diff --git a/include/llmr/map/coverage.hpp b/include/llmr/map/coverage.hpp
new file mode 100644
index 000000000..0d50cd9f7
--- /dev/null
+++ b/include/llmr/map/coverage.hpp
@@ -0,0 +1,13 @@
+#ifndef LLMR_MAP_COVERAGE
+#define LLMR_MAP_COVERAGE
+
+#include <llmr/util/vec.hpp>
+#include <forward_list>
+
+namespace llmr {
+
+std::forward_list<vec3<int32_t>> covering_tiles(int32_t zoom, const box& points);
+
+}
+
+#endif
diff --git a/include/llmr/map/transform.hpp b/include/llmr/map/transform.hpp
index a628bf33d..4a07c98f9 100644
--- a/include/llmr/map/transform.hpp
+++ b/include/llmr/map/transform.hpp
@@ -51,7 +51,7 @@ public:
     void stopScaling();
 
     // Temporary
-    void mapCornersToBox(uint32_t z, box& b) const;
+    box mapCornersToBox(uint32_t z) const;
 
 private:
     void setScaleXY(double new_scale, double xn, double yn, double duration = 0);
diff --git a/include/llmr/util/vec.hpp b/include/llmr/util/vec.hpp
index 70aa11134..dbc31187b 100644
--- a/include/llmr/util/vec.hpp
+++ b/include/llmr/util/vec.hpp
@@ -55,6 +55,7 @@ struct vec4 {
 
 struct box {
     vec2<double> tl, tr, bl, br;
+    vec2<double> center;
 };
 
 }
diff --git a/src/map/coverage.cpp b/src/map/coverage.cpp
new file mode 100644
index 000000000..e65e3469d
--- /dev/null
+++ b/src/map/coverage.cpp
@@ -0,0 +1,98 @@
+#include <llmr/map/coverage.hpp>
+#include <functional>
+#include <cmath>
+
+// Taken from polymaps src/Layer.js
+// https://github.com/simplegeo/polymaps/blob/master/src/Layer.js#L333-L383
+
+struct edge {
+    double x0 = 0, y0 = 0;
+    double x1 = 0, y1 = 0;
+    double dx = 0, dy = 0;
+    edge(double x0, double y0, double x1, double y1, double dx, double dy)
+        : x0(x0), y0(y0), x1(x1), y1(y1), dx(dx), dy(dy) {}
+};
+
+typedef const std::function<void(int32_t, int32_t, int32_t, int32_t)> ScanLine;
+
+// scan-line conversion
+edge _edge(const llmr::vec2<double> a, const llmr::vec2<double> b) {
+    if (a.y > b.y) {
+        return { b.x, b.y, a.x, a.y, a.x - b.x, a.y - b.y };
+    } else {
+        return { a.x, a.y, b.x, b.y, b.x - a.x, b.y - a.y };
+    }
+}
+
+// scan-line conversion
+void _scanSpans(edge e0, edge e1, int32_t ymin, int32_t ymax, ScanLine scanLine) {
+    double y0 = fmax(ymin, floor(e1.y0)),
+           y1 = fmin(ymax, ceil(e1.y1));
+
+    // sort edges by x-coordinate
+    if ((e0.x0 == e1.x0 && e0.y0 == e1.y0) ?
+        (e0.x0 + e1.dy / e0.dy * e0.dx < e1.x1) :
+        (e0.x1 - e1.dy / e0.dy * e0.dx < e1.x0)) {
+        std::swap(e0, e1);
+    }
+
+    // scan lines!
+    double m0 = e0.dx / e0.dy,
+           m1 = e1.dx / e1.dy,
+           d0 = e0.dx > 0, // use y + 1 to compute x0
+           d1 = e1.dx < 0; // use y + 1 to compute x1
+    for (int32_t y = y0; y < y1; y++) {
+        double x0 = m0 * fmax(0, fmin(e0.dy, y + d0 - e0.y0)) + e0.x0,
+            x1 = m1 * fmax(0, fmin(e1.dy, y + d1 - e1.y0)) + e1.x0;
+        scanLine(floor(x1), ceil(x0), y, ymax);
+    }
+}
+
+// scan-line conversion
+void _scanTriangle(const llmr::vec2<double> a, const llmr::vec2<double> b, const llmr::vec2<double> c, int32_t ymin, int32_t ymax, ScanLine& scanLine) {
+    edge ab = _edge(a, b);
+    edge bc = _edge(b, c);
+    edge ca = _edge(c, a);
+
+    // sort edges by y-length
+    if (ab.dy > bc.dy) { std::swap(ab, bc); }
+    if (ab.dy > ca.dy) { std::swap(ab, ca); }
+    if (bc.dy > ca.dy) { std::swap(bc, ca); }
+
+    // scan span! scan span!
+    if (ab.dy) _scanSpans(ca, ab, ymin, ymax, scanLine);
+    if (bc.dy) _scanSpans(ca, bc, ymin, ymax, scanLine);
+}
+
+std::forward_list<llmr::vec3<int32_t>> llmr::covering_tiles(int32_t zoom, const box& points) {
+    int32_t dim = pow(2, zoom);
+    std::forward_list<vec3<int32_t>> tiles;
+
+    auto scanLine = [&tiles, zoom](int32_t x0, int32_t x1, int32_t y, int32_t ymax) {
+        int32_t x, wx;
+        if (y >= 0 && y <= ymax) {
+            for (x = x0; x < x1; x++) {
+                wx = (x + ymax) % ymax;
+                tiles.emplace_front(wx, y, zoom);
+            }
+        }
+    };
+
+    // Divide the screen up in two triangles and scan each of them:
+    // \---+
+    // | \ |
+    // +---\.
+    _scanTriangle(points.tl, points.tr, points.br, 0, dim, scanLine);
+    _scanTriangle(points.br, points.bl, points.tl, 0, dim, scanLine);
+
+    const vec2<double>& center = points.center;
+    tiles.sort([&center](const vec3<int32_t>& a, const vec3<int32_t>& b) {
+        // Sorts by distance from the box center
+        return fabs(a.x - center.x) + fabs(a.y - center.y) <
+               fabs(b.x - center.x) + fabs(b.y - center.y);
+    });
+
+    tiles.unique();
+
+    return tiles;
+}
diff --git a/src/map/map.cpp b/src/map/map.cpp
index dc6780951..68360db03 100644
--- a/src/map/map.cpp
+++ b/src/map/map.cpp
@@ -3,6 +3,7 @@
 #include <llmr/platform/platform.hpp>
 #include <llmr/style/resources.hpp>
 #include <llmr/style/sprite.hpp>
+#include <llmr/map/coverage.hpp>
 
 #include <algorithm>
 
@@ -329,27 +330,12 @@ bool Map::updateTiles() {
     int32_t min_covering_zoom = zoom - 10;
     if (min_covering_zoom < min_zoom) min_covering_zoom = min_zoom;
 
-
-    int32_t max_dim = pow(2, zoom);
-
     // Map four viewport corners to pixel coordinates
-    box box;
-    transform.mapCornersToBox(zoom, box);
+    box box = transform.mapCornersToBox(zoom);
 
-    vec2<int32_t> tl, br;
-    tl.x = fmax(0, floor(fmin(box.tl.x, box.bl.x)));
-    tl.y = fmax(0, floor(fmin(box.tl.y, box.tr.y)));
-    br.x = fmin(max_dim, ceil(fmax(box.tr.x, box.br.x)));
-    br.y = fmin(max_dim, ceil(fmax(box.bl.y, box.br.y)));
-
-
-    // TODO: Discard tiles that are outside the viewport
-    std::forward_list<Tile::ID> required;
-    for (int32_t y = tl.y; y < br.y; ++y) {
-        for (int32_t x = tl.x; x < br.x; ++x) {
-            required.emplace_front(x, y, zoom);
-        }
-    }
+    // Performs a scanline algorithm search that covers the rectangle of the box
+    // and sorts them by proximity to the center.
+    std::forward_list<Tile::ID> required = llmr::covering_tiles(zoom, box);
 
     // Retain is a list of tiles that we shouldn't delete, even if they are not
     // the most ideal tile for the current viewport. This may include tiles like
diff --git a/src/map/transform.cpp b/src/map/transform.cpp
index 12c55e1f9..f8f8380a7 100644
--- a/src/map/transform.cpp
+++ b/src/map/transform.cpp
@@ -271,33 +271,37 @@ double Transform::getAngle() const {
     return angle;
 }
 
-void Transform::mapCornersToBox(uint32_t z, box& b) const {
+box Transform::mapCornersToBox(uint32_t z) const {
     const double ref_scale = pow(2, z);
 
-    // Keep the map as upright as possible.
-    double local_angle = angle;
-    if (local_angle >= M_PI_2) local_angle -= M_PI;
-    if (local_angle < -M_PI_2) local_angle += M_PI;
-
-    const double angle_sin = sin(-local_angle);
-    const double angle_cos = cos(-local_angle);
+    const double angle_sin = sin(-angle);
+    const double angle_cos = cos(-angle);
 
     const double w_2 = width / 2;
     const double h_2 = height / 2;
-    const double ss_1 = ref_scale / (scale * util::tileSize);
-    const double ss_2 = (scale * util::tileSize) / 2;
+    const double ss_0 = scale * util::tileSize;
+    const double ss_1 = ref_scale / ss_0;
+    const double ss_2 = ss_0 / 2.0;
 
     // Calculate the corners of the map view. The resulting coordinates will be
     // in fractional tile coordinates.
+    box b;
+
     b.tl.x = ((-w_2) * angle_cos - (-h_2) * angle_sin + ss_2 - x) * ss_1;
     b.tl.y = ((-w_2) * angle_sin + (-h_2) * angle_cos + ss_2 - y) * ss_1;
+
     b.tr.x = ((+w_2) * angle_cos - (-h_2) * angle_sin + ss_2 - x) * ss_1;
     b.tr.y = ((+w_2) * angle_sin + (-h_2) * angle_cos + ss_2 - y) * ss_1;
+
     b.bl.x = ((-w_2) * angle_cos - (+h_2) * angle_sin + ss_2 - x) * ss_1;
     b.bl.y = ((-w_2) * angle_sin + (+h_2) * angle_cos + ss_2 - y) * ss_1;
+
     b.br.x = ((+w_2) * angle_cos - (+h_2) * angle_sin + ss_2 - x) * ss_1;
     b.br.y = ((+w_2) * angle_sin + (+h_2) * angle_cos + ss_2 - y) * ss_1;
 
-    // Quick hack: use the entire non-rotated bounding box.
+    b.center.x = (ss_2 - x) * ss_1;
+    b.center.y = (ss_2 - y) * ss_1;
+
+    return b;
 }
 
diff --git a/src/renderer/painter.cpp b/src/renderer/painter.cpp
index 6cc6eb009..90ba77631 100644
--- a/src/renderer/painter.cpp
+++ b/src/renderer/painter.cpp
@@ -119,7 +119,6 @@ void Painter::drawClippingMask(const mat4& matrix, uint8_t clip_id) {
 
 void Painter::finishClippingMask() {
     glColorMask(true, true, true, true);
-    glEnable(GL_STENCIL_TEST);
     glEnable(GL_DEPTH_TEST);
     glStencilMask(0x0);
 }