpp

@@ -37,11 +37,14 @@ void glPopMatrix()
 
 void glLoadMatrixf(const GLfloat* matrix)
 {
+    // Transpose the matrix here because glLoadMatrix expects elements
+    // in column major order but out Matrix class stores elements in
+    // row major order.
     FloatMatrix4x4 mat(
-        matrix[0], matrix[1], matrix[2], matrix[3],
+        matrix[0], matrix[4], matrix[8], matrix[12],
-        matrix[4], matrix[5], matrix[6], matrix[7],
+        matrix[1], matrix[5], matrix[9], matrix[13],
-        matrix[8], matrix[9], matrix[10], matrix[11],
+        matrix[2], matrix[6], matrix[10], matrix[14],
-        matrix[12], matrix[13], matrix[14], matrix[15]);
+        matrix[3], matrix[7], matrix[11], matrix[15]);
 
     g_gl_context->gl_load_matrix(mat);
 }

Userland/Libraries/LibGfx/Matrix.h

@@ -49,23 +49,23 @@ public:
                 auto& element = product.m_elements[i][j];
 
                 if constexpr (N == 4) {
-                    element = m_elements[0][j] * other.m_elements[i][0]
+                    element = m_elements[i][0] * other.m_elements[0][j]
-                        + m_elements[1][j] * other.m_elements[i][1]
+                        + m_elements[i][1] * other.m_elements[1][j]
-                        + m_elements[2][j] * other.m_elements[i][2]
+                        + m_elements[i][2] * other.m_elements[2][j]
-                        + m_elements[3][j] * other.m_elements[i][3];
+                        + m_elements[i][3] * other.m_elements[3][j];
                 } else if constexpr (N == 3) {
-                    element = m_elements[0][j] * other.m_elements[i][0]
+                    element = m_elements[i][0] * other.m_elements[0][j]
-                        + m_elements[1][j] * other.m_elements[i][1]
+                        + m_elements[i][1] * other.m_elements[1][j]
-                        + m_elements[2][j] * other.m_elements[i][2];
+                        + m_elements[i][2] * other.m_elements[2][j];
                 } else if constexpr (N == 2) {
-                    element = m_elements[0][j] * other.m_elements[i][0]
+                    element = m_elements[i][0] * other.m_elements[0][j]
-                        + m_elements[1][j] * other.m_elements[i][1];
+                        + m_elements[i][1] * other.m_elements[1][j];
                 } else if constexpr (N == 1) {
-                    element = m_elements[0][j] * other.m_elements[i][0];
+                    element = m_elements[i][0] * other.m_elements[0][j];
                 } else {
                     T value {};
                     for (size_t k = 0; k < N; ++k)
-                        value += m_elements[k][j] * other.m_elements[i][k];
+                        value += m_elements[i][k] * other.m_elements[k][j];
 
                     element = value;
                 }

Userland/Libraries/LibGfx/Matrix4x4.h

@@ -14,7 +14,7 @@
 namespace Gfx {
 
 template<typename T>
-class Matrix4x4 final : public Matrix<4, T> {
+class Matrix4x4 final {
 public:
     constexpr Matrix4x4() = default;
     constexpr Matrix4x4(T _11, T _12, T _13, T _14,
@@ -38,10 +38,10 @@ public:
         Matrix4x4 product;
         for (int i = 0; i < 4; ++i) {
             for (int j = 0; j < 4; ++j) {
-                product.m_elements[i][j] = m_elements[0][j] * other.m_elements[i][0]
+                product.m_elements[i][j] = m_elements[i][0] * other.m_elements[0][j]
-                    + m_elements[1][j] * other.m_elements[i][1]
+                    + m_elements[i][1] * other.m_elements[1][j]
-                    + m_elements[2][j] * other.m_elements[i][2]
+                    + m_elements[i][2] * other.m_elements[2][j]
-                    + m_elements[3][j] * other.m_elements[i][3];
+                    + m_elements[i][3] * other.m_elements[3][j];
             }
         }
         return product;
@@ -50,18 +50,18 @@ public:
     constexpr Vector4<T> operator*(const Vector4<T>& v) const
     {
         return Vector4<T>(
-            v.x() * m_elements[0][0] + v.y() * m_elements[1][0] + v.z() * m_elements[2][0] + v.w() * m_elements[3][0],
+            v.x() * m_elements[0][0] + v.y() * m_elements[0][1] + v.z() * m_elements[0][2] + v.w() * m_elements[0][3],
-            v.x() * m_elements[0][1] + v.y() * m_elements[1][1] + v.z() * m_elements[2][1] + v.w() * m_elements[3][1],
+            v.x() * m_elements[1][0] + v.y() * m_elements[1][1] + v.z() * m_elements[1][2] + v.w() * m_elements[1][3],
-            v.x() * m_elements[0][2] + v.y() * m_elements[1][2] + v.z() * m_elements[2][2] + v.w() * m_elements[3][2],
+            v.x() * m_elements[2][0] + v.y() * m_elements[2][1] + v.z() * m_elements[2][2] + v.w() * m_elements[2][3],
-            v.x() * m_elements[0][3] + v.y() * m_elements[1][3] + v.z() * m_elements[2][3] + v.w() * m_elements[3][3]);
+            v.x() * m_elements[3][0] + v.y() * m_elements[3][1] + v.z() * m_elements[3][2] + v.w() * m_elements[3][3]);
     }
 
     constexpr Vector3<T> transform_point(const Vector3<T>& p) const
     {
         return Vector3<T>(
-            p.x() * m_elements[0][0] + p.y() * m_elements[1][0] + p.z() * m_elements[2][0] + m_elements[3][0],
+            p.x() * m_elements[0][0] + p.y() * m_elements[0][1] + p.z() * m_elements[0][2] + m_elements[0][3],
-            p.x() * m_elements[0][1] + p.y() * m_elements[1][1] + p.z() * m_elements[2][1] + m_elements[3][1],
+            p.x() * m_elements[1][0] + p.y() * m_elements[1][1] + p.z() * m_elements[1][2] + m_elements[1][3],
-            p.x() * m_elements[0][2] + p.y() * m_elements[1][2] + p.z() * m_elements[2][2] + m_elements[3][2]);
+            p.x() * m_elements[2][0] + p.y() * m_elements[2][1] + p.z() * m_elements[2][2] + m_elements[2][3]);
     }
 
     constexpr static Matrix4x4 identity()
@@ -76,10 +76,10 @@ public:
     constexpr static Matrix4x4 translate(const Vector3<T>& p)
     {
         return Matrix4x4(
-            1, 0, 0, 0,
+            1, 0, 0, p.x(),
-            0, 1, 0, 0,
+            0, 1, 0, p.y(),
-            0, 0, 1, 0,
+            0, 0, 1, p.z(),
-            p.x(), p.y(), p.z(), 1);
+            0, 0, 0, 1);
     }
 
     constexpr static Matrix4x4 scale(const Vector3<T>& s)
@@ -107,6 +107,17 @@ public:
             0, 0, 0, 1);
     }
 
+    constexpr Matrix4x4 transpose() const
+    {
+        Matrix4x4 result;
+        for (int i = 0; i < 4; ++i) {
+            for (int j = 0; j < 4; ++j) {
+                result.m_elements[i][j] = m_elements[j][i];
+            }
+        }
+        return result;
+    }
+
 private:
     T m_elements[4][4];
 };