special values as functions

src/tg/types/mat.hh

@@ -141,8 +141,6 @@ struct mat
     using row_t = vec<C, ScalarT>;
     using col_t = vec<R, ScalarT>;
 
-    static const mat id;
-
     col_t m[R];
 
     constexpr col_t& operator[](int i) { return m[i]; }
@@ -150,6 +148,37 @@ struct mat
 
     constexpr col_t col(int i) const { return m[i]; }
     constexpr row_t row(int i) const { return detail::mat_row(*this, i); }
+
+    static constexpr mat<C, R, ScalarT> zero() { return {}; }
+    static constexpr mat<C, R, ScalarT> ones()
+    {
+        mat<C, R, ScalarT> m;
+        for (auto c = 0; c < C; ++c)
+            for (auto r = 0; r < R; ++r)
+                m[c][r] = ScalarT(1);
+        return m;
+    }
+    static constexpr mat<C, R, ScalarT> identity()
+    {
+        mat<C, R, ScalarT> m;
+        for (auto i = 0; i < (C < R ? C : R); ++i)
+            m[i][i] = ScalarT(1);
+        return m;
+    }
+    static constexpr mat<C, R, ScalarT> diag(ScalarT v)
+    {
+        mat<C, R, ScalarT> m;
+        for (auto i = 0; i < (C < R ? C : R); ++i)
+            m[i][i] = v;
+        return m;
+    }
+    static constexpr mat<C, R, ScalarT> diag(vec<(C < R ? C : R), ScalarT> const& v)
+    {
+        mat<C, R, ScalarT> m;
+        for (auto i = 0; i < (C < R ? C : R); ++i)
+            m[i][i] = v[i];
+        return m;
+    }
 };
 
 } // namespace tg

src/tg/types/pos.hh

@@ -64,6 +64,9 @@ struct pos<1, ScalarT>
     {
         return pos<D, T>(*this);
     }
+
+    static constexpr pos<1, ScalarT> zero() { return {ScalarT(0)}; }
+    static constexpr pos<1, ScalarT> ones() { return {ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -91,6 +94,9 @@ struct pos<2, ScalarT>
     {
         return pos<D, T>(*this);
     }
+
+    static constexpr pos<2, ScalarT> zero() { return {ScalarT(0), ScalarT(0)}; }
+    static constexpr pos<2, ScalarT> ones() { return {ScalarT(1), ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -123,6 +129,9 @@ struct pos<3, ScalarT>
     {
         return pos<D, T>(*this);
     }
+
+    static constexpr pos<3, ScalarT> zero() { return {ScalarT(0), ScalarT(0), ScalarT(0)}; }
+    static constexpr pos<3, ScalarT> ones() { return {ScalarT(1), ScalarT(1), ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -160,6 +169,9 @@ struct pos<4, ScalarT>
     {
         return pos<D, T>(*this);
     }
+
+    static constexpr pos<4, ScalarT> zero() { return {ScalarT(0), ScalarT(0), ScalarT(0), ScalarT(0)}; }
+    static constexpr pos<4, ScalarT> ones() { return {ScalarT(1), ScalarT(1), ScalarT(1), ScalarT(1)}; }
 };
 
 // comparison operators

src/tg/types/size.hh

@@ -68,6 +68,10 @@ struct size<1, ScalarT>
     {
         return size<D, T>(*this);
     }
+
+    static constexpr size<1, ScalarT> zero() { return {ScalarT(0)}; }
+    static constexpr size<1, ScalarT> ones() { return {ScalarT(1)}; }
+    static constexpr size<1, ScalarT> unit() { return {ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -95,6 +99,10 @@ struct size<2, ScalarT>
     {
         return size<D, T>(*this);
     }
+
+    static constexpr size<2, ScalarT> zero() { return {ScalarT(0), ScalarT(0)}; }
+    static constexpr size<2, ScalarT> ones() { return {ScalarT(1), ScalarT(1)}; }
+    static constexpr size<2, ScalarT> unit() { return {ScalarT(1), ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -123,6 +131,10 @@ struct size<3, ScalarT>
     {
         return size<D, T>(*this);
     }
+
+    static constexpr size<3, ScalarT> zero() { return {ScalarT(0), ScalarT(0), ScalarT(0)}; }
+    static constexpr size<3, ScalarT> ones() { return {ScalarT(1), ScalarT(1), ScalarT(1)}; }
+    static constexpr size<3, ScalarT> unit() { return {ScalarT(1), ScalarT(1), ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -152,6 +164,10 @@ struct size<4, ScalarT>
     {
         return size<D, T>(*this);
     }
+
+    static constexpr size<4, ScalarT> zero() { return {ScalarT(0), ScalarT(0), ScalarT(0), ScalarT(0)}; }
+    static constexpr size<4, ScalarT> ones() { return {ScalarT(1), ScalarT(1), ScalarT(1), ScalarT(1)}; }
+    static constexpr size<4, ScalarT> unit() { return {ScalarT(1), ScalarT(1), ScalarT(1), ScalarT(1)}; }
 };
 
 // comparison operators

src/tg/types/vec.hh

@@ -139,6 +139,10 @@ struct vec<1, ScalarT>
     {
         return vec<D, T>(*this);
     }
+
+    static constexpr vec<1, ScalarT> zero() { return {ScalarT(0)}; }
+    static constexpr vec<1, ScalarT> unit_x() { return {ScalarT(1)}; }
+    static constexpr vec<1, ScalarT> ones() { return {ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -166,6 +170,11 @@ struct vec<2, ScalarT>
     {
         return vec<D, T>(*this);
     }
+
+    static constexpr vec<2, ScalarT> zero() { return {ScalarT(0), ScalarT(0)}; }
+    static constexpr vec<2, ScalarT> unit_x() { return {ScalarT(1), ScalarT(0)}; }
+    static constexpr vec<2, ScalarT> unit_y() { return {ScalarT(0), ScalarT(1)}; }
+    static constexpr vec<2, ScalarT> ones() { return {ScalarT(1), ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -198,6 +207,12 @@ struct vec<3, ScalarT>
     {
         return vec<D, T>(*this);
     }
+
+    static constexpr vec<3, ScalarT> zero() { return {ScalarT(0), ScalarT(0), ScalarT(0)}; }
+    static constexpr vec<3, ScalarT> unit_x() { return {ScalarT(1), ScalarT(0), ScalarT(0)}; }
+    static constexpr vec<3, ScalarT> unit_y() { return {ScalarT(0), ScalarT(1), ScalarT(0)}; }
+    static constexpr vec<3, ScalarT> unit_z() { return {ScalarT(0), ScalarT(0), ScalarT(1)}; }
+    static constexpr vec<3, ScalarT> ones() { return {ScalarT(1), ScalarT(1), ScalarT(1)}; }
 };
 
 template <class ScalarT>
@@ -235,6 +250,13 @@ struct vec<4, ScalarT>
     {
         return vec<D, T>(*this);
     }
+
+    static constexpr vec<4, ScalarT> zero() { return {ScalarT(0), ScalarT(0), ScalarT(0), ScalarT(0)}; }
+    static constexpr vec<4, ScalarT> unit_x() { return {ScalarT(1), ScalarT(0), ScalarT(0), ScalarT(0)}; }
+    static constexpr vec<4, ScalarT> unit_y() { return {ScalarT(0), ScalarT(1), ScalarT(0), ScalarT(0)}; }
+    static constexpr vec<4, ScalarT> unit_z() { return {ScalarT(0), ScalarT(0), ScalarT(1), ScalarT(0)}; }
+    static constexpr vec<4, ScalarT> unit_w() { return {ScalarT(0), ScalarT(0), ScalarT(0), ScalarT(1)}; }
+    static constexpr vec<4, ScalarT> ones() { return {ScalarT(1), ScalarT(1), ScalarT(1), ScalarT(1)}; }
 };
 
 // comparison operators