diff --git a/src/utils.c b/src/utils.c
index ef97806..124d086 100644
--- a/src/utils.c
+++ b/src/utils.c
@@ -117,6 +117,36 @@ SYMBOL_EXPORT int DrawWrappedTextWithShadow(ALLEGRO_FONT* font, ALLEGRO_COLOR co
 	return DrawWrappedText(font, color, x, y, width, flags, text);
 }
 
+SYMBOL_EXPORT void DrawCentered(ALLEGRO_BITMAP* bitmap, int x, int y, int flags) {
+	al_draw_bitmap(bitmap, x - al_get_bitmap_width(bitmap) / 2.0, y - al_get_bitmap_height(bitmap) / 2.0, flags);
+}
+
+SYMBOL_EXPORT double DotProduct(const double v[], const double u[], int n) {
+	float result = 0.0;
+	for (int i = 0; i < n; i++) {
+		result += v[i] * u[i];
+	}
+	return result;
+}
+
+SYMBOL_EXPORT double VectorLength(double x, double y, double z) {
+	return sqrt(pow(x, 2) + pow(y, 2) + pow(z, 2));
+}
+
+SYMBOL_EXPORT double Clip(double left, double right, double val) {
+	if (val > right) {
+		return right;
+	}
+	if (val < left) {
+		return left;
+	}
+	return val;
+}
+
+SYMBOL_EXPORT double Lerp(double left, double right, double pos) {
+	return left + (right - left) * pos;
+}
+
 /* linear filtering code written by SiegeLord */
 SYMBOL_EXPORT ALLEGRO_COLOR InterpolateColor(ALLEGRO_COLOR c1, ALLEGRO_COLOR c2, float frac) {
 	return al_map_rgba_f(c1.r + frac * (c2.r - c1.r),
diff --git a/src/utils.h b/src/utils.h
index 1d792b6..19555e9 100644
--- a/src/utils.h
+++ b/src/utils.h
@@ -52,6 +52,13 @@ void DrawTextWithShadow(ALLEGRO_FONT* font, ALLEGRO_COLOR color, float x, float
 int DrawWrappedText(ALLEGRO_FONT* font, ALLEGRO_COLOR color, float x, float y, int width, int flags, char const* text);
 int DrawWrappedTextWithShadow(ALLEGRO_FONT* font, ALLEGRO_COLOR color, float x, float y, int width, int flags, char const* text);
 
+void DrawCentered(ALLEGRO_BITMAP* bitmap, int x, int y, int flags);
+
+double DotProduct(const double v[], const double u[], int n);
+double VectorLength(double x, double y, double z);
+double Clip(double left, double right, double val);
+double Lerp(double left, double right, double pos);
+
 ALLEGRO_COLOR InterpolateColor(ALLEGRO_COLOR c1, ALLEGRO_COLOR c2, float frac);
 void ScaleBitmap(ALLEGRO_BITMAP* source, int width, int height);