perf(l2): no redraws while nothing changes

Found by counting flushes on idle screens in the sim:
- The compose field's cursor blinked (a redraw every 400 ms) as soon as
  a conversation opened, the keyboard hidden: lv_keyboard_set_textarea()
  focuses the field, and LVGL only stops a blink when the cursor moves.
  fieldFocus() sets the state and nudges the blink; also used for the
  WiFi and channel fields, which left theirs running.
- lv_obj_align_to() restyles on every call, so the status bar's icons
  redrew every second; placeLeftOf() moves them only when they move.
- Text colours set every second (nav bar, GPS status, Diag errors) go
  through setTextColor(), which skips an unchanged colour.
- A LV_LABEL_LONG_DOT label writes its "..." into its own text, so
  setText() never matched and rewrote it every refresh (the nav bar's
  hint); labelShows() reads past the dots.
- The map area, the area-outline, trail and vector-label layers were
  invalidated on every map refresh (every 3 s, a full-map redraw); now
  only when the view or what they draw changed.

Idle map: 17 -> 1 flush in 5 s; list and settings screens: 0.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

examples/companion_radio/ui-lvgl/ChannelScreen.h

@@ -262,10 +262,10 @@ void UITask::channelEditHex(bool hex) {
 void UITask::channelEditField(lv_obj_t* ta) {
   using namespace chanview;
   if (!s_kb) return;
-  lv_obj_remove_state(s_name, LV_STATE_FOCUSED);
-  lv_obj_remove_state(s_secret, LV_STATE_FOCUSED);
-  lv_obj_add_state(ta, LV_STATE_FOCUSED);   // draws the cursor
+  fieldFocus(s_name, false);
+  fieldFocus(s_secret, false);
   lv_keyboard_set_textarea(s_kb, ta);
+  fieldFocus(ta, true);
   if (lv_obj_has_flag(s_kb, LV_OBJ_FLAG_HIDDEN)) {
     lv_obj_remove_flag(s_kb, LV_OBJ_FLAG_HIDDEN);
     if (_body) lv_obj_set_height(_body, lv_obj_get_height(_body) - lv_obj_get_height(s_kb));
@@ -278,8 +278,8 @@ void UITask::channelEditKbHide() {
   using namespace chanview;
   if (!s_kb || lv_obj_has_flag(s_kb, LV_OBJ_FLAG_HIDDEN)) return;
   lv_obj_add_flag(s_kb, LV_OBJ_FLAG_HIDDEN);
-  lv_obj_remove_state(s_name, LV_STATE_FOCUSED);
-  lv_obj_remove_state(s_secret, LV_STATE_FOCUSED);
+  fieldFocus(s_name, false);
+  fieldFocus(s_secret, false);
   if (_body) lv_obj_set_height(_body, lv_obj_get_height(_body) + lv_obj_get_height(s_kb));
 }
 

examples/companion_radio/ui-lvgl/DiagScreen.h

@@ -99,7 +99,7 @@ static void setLive(int i, const diag::Row& r) {
   char v[40];
   showValue(r.label, r.value, v, sizeof(v));
   setText(lv.val, v);
-  if (!strcmp(r.label, "Errors")) lv_obj_set_style_text_color(lv.val, lv_color_hex(strcmp(r.value, "OK") ? theme::FAIL : theme::OK), 0);
+  if (!strcmp(r.label, "Errors")) setTextColor(lv.val, strcmp(r.value, "OK") ? theme::FAIL : theme::OK);
 }
 
 // A packets row: the name, then received and sent in fixed columns.

examples/companion_radio/ui-lvgl/GpsScreen.h

@@ -325,13 +325,13 @@ void UITask::refreshGps() {
   bool fix = false;
   if (!g) {
     setText(s_status, "Not available");
-    lv_obj_set_style_text_color(s_status, lv_color_hex(theme::TEXT_MUTED), 0);
+    setTextColor(s_status, theme::TEXT_MUTED);
   } else if (off) {
     setText(s_status, "GPS is off");
-    lv_obj_set_style_text_color(s_status, lv_color_hex(theme::TEXT_MUTED), 0);
+    setTextColor(s_status, theme::TEXT_MUTED);
   } else if (!data) {
     setText(s_status, "No data");
-    lv_obj_set_style_text_color(s_status, lv_color_hex(theme::FAIL), 0);
+    setTextColor(s_status, theme::FAIL);
 #if defined(SEEED_WIO_TRACKER_L2)
     snprintf(used, sizeof(used), "Nothing from the receiver (%lu B)", (unsigned long)gps.rxChars());
 #else
@@ -343,10 +343,10 @@ void UITask::refreshGps() {
     fix = g->hasFix();
     if (fix) {
       setText(s_status, g->fix_mode == 2 ? "2D fix" : "3D fix");
-      lv_obj_set_style_text_color(s_status, lv_color_hex(theme::OK), 0);
+      setTextColor(s_status, theme::OK);
     } else {
       setText(s_status, "Searching");
-      lv_obj_set_style_text_color(s_status, lv_color_hex(theme::ACCENT), 0);
+      setTextColor(s_status, theme::ACCENT);
     }
     snprintf(used, sizeof(used), "%d of %d used", fix ? (used_n ? used_n : g->sats_used) : 0, s_n);
     snprintf(inview, sizeof(inview), "%d heard", tracked);

examples/companion_radio/ui-lvgl/HomeScreen.h

@@ -721,8 +721,7 @@ void UITask::homeMapLayout() {
   int shown = 0;
   char sl[16];
   double lat = atan(sinh(M_PI * (1 - 2 * s_cy / (double)n))) * 180.0 / M_PI;
-  s_grid = { left, top, mapview::gridStep(s_z, lat, _prefs && _prefs->units_imperial, 48, sl, sizeof(sl)) };
-  lv_obj_invalidate(s_area);
+  mapview::setGrid(s_area, s_grid, left, top, mapview::gridStep(s_z, lat, _prefs && _prefs->units_imperial, 48, sl, sizeof(sl)));
   bool tiled = true;
   for (int j = 0; j < ROWS; j++) {
     for (int i = 0; i < COLS; i++) {

examples/companion_radio/ui-lvgl/MapAreas.h

@@ -28,6 +28,7 @@ static lv_obj_t* s_info = nullptr;
 static lv_obj_t* s_zoom = nullptr;
 static lv_obj_t* s_trails_btn = nullptr;
 static int       s_show = -1;            // area outlined while its sheet is open
+static bool      s_drawn = false;        // the layer's last draw put something on the map
 static bool      s_preview = false;      // the map is framing it; the view before:
 static double    s_prev_cx, s_prev_cy;
 static int       s_prev_z;
@@ -91,7 +92,8 @@ static void onRenameKb(lv_event_t* e) { s_ui->mapAreaRenameDone(lv_event_get_cod
 
 // LV_EVENT_DRAW_MAIN of the layer: outlines, the frame and the dim outside it.
 static void drawLayer(lv_event_t* e) {
-  if (!s_sel && s_show < 0) return;
+  s_drawn = s_sel || s_show >= 0;
+  if (!s_drawn) return;
   lv_obj_t* o = (lv_obj_t*)lv_event_get_target(e);
   lv_layer_t* layer = lv_event_get_layer(e);
   lv_area_t a;
@@ -291,7 +293,7 @@ void UITask::areaHandleDrag(int corner, int dx, int dy) {
 void UITask::areaLayout() {
   using namespace areas;
   if (!s_layer || !_map_area) return;
-  lv_obj_invalidate(s_layer);
+  if (s_sel || s_show >= 0 || s_drawn) lv_obj_invalidate(s_layer);   // not a full-map redraw each refresh for nothing
   if (!s_sel) return;
   double scale = (double)(1 << _map_z) * mapview::TILE_PX;
   double xs[2] = { s_fx0 * scale - mapview::s_left, s_fx1 * scale - mapview::s_left };

examples/companion_radio/ui-lvgl/MapScreen.h

@@ -72,6 +72,14 @@ struct Grid {
   bool tiled = false;         // every visible cell holds a tile: grid and fill are under them
 };
 static Grid s_grid;           // the main map's
+
+// The view moved (or the step changed): the grid with it, and the area
+// redrawn -- not when a refresh finds it where it was.
+static void setGrid(lv_obj_t* area, Grid& g, double left, double top, double step_px) {
+  if (g.left == left && g.top == top && g.step_px == step_px) return;
+  g.left = left; g.top = top; g.step_px = step_px;
+  lv_obj_invalidate(area);
+}
 static lv_obj_t* s_scale_bar = nullptr;
 static lv_obj_t* s_scale_lbl = nullptr;
 
@@ -280,10 +288,7 @@ static void onMapMarker(lv_event_t* e) {
 
 // The centre-on-me button in the accent colour while the map follows you.
 static void followShown(lv_obj_t* btn, bool on) {
-  if (!btn) return;
-  lv_obj_t* l = lv_obj_get_child(btn, 0);
-  lv_color_t c = lv_color_hex(on ? theme::ACCENT : theme::TEXT);
-  if (!lv_color_eq(lv_obj_get_style_text_color(l, LV_PART_MAIN), c)) lv_obj_set_style_text_color(l, c, 0);
+  if (btn) setTextColor(lv_obj_get_child(btn, 0), on ? theme::ACCENT : theme::TEXT);
 }
 
 static lv_obj_t* mapButton(lv_obj_t* parent, const char* text, lv_event_cb_t cb) {
@@ -505,12 +510,11 @@ void UITask::layoutMap() {
   {   // the grid under the tiles, the scale bar
     char sl[16];
     double lat = atan(sinh(M_PI * (1 - 2 * _map_cy / (double)(1 << _map_z)))) * 180.0 / M_PI;
-    mapview::s_grid = { left, top, mapview::gridStep(_map_z, lat, _prefs && _prefs->units_imperial, 56, sl, sizeof(sl)) };
+    mapview::setGrid(_map_area, mapview::s_grid, left, top, mapview::gridStep(_map_z, lat, _prefs && _prefs->units_imperial, 56, sl, sizeof(sl)));
     if (mapview::s_scale_lbl) {
       setText(mapview::s_scale_lbl, sl);
       lv_obj_set_width(mapview::s_scale_bar, (int)lround(mapview::s_grid.step_px));
     }
-    lv_obj_invalidate(_map_area);
   }
   int tx0 = (int)floor(left / mapview::TILE_PX), ty0 = (int)floor(top / mapview::TILE_PX);
   int n = 1 << _map_z;

examples/companion_radio/ui-lvgl/NavMap.h

@@ -280,7 +280,16 @@ static void layoutNavTrail(double scale) {
   using namespace navmap;
   s_pts_n = 0;
   if (!s_trail) return;
-  lv_obj_invalidate(s_trail);
+  {   // redrawn when the view or the trail changed, not on every map refresh
+    static double v_left = NAN, v_top, v_scale;
+    static int v_n;
+    static uint32_t v_gen, v_seq;
+    if (v_left != mapview::s_left || v_top != mapview::s_top || v_scale != scale || v_n != s_sync_n || v_gen != s_sync_gen || v_seq != s_sync_seq) {
+      v_left = mapview::s_left; v_top = mapview::s_top; v_scale = scale;
+      v_n = s_sync_n; v_gen = s_sync_gen; v_seq = s_sync_seq;
+      lv_obj_invalidate(s_trail);
+    }
+  }
   int n = s_sync_n;
   if (!s_pts || n < 2) return;
   lv_area_t a;
@@ -393,12 +402,12 @@ void UITask::refreshNavBar() {
   bool pos = navCurrentTarget(tlat, tlon, name, sizeof(name), person, set);
   if (!set) {
     setText(_nav_title, "No target");
-    lv_obj_set_style_text_color(_nav_title, lv_color_hex(theme::TEXT_MUTED), 0);
+    setTextColor(_nav_title, theme::TEXT_MUTED);
     setText(_nav_info, "Tap here to pick a target, or hold the map on a spot");
     lv_obj_add_flag(_nav_clear, LV_OBJ_FLAG_HIDDEN);
     return;
   }
-  lv_obj_set_style_text_color(_nav_title, lv_color_hex(theme::ACCENT), 0);
+  setTextColor(_nav_title, theme::ACCENT);
   lv_obj_remove_flag(_nav_clear, LV_OBJ_FLAG_HIDDEN);
   setTextFmt(_nav_title, "%s %s", navmap::s_tb.active() ? LV_SYMBOL_LOOP : person ? UI_SYMBOL_USERS : UI_SYMBOL_FLAG,
                         name);
@@ -1039,19 +1048,19 @@ void UITask::refreshNavTools() {
   navmap::fmtDuration(dur, sizeof(dur), ts.elapsedSeconds());
   const char* state = !ts.isActive() ? (ts.empty() ? "Not recording" : "Stopped")
                     : ts.isPaused() ? "Paused (standing still)" : "Recording";
-  if (ts.empty()) lv_label_set_text(_nav_trail_lbl, state);
-  else lv_label_set_text_fmt(_nav_trail_lbl, "%s  -  %s, %s, %d points", state, dist, dur, ts.count());
-  lv_label_set_text(_nav_trail_btn, ts.isActive() ? LV_SYMBOL_STOP " Stop" : LV_SYMBOL_PLAY " Record");
-  lv_label_set_text(_nav_tb_btn, navmap::s_tb.active() ? LV_SYMBOL_STOP " Stop back" : LV_SYMBOL_LOOP " Track back");
+  if (ts.empty()) setText(_nav_trail_lbl, state);
+  else setTextFmt(_nav_trail_lbl, "%s  -  %s, %s, %d points", state, dist, dur, ts.count());
+  setText(_nav_trail_btn, ts.isActive() ? LV_SYMBOL_STOP " Stop" : LV_SYMBOL_PLAY " Record");
+  setText(_nav_tb_btn, navmap::s_tb.active() ? LV_SYMBOL_STOP " Stop back" : LV_SYMBOL_LOOP " Track back");
 
   if (_prefs->loc_share_enabled) {
     char left[12];
     navmap::fmtDuration(left, sizeof(left), _core->live_share.remainingSecs());
-    lv_label_set_text_fmt(_nav_share_lbl, "Sharing your position  -  %s left", left);
+    setTextFmt(_nav_share_lbl, "Sharing your position  -  %s left", left);
   } else {
-    lv_label_set_text(_nav_share_lbl, "Off. Sends your position while you move, then stops by itself.");
+    setText(_nav_share_lbl, "Off. Sends your position while you move, then stops by itself.");
   }
-  lv_label_set_text(_nav_share_btn, _prefs->loc_share_enabled ? LV_SYMBOL_STOP " Stop sharing" : LV_SYMBOL_PLAY " Share live");
+  setText(_nav_share_btn, _prefs->loc_share_enabled ? LV_SYMBOL_STOP " Stop sharing" : LV_SYMBOL_PLAY " Share live");
 }
 
 void UITask::navSetShareTarget(int sel) {

examples/companion_radio/ui-lvgl/UITask.cpp

@@ -12,6 +12,7 @@
 #endif
 #include <new>
 #include <src/core/lv_obj_event_private.h>   // lv_cover_check_info_t (coversOwnArea)
+#include <src/widgets/label/lv_label_private.h>   // lv_label_t (labelShows)
 #include <stdarg.h>
 #include <sys/stat.h>
 
@@ -170,14 +171,32 @@ static lv_obj_t* label(lv_obj_t* parent, const char* text, const lv_font_t* font
   lv_obj_set_style_text_color(l, lv_color_hex(color), 0);
   return l;
 }
+// Whether label `l` holds `text`. A LV_LABEL_LONG_DOT one that's cut short
+// has the "..." written into its own copy of the text, the bytes they cover
+// kept aside (lv_label_set_dots): it's read back past them.
+static bool labelShows(lv_obj_t* l, const char* text) {
+  const lv_label_t* lb = (const lv_label_t*)l;
+  const char* cur = lb->text;
+  if (!cur) return false;
+  uint32_t d = lb->dot_begin;
+  if (d == 0xFFFFFFFF || lb->static_txt) return strcmp(cur, text) == 0;   // no dots (lv_label.c LV_LABEL_DOT_BEGIN_INV)
+  if (strncmp(cur, text, d) != 0) return false;
+  size_t k = strnlen(lb->dot, sizeof(lb->dot));   // the bytes under the dots
+  if (strncmp(lb->dot, text + d, k) != 0) return false;
+  return k < sizeof(lb->dot) ? text[d + k] == '\0' : strcmp(cur + d + k, text + d + k) == 0;
+}
 // A label's text, set only when it differs: LVGL redraws a label on every
 // set_text, the same text or not, and the refreshes that run every second
 // mostly write back what's already there.
 static void setText(lv_obj_t* l, const char* text) {
-  const char* cur = lv_label_get_text(l);
-  if (cur && strcmp(cur, text) == 0) return;
+  if (labelShows(l, text)) return;
   lv_label_set_text(l, text);
 }
+// The same for a text colour: LVGL restyles, and redraws, on every set.
+static void setTextColor(lv_obj_t* l, uint32_t color) {
+  lv_color_t c = lv_color_hex(color);
+  if (!lv_color_eq(lv_obj_get_style_text_color(l, LV_PART_MAIN), c)) lv_obj_set_style_text_color(l, c, 0);
+}
 static void setTextFmt(lv_obj_t* l, const char* fmt, ...) __attribute__((format(printf, 2, 3)));
 static void setTextFmt(lv_obj_t* l, const char* fmt, ...) {
   char b[160];
@@ -842,6 +861,16 @@ static lv_obj_t* textField(lv_obj_t* parent, const char* placeholder = NULL) {
   lv_obj_set_style_border_width(ta, 2, LV_PART_CURSOR | LV_STATE_FOCUSED);
   return ta;
 }
+// A field's cursor shown (FOCUSED, blinking) or not. LVGL starts and stops
+// the blink only as the cursor moves, so it's nudged here: left running on a
+// field without focus, it redraws the field every 400 ms for nothing.
+// (lv_keyboard_set_textarea() focuses the field it's given.)
+static void fieldFocus(lv_obj_t* ta, bool on) {
+  if (!ta) return;
+  if (on) lv_obj_add_state(ta, LV_STATE_FOCUSED);
+  else lv_obj_remove_state(ta, LV_STATE_FOCUSED);
+  lv_textarea_set_cursor_pos(ta, lv_textarea_get_cursor_pos(ta));
+}
 
 // The primary action of a screen or popup: full amber, dark text (Theme.h);
 // call after its label is made.
@@ -1857,6 +1886,17 @@ void UITask::buildStatusBar() {
   refreshStatusBar();
 }
 
+// lv_obj_align_to(o, base, LV_ALIGN_OUT_LEFT_MID, dx, 0), `base` a sibling,
+// for what's refreshed every second: LVGL restyles the box on every call, so
+// it redraws moved or not -- here it's only moved.
+static void placeLeftOf(lv_obj_t* o, lv_obj_t* base, int32_t dx) {
+  lv_obj_update_layout(o);
+  int32_t x = lv_obj_get_x(base) - lv_obj_get_width(o) + dx;
+  int32_t y = lv_obj_get_y(base) + (lv_obj_get_height(base) - lv_obj_get_height(o)) / 2;
+  if (lv_obj_get_style_align(o, LV_PART_MAIN) != LV_ALIGN_TOP_LEFT || lv_obj_get_x(o) != x || lv_obj_get_y(o) != y)
+    lv_obj_align_to(o, base, LV_ALIGN_OUT_LEFT_MID, dx, 0);
+}
+
 void UITask::refreshStatusBar() {
   if (!_status_time) return;
   struct tm ti;
@@ -1884,7 +1924,7 @@ void UITask::refreshStatusBar() {
   lv_obj_t* left_of = _status_batt;   // the icons pack up to this
   if (_board->isExternalPowered()) {
     lv_obj_remove_flag(_status_chg, LV_OBJ_FLAG_HIDDEN);
-    lv_obj_align_to(_status_chg, _status_batt, LV_ALIGN_OUT_LEFT_MID, -2, 0);
+    placeLeftOf(_status_chg, _status_batt, -2);
     left_of = _status_chg;
   } else lv_obj_add_flag(_status_chg, LV_OBJ_FLAG_HIDDEN);
 
@@ -1921,7 +1961,7 @@ void UITask::refreshStatusBar() {
     for (int i = n - 1; i >= 0; i--)   // the icon font gives each the same size and cell
       label(_status_icons, icons[i].sym, THEME_FONT_ICONS, icons[i].col);
   }
-  lv_obj_align_to(_status_icons, left_of, LV_ALIGN_OUT_LEFT_MID, -5, 0);
+  placeLeftOf(_status_icons, left_of, -5);
 }
 
 void UITask::setGps(bool on) {
@@ -3131,10 +3171,10 @@ void UITask::setKeyboardVisible(bool show) {
   if (show == !lv_obj_has_flag(_keyboard, LV_OBJ_FLAG_HIDDEN)) return;
   if (show) {
     lv_obj_remove_flag(_keyboard, LV_OBJ_FLAG_HIDDEN);
-    lv_obj_add_state(_compose_ta, LV_STATE_FOCUSED);
+    fieldFocus(_compose_ta, true);
   } else {
     lv_obj_add_flag(_keyboard, LV_OBJ_FLAG_HIDDEN);
-    lv_obj_remove_state(_compose_ta, LV_STATE_FOCUSED);
+    fieldFocus(_compose_ta, false);
   }
   if (_header && _body) {
     int top = theme::STATUS_H + (show ? 0 : lv_obj_get_height(_header));
@@ -3221,6 +3261,7 @@ void UITask::buildThread() {
     _keyboard = kb::create(body, _prefs);   // phone-style, scripts from prefs, hold for accents (Keyboard.h)
     lv_obj_set_size(_keyboard, LV_PCT(100), 124);
     lv_keyboard_set_textarea(_keyboard, _compose_ta);
+    fieldFocus(_compose_ta, false);   // until the keyboard is up
     lv_obj_add_event_cb(_keyboard, onKeyboard, LV_EVENT_READY, _keyboard);
     lv_obj_add_event_cb(_keyboard, onKeyboard, LV_EVENT_CANCEL, _keyboard);
     lv_obj_add_flag(_keyboard, LV_OBJ_FLAG_HIDDEN);

examples/companion_radio/ui-lvgl/WifiScreen.h

@@ -152,10 +152,10 @@ static void wifiRebuild(UITask* ui, lv_obj_t*& body) {
 
 void UITask::wifiEdit(lv_obj_t* ta) {
   if (!_wifi_kb) return;
-  lv_obj_remove_state(_wifi_ssid, LV_STATE_FOCUSED);
-  lv_obj_remove_state(_wifi_pass, LV_STATE_FOCUSED);
-  lv_obj_add_state(ta, LV_STATE_FOCUSED);   // draws the cursor
+  fieldFocus(_wifi_ssid, false);
+  fieldFocus(_wifi_pass, false);
   lv_keyboard_set_textarea(_wifi_kb, ta);
+  fieldFocus(ta, true);
   if (lv_obj_has_flag(_wifi_kb, LV_OBJ_FLAG_HIDDEN)) {
     lv_obj_remove_flag(_wifi_kb, LV_OBJ_FLAG_HIDDEN);
     if (_body) lv_obj_set_height(_body, lv_obj_get_height(_body) - lv_obj_get_height(_wifi_kb));
@@ -167,8 +167,8 @@ void UITask::wifiEdit(lv_obj_t* ta) {
 void UITask::wifiKeyboardHide() {
   if (!_wifi_kb || lv_obj_has_flag(_wifi_kb, LV_OBJ_FLAG_HIDDEN)) return;
   lv_obj_add_flag(_wifi_kb, LV_OBJ_FLAG_HIDDEN);
-  lv_obj_remove_state(_wifi_ssid, LV_STATE_FOCUSED);
-  lv_obj_remove_state(_wifi_pass, LV_STATE_FOCUSED);
+  fieldFocus(_wifi_ssid, false);
+  fieldFocus(_wifi_pass, false);
   if (_body) lv_obj_set_height(_body, lv_obj_get_height(_body) + lv_obj_get_height(_wifi_kb));
 }
 

examples/companion_radio/ui-lvgl/map/VectorLabels.h

@@ -118,8 +118,12 @@ static void clear() {
 // Places the labels for a view (world px of its top-left at zoom z, size;
 // `bottom` px taken by a bar along the bottom).
 static void layout(double left, double top, int w, int h, int z, bool on, int bottom) {
+  int had = s_n;
   clear();
-  if (!on || z < 10 || !s_layer || !s_placed || !s_cand) { if (s_layer) lv_obj_invalidate(s_layer); return; }
+  if (!on || z < 10 || !s_layer || !s_placed || !s_cand) {   // none: those shown go (none shown, nothing to redraw)
+    if (s_layer && had) lv_obj_invalidate(s_layer);
+    return;
+  }
   int dz = z >= 14 ? 14 : z >= 12 ? 12 : 10, k = z - dz;
   double span = (double)(TILE_PX << k);   // a data tile, in px at zoom z
   int x0 = (int)floor(left / span), x1 = (int)floor((left + w) / span);