output: add initial renderer

This will only render the clearing for now as there is no damage
tracking yet.

desktop/util.c

@@ -0,0 +1,36 @@
+/*
+ * Cage: A Wayland kiosk.
+ *
+ * Copyright (C) 2019 The Sway authors
+ *
+ * See the LICENSE file accompanying this file.
+ */
+
+#include <wlr/types/wlr_box.h>
+
+#include "util.h"
+
+int
+scale_length(int length, int offset, float scale)
+{
+	/**
+	 * One does not simply multiply the width by the scale. We allow fractional
+	 * scaling, which means the resulting scaled width might be a decimal.
+	 * So we round it.
+	 *
+	 * But even this can produce undesirable results depending on the X or Y
+	 * offset of the box. For example, with a scale of 1.5, a box with
+	 * width=1 should not scale to 2px if its X coordinate is 1, because the
+	 * X coordinate would have scaled to 2px.
+	 */
+	return round((offset + length) * scale) - round(offset * scale);
+}
+
+void
+scale_box(struct wlr_box *box, float scale)
+{
+	box->width = scale_length(box->width, box->x, scale);
+	box->height = scale_length(box->height, box->y, scale);
+	box->x = round(box->x * scale);
+	box->y = round(box->y * scale);
+}