diff --git a/src/display.cpp b/src/display.cpp
index 6ba42b97b21..9a38872418a 100644
--- a/src/display.cpp
+++ b/src/display.cpp
@@ -331,48 +331,59 @@ const gamemap::location display::pixel_position_to_hex(int x, int y,
 	return res;
 }
 
-void display::get_rect_hex_bounds(SDL_Rect rect, gamemap::location &topleft, gamemap::location &bottomright) const
+void display::rect_of_hexes::iterator::operator++()
 {
-	// Change the coordinates of the rect send
-	// to be relative to the map area, instead of the screen area.
-	const SDL_Rect& map_rect = map_area();
-	rect.x -= map_rect.x;
-	rect.y -= map_rect.y;
-	// Only move the left side.
-	// The right side should remain
-	// at the same coordinates, so fix that
-	rect.w += map_rect.x;
-	rect.h += map_rect.y;
-
-	const int tile_width = hex_width();
-
-	// Adjust for the border
-	topleft.x = static_cast<int>(-theme_.border().size + (xpos_ + rect.x) / tile_width);
-	topleft.y = static_cast<int>(-theme_.border().size + (ypos_ + rect.y - (is_odd(topleft.x) ? zoom_/2 : 0)) / zoom_);
-
-	bottomright.x = static_cast<int>(-theme_.border().size + (xpos_ + rect.x + rect.w) / tile_width);
-	bottomright.y = static_cast<int>(-theme_.border().size + ((ypos_ + rect.y + rect.h) - (is_odd(bottomright.x) ? zoom_/2 : 0)) / zoom_);
-
-	// This routine does a rough approximation, so might be off by one.
-	// To be sure enough tiles are included, the boundaries are increased
-	// by one if the terrain is "on the map" due to the extra border.
-	// This uses a bit larger area.
-	//! @todo FIXME This routine should properly determine what to update,
-	//! and not increase by one just to be sure.
-	if(topleft.x >= -1) {
-		topleft.x--;
-	}
-	if(topleft.y >= -1) {
-		topleft.y--;
-	}
-	if(bottomright.x <= map_.w()) {
-		bottomright.x++;
-	}
-	if(bottomright.y <= map_.h()) {
-		bottomright.y++;
+	if (loc_.y < rect_.bottom[loc_.x & 1])
+		loc_.y++;
+	else {
+		loc_.x++;
+		loc_.y = rect_.top[loc_.x & 1];
 	}
 }
 
+// begin is top left, and end is after bottom right
+display::rect_of_hexes::iterator display::rect_of_hexes::begin()
+{
+	return iterator(gamemap::location(left, top[left & 1]), *this);
+}
+display::rect_of_hexes::iterator display::rect_of_hexes::end()
+{
+	return iterator(gamemap::location(right+1, top[(right+1) & 1]), *this);
+}
+
+const display::rect_of_hexes display::hexes_under_rect(const SDL_Rect& r) const
+{
+	rect_of_hexes res;
+
+	SDL_Rect map_rect = map_area();
+	// translate rect coordinates from screen-based to map_area-based
+	int x = xpos_ - map_rect.x + r.x;
+	int y = ypos_ - map_rect.y + r.y;
+	// we use the "double" type to avoid important rounding error (size of an hex!)
+	// we will also need to use std::floor to avoid bad rounding at border (negative values)
+	double tile_width = hex_width();
+	double tile_size = hex_size();
+	double border = theme_.border().size;
+	// the "-0.25" is for the horizontal imbrication of hexes (1/4 overlaps).
+	res.left = static_cast<int>(std::floor(-border + x / tile_width - 0.25));
+	// we remove 1 pixel of the rectangle dimensions
+	// (the rounded division take one pixel more than needed)
+	res.right = static_cast<int>(std::floor(-border + (x + r.w-1) / tile_width));
+
+	// for odd x, we must shift up one half-hex. Since x will vary along the edge,
+	// we store here the y values for even and odd x, respectively
+	res.top[0] = static_cast<int>(std::floor(-border + y / tile_size));
+	res.top[1] = static_cast<int>(std::floor(-border + y / tile_size - 0.5));
+	res.bottom[0] = static_cast<int>(std::floor(-border + (y + r.h-1) / tile_size));
+	res.bottom[1] = static_cast<int>(std::floor(-border + (y + r.h-1) / tile_size - 0.5));
+
+	// TODO: in some rare cases (1/16), a corner of the big rect is on a tile
+	// (the 72x72 rectangle containing the hex) but not on the hex itself
+	// Can maybe be optimized by using pixel_position_to_hex
+
+	return res;
+};
+
 int display::get_location_x(const gamemap::location& loc) const
 {
 	return static_cast<int>(map_area().x + (loc.x + theme_.border().size) * hex_width() - xpos_);
@@ -413,12 +424,6 @@ gamemap::location display::minimap_location_on(int x, int y)
 	return loc;
 }
 
-void display::get_visible_hex_bounds(gamemap::location &topleft, gamemap::location &bottomright) const
-{
-	SDL_Rect r = map_area();
-	get_rect_hex_bounds(r, topleft, bottomright);
-}
-
 int display::screenshot(std::string filename, bool map_screenshot)
 {
 	int size = 0;
@@ -1051,16 +1056,13 @@ void display::highlight_hex(gamemap::location hex)
 	invalidate(mouseoverHex_);
 }
 
-bool display::invalidate_locations_in_rect(SDL_Rect r)
+bool display::invalidate_locations_in_rect(const SDL_Rect& rect)
 {
 	bool result = false;
-	gamemap::location topleft, bottomright;
-	get_rect_hex_bounds(r, topleft, bottomright);
-	for (int x = topleft.x; x <= bottomright.x; ++x) {
-		for (int y = topleft.y; y <= bottomright.y; ++y) {
-			gamemap::location loc(x, y);
-			result |= invalidate(loc);
-		}
+	rect_of_hexes hexes = hexes_under_rect(rect);
+	rect_of_hexes::iterator i = hexes.begin(), end = hexes.end();
+	for (;i != end; ++i) {
+		result |= invalidate(*i);
 	}
 	return result;
 }
@@ -1114,13 +1116,10 @@ bool display::draw_init()
 
 	if(invalidateAll_) {
 		DBG_DP << "draw() with invalidateAll\n";
-		gamemap::location topleft;
-		gamemap::location bottomright;
-		get_visible_hex_bounds(topleft, bottomright);
-		for(int x = topleft.x; x <= bottomright.x; ++x)
-			for(int y = topleft.y; y <= bottomright.y; ++y)
-				invalidated_.insert(gamemap::location(x,y));
+
+		// toggle invalidateAll_ first to allow regular invalidations
 		invalidateAll_ = false;
+		invalidate_locations_in_rect(map_area());
 
 		redrawMinimap_ = true;
 	}
@@ -1395,15 +1394,15 @@ void display::scroll(int xmove, int ymove)
 
 	if (dy != 0) {
 		SDL_Rect r = map_area();
-		r.x = 0;
-		r.y = dy < 0 ? r.h+dy : 0;
+		if(dy < 0)
+			r.y = r.y + r.h + dy;
 		r.h = abs(dy);
 		invalidate_locations_in_rect(r);
 	}
 	if (dx != 0) {
 		SDL_Rect r = map_area();
-		r.x = dx < 0 ? r.w+dx : 0;
-		r.y = 0;
+		if (dx < 0)
+			r.x = r.x + r.w + dx;
 		r.w = abs(dx);
 		invalidate_locations_in_rect(r);
 	}
@@ -2134,71 +2133,29 @@ void display::refresh_report(reports::TYPE report_num, reports::report report,
 		reportSurfaces_[report_num].assign(NULL);
 	}
 }
-bool display::invalidate_rectangle(const gamemap::location& first_corner, const gamemap::location& second_corner) {
-	// unused variable - const SDL_Rect& rect = map_area();
-	bool result = false;
 
-	const int min_x = minimum<int>(first_corner.x,second_corner.x);
-	const int min_y = minimum<int>(first_corner.y,second_corner.y);
-	const int max_x = maximum<int>(first_corner.x,second_corner.x);
-	const int max_y = maximum<int>(first_corner.y,second_corner.y);
-
-	for (int x = min_x; x <= max_x;x++) {
-		for (int y = min_y; y <= max_y;y++) {
-			result |= invalidate(gamemap::location(x,y));
-		}
-		// take a margin on Y because of "misaligned hexes"
-		gamemap::location margein(x, is_odd(x) ? min_y-1 : max_y+1);
-		result |= invalidate(margein);
-	}
-	return result;
-}
-
-bool display::invalidate_zone(const int x1,const int y1, const int x2, const int y2) {
-	const SDL_Rect& rect = map_area();
-	return invalidate_rectangle(pixel_position_to_hex(x1 - rect.x+xpos_, y1 - rect.y+ypos_),pixel_position_to_hex(x2 - rect.x+xpos_, y2 - rect.y+ypos_));
-}
-
-bool display::rectangle_need_update(const gamemap::location& first_corner, const gamemap::location& second_corner) const {
-	const int min_x = minimum<int>(first_corner.x,second_corner.x);
-	const int min_y = minimum<int>(first_corner.y,second_corner.y);
-	const int max_x = maximum<int>(first_corner.x,second_corner.x);
-	const int max_y = maximum<int>(first_corner.y,second_corner.y);
-
-	for (int x = min_x; x <= max_x;x++) {
-		for (int y = min_y; y <= max_y;y++) {
-			// take a margin on Y because of "misaligned hexes"
-			if(invalidated_.find(gamemap::location(x,y)) != invalidated_.end())
-				return true;
-		}
-		// take a margin on Y because of "misaligned hexes"
-		gamemap::location margein(x, is_odd(x) ? min_y-1 : max_y+1);
-		if(invalidated_.find(margein) != invalidated_.end())
+bool display::rectangle_need_update(const SDL_Rect& rect) const
+{
+	rect_of_hexes hexes = hexes_under_rect(rect);
+	rect_of_hexes::iterator i = hexes.begin(), end = hexes.end();
+	for (;i != end; ++i) {
+		if(invalidated_.find(*i) != invalidated_.end())
 			return true;
 	}
 
 	return false;
 }
 
-bool display::zone_need_update(const int x1,const int y1, const int x2, const int y2) const {
-	const SDL_Rect& rect = map_area();
-	return rectangle_need_update(pixel_position_to_hex(x1 - rect.x+xpos_, y1 - rect.y+ypos_),pixel_position_to_hex(x2 - rect.x+xpos_, y2 - rect.y+ypos_));
-}
-
 void display::invalidate_animations() {
 	if (preferences::animate_map()) {
-		gamemap::location topleft;
-		gamemap::location bottomright;
-		get_visible_hex_bounds(topleft, bottomright);
-		for(int x = topleft.x; x <= bottomright.x; ++x) {
-			for(int y = topleft.y; y <= bottomright.y; ++y) {
-				const gamemap::location loc(x,y);
-				if (!shrouded(loc)) {
-					if (builder_.update_animation(loc)) {
-						invalidate(loc);
-					} else {
-						invalidate_animations_location(loc);
-					}
+		rect_of_hexes hexes = get_visible_hexes();
+		rect_of_hexes::iterator i = hexes.begin(), end = hexes.end();
+		for (;i != end; ++i) {
+			if (!shrouded(*i)) {
+				if (builder_.update_animation(*i)) {
+					invalidate(*i);
+				} else {
+					invalidate_animations_location(*i);
 				}
 			}
 		}
diff --git a/src/display.hpp b/src/display.hpp
index aad90026b79..edab2cbf117 100644
--- a/src/display.hpp
+++ b/src/display.hpp
@@ -151,12 +151,45 @@ public:
 	//! Function to invalidate the game status displayed on the sidebar.
 	void invalidate_game_status() { invalidateGameStatus_ = true; }
 
-	void get_rect_hex_bounds(SDL_Rect rect, gamemap::location &topleft, gamemap::location &bottomright) const;
-
 	//! Functions to get the on-screen positions of hexes.
 	int get_location_x(const gamemap::location& loc) const;
 	int get_location_y(const gamemap::location& loc) const;
 
+	/**
+	 * Rectangular area of hexes, allowing to decide how the top and bottom
+	 * edges handles the vertical shift for each parity of the x coordinate
+	 */
+	struct rect_of_hexes{
+		int left;
+		int right;
+		int top[2]; // for even and odd values of x, respectively
+		int bottom[2]; 
+
+		//!  very simple iterator to walk into the rect_of_hexes
+		struct iterator {
+			iterator(gamemap::location loc, rect_of_hexes& rect)
+				: loc_(loc), rect_(rect){};
+
+			//! increment y first, then when reaching bottom, increment x
+			void operator++();
+			bool operator!=(const iterator &that) const {return that.loc_ != loc_;};
+			const gamemap::location& operator*() const {return loc_;};
+
+			private:
+				gamemap::location loc_;
+				rect_of_hexes& rect_;
+		};
+
+		iterator begin();
+		iterator end();
+	};
+
+	//! Return the rectangular area of hexes overlapped by r (r is in screen coordinates)
+	const rect_of_hexes hexes_under_rect(const SDL_Rect& r) const;
+
+	//! Returns the rectangular area of visible hexes
+	const rect_of_hexes get_visible_hexes() const {return hexes_under_rect(map_area());};
+
 	//! Returns true if location (x,y) is covered in shroud.
 	bool shrouded(const gamemap::location& loc) const {
 		return viewpoint_ && viewpoint_->shrouded(loc);
@@ -170,10 +203,6 @@ public:
 	//! (to more clearly show where hexes are)
 	void set_grid(const bool grid) { grid_ = grid; }
 
-	//! Returns the locations of 2 hexes
-	//! that bind the visible area of the map.
-	void get_visible_hex_bounds(gamemap::location &topleft, gamemap::location &bottomright) const;
-
 	//! Save a (map-)screenshot and return the estimated file size
 	int screenshot(std::string filename, bool map_screenshot = false);
 
@@ -191,12 +220,11 @@ public:
 
 	// Will be overridden in the display subclass
 	virtual bool invalidate(const gamemap::location& loc) {return invalidated_.insert(loc).second;};
-	virtual bool invalidate_rectangle(const gamemap::location& first_corner, const gamemap::location& second_corner) ;
-	virtual bool invalidate_zone(const int x1,const int y1, const int x2, const int y2);
-	virtual bool rectangle_need_update(const gamemap::location& first_corner, const gamemap::location& second_corner) const;
-	virtual bool zone_need_update(const int x1,const int y1, const int x2, const int y2) const;
+	bool rectangle_need_update(const SDL_Rect& rect) const;
 	virtual void draw_minimap_units() {};
-	
+
+	bool invalidate_locations_in_rect(const SDL_Rect& rect);
+
 	/**
 	 * Function to invalidate animated terrains which may have changed.
 	 */
@@ -623,8 +651,6 @@ protected:
 	//! redraw all panels associated with the map display
 	void draw_all_panels();
 
-	bool invalidate_locations_in_rect(SDL_Rect r);
-
 	//! Strict weak ordering to sort a STL-set of hexes
 	//! for drawing using the z-order.
 	//! (1000 are just to weight the y compare to x)
diff --git a/src/game_display.cpp b/src/game_display.cpp
index 825bd1f04d8..c8152a4ee45 100644
--- a/src/game_display.cpp
+++ b/src/game_display.cpp
@@ -775,20 +775,17 @@ void game_display::process_reachmap_changes()
 	if (reach_map_.empty() != reach_map_old_.empty()) {
 		// Invalidate everything except the non-darkened tiles
 		reach_map &full = reach_map_.empty() ? reach_map_old_ : reach_map_;
-		gamemap::location topleft;
-		gamemap::location bottomright;
-		get_visible_hex_bounds(topleft, bottomright);
-		for(int x = topleft.x; x <= bottomright.x; ++x) {
-			for(int y = topleft.y; y <= bottomright.y; ++y) {
-				gamemap::location loc(x, y);
-				reach_map::iterator reach = full.find(loc);
-				if (reach == full.end()) {
-					// Location needs to be darkened or brightened
-					invalidate(loc);
-				} else if (reach->second != 1) {
-					// Number needs to be displayed or cleared
-					invalidate(loc);
-				}
+
+		rect_of_hexes hexes = get_visible_hexes();
+		rect_of_hexes::iterator i = hexes.begin(), end = hexes.end();
+		for (;i != end; ++i) {
+			reach_map::iterator reach = full.find(*i);
+			if (reach == full.end()) {
+				// Location needs to be darkened or brightened
+				invalidate(*i);
+			} else if (reach->second != 1) {
+				// Number needs to be displayed or cleared
+				invalidate(*i);
 			}
 		}
 	} else if (!reach_map_.empty()) {
diff --git a/src/halo.cpp b/src/halo.cpp
index 72e13569108..63a73f3a32b 100644
--- a/src/halo.cpp
+++ b/src/halo.cpp
@@ -171,12 +171,10 @@ bool effect::render()
 	// If rendered the first time, need to determine the area affected. 
 	// If a halo changes size, it is not updated.
 	if(overlayed_hexes_.empty()) {
-		gamemap::location topleft, bottomright;
-		disp->get_rect_hex_bounds(rect, topleft, bottomright);
-		for (int x = topleft.x; x <= bottomright.x; ++x) {
-			for (int y = topleft.y; y <= bottomright.y; ++y) {
-				overlayed_hexes_.push_back(gamemap::location(x, y));
-			}
+		display::rect_of_hexes hexes = disp->hexes_under_rect(rect);
+		display::rect_of_hexes::iterator i = hexes.begin(), end = hexes.end();
+		for (;i != end; ++i) {
+			overlayed_hexes_.push_back(*i);
 		}
 	}
 
diff --git a/src/unit_frame.cpp b/src/unit_frame.cpp
index 2a2f4b116d0..4f06008be4c 100644
--- a/src/unit_frame.cpp
+++ b/src/unit_frame.cpp
@@ -455,14 +455,14 @@ bool unit_frame::invalidate(const bool force,const int frame_time,const gamemap:
 		} else {
 			// if we need to update ourselve because we changed, invalidate our hexs
 			// and return whether or not our hexs was invalidated
-			 if(force || need_update()){
-				 bool tmp = game_display::get_singleton()->invalidate_zone(x,y,x+image->w,y+image->h);
-				 return tmp;
+			if(force || need_update()){
+				const SDL_Rect r = {x,y,image->w,image->h};
+				return game_display::get_singleton()->invalidate_locations_in_rect(r);
 			}
 			// if not, check if any of our hexes is already invalidated, if any is, invalidate all of them
-			if(game_display::get_singleton()->zone_need_update(x,y,x+image->w,y+image->h)) {
-			       	bool tmp = game_display::get_singleton()->invalidate_zone(x,y,x+image->w,y+image->h);
-				 return tmp;
+			const SDL_Rect r = {x,y,image->w,image->h};
+			if(game_display::get_singleton()->rectangle_need_update(r)) {
+				return game_display::get_singleton()->invalidate_locations_in_rect(r);
 			}
 			return false;