matplotlib · jklymak · Jun 23, 2022 · Jun 16, 2022 · Jun 16, 2022 · Jun 16, 2022
diff --git a/doc/users/next_whats_new/url_active_areas_rotate.rst b/doc/users/next_whats_new/url_active_areas_rotate.rst
@@ -0,0 +1,5 @@
+The active URL area rotates when link text is rotated
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+When link text is rotated in a matplotlib figure, the active URL
+area will now include the link area. Previously, the active area
+remained in the original, non-rotated, position.
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
@@ -250,6 +250,68 @@ def _datetime_to_pdf(d):
     return r
 
 
+def _calculate_quad_point_coordinates(x, y, width, height, angle=0):
+    """
+    Calculate the coordinates of rectangle when rotated by angle around x, y
+    """
+
+    angle = math.radians(-angle)
+    sin_angle = math.sin(angle)
+    cos_angle = math.cos(angle)
+    a = x + height * sin_angle
+    b = y + height * cos_angle
+    c = x + width * cos_angle + height * sin_angle
+    d = y - width * sin_angle + height * cos_angle
+    e = x + width * cos_angle
+    f = y - width * sin_angle
+    return ((x, y), (e, f), (c, d), (a, b))
+
+
+def _get_coordinates_of_block(x, y, width, height, angle=0):
+    """
+    Get the coordinates of rotated rectangle and rectangle that covers the
+    rotated rectangle.
+    """
+
+    vertices = _calculate_quad_point_coordinates(x, y, width,
+                                                 height, angle)
+
+    # Find min and max values for rectangle
+    # adjust so that QuadPoints is inside Rect
+    # PDF docs says that QuadPoints should be ignored if any point lies
+    # outside Rect, but for Acrobat it is enough that QuadPoints is on the
+    # border of Rect.
+
+    pad = 0.00001 if angle % 90 else 0
+    min_x = min(v[0] for v in vertices) - pad
+    min_y = min(v[1] for v in vertices) - pad
+    max_x = max(v[0] for v in vertices) + pad
+    max_y = max(v[1] for v in vertices) + pad
+    return (tuple(itertools.chain.from_iterable(vertices)),
+            (min_x, min_y, max_x, max_y))
+
+
+def _get_link_annotation(gc, x, y, width, height, angle=0):
+    """
+    Create a link annotation object for embedding URLs.
+    """
+    quadpoints, rect = _get_coordinates_of_block(x, y, width, height, angle)
+    link_annotation = {
+        'Type': Name('Annot'),
+        'Subtype': Name('Link'),
+        'Rect': rect,
+        'Border': [0, 0, 0],
+        'A': {
+            'S': Name('URI'),
+            'URI': gc.get_url(),
+        },
+    }
+    if angle % 90:
+        # Add QuadPoints
+        link_annotation['QuadPoints'] = quadpoints
+    return link_annotation
+
+
 def pdfRepr(obj):
     """Map Python objects to PDF syntax."""
 
@@ -2154,17 +2216,8 @@ def draw_mathtext(self, gc, x, y, s, prop, angle):
             self._text2path.mathtext_parser.parse(s, 72, prop)
 
         if gc.get_url() is not None:
-            link_annotation = {
-                'Type': Name('Annot'),
-                'Subtype': Name('Link'),
-                'Rect': (x, y, x + width, y + height),
-                'Border': [0, 0, 0],
-                'A': {
-                    'S': Name('URI'),
-                    'URI': gc.get_url(),
-                },
-            }
-            self.file._annotations[-1][1].append(link_annotation)
+            self.file._annotations[-1][1].append(_get_link_annotation(
+                gc, x, y, width, height, angle))
 
         fonttype = mpl.rcParams['pdf.fonttype']
 
@@ -2220,17 +2273,8 @@ def draw_tex(self, gc, x, y, s, prop, angle, *, mtext=None):
             page, = dvi
 
         if gc.get_url() is not None:
-            link_annotation = {
-                'Type': Name('Annot'),
-                'Subtype': Name('Link'),
-                'Rect': (x, y, x + page.width, y + page.height),
-                'Border': [0, 0, 0],
-                'A': {
-                    'S': Name('URI'),
-                    'URI': gc.get_url(),
-                },
-            }
-            self.file._annotations[-1][1].append(link_annotation)
+            self.file._annotations[-1][1].append(_get_link_annotation(
+                gc, x, y, page.width, page.height, angle))
 
         # Gather font information and do some setup for combining
         # characters into strings. The variable seq will contain a
@@ -2330,17 +2374,8 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
         if gc.get_url() is not None:
             font.set_text(s)
             width, height = font.get_width_height()
-            link_annotation = {
-                'Type': Name('Annot'),
-                'Subtype': Name('Link'),
-                'Rect': (x, y, x + width / 64, y + height / 64),
-                'Border': [0, 0, 0],
-                'A': {
-                    'S': Name('URI'),
-                    'URI': gc.get_url(),
-                },
-            }
-            self.file._annotations[-1][1].append(link_annotation)
+            self.file._annotations[-1][1].append(_get_link_annotation(
+                gc, x, y, width / 64, height / 64, angle))
 
         # If fonttype is neither 3 nor 42, emit the whole string at once
         # without manual kerning.

diff --git a/lib/matplotlib/tests/test_backend_pdf.py b/lib/matplotlib/tests/test_backend_pdf.py
@@ -243,10 +243,37 @@ def test_text_urls():
                     (a for a in annots if a.A.URI == f'{test_url}{fragment}'),
                     None)
                 assert annot is not None
+                assert getattr(annot, 'QuadPoints', None) is None
                 # Positions in points (72 per inch.)
                 assert annot.Rect[1] == decimal.Decimal(y) * 72
 
 
+def test_text_rotated_urls():
+    pikepdf = pytest.importorskip('pikepdf')
+
+    test_url = 'https://test_text_urls.matplotlib.org/'
+
+    fig = plt.figure(figsize=(1, 1))
+    fig.text(0.1, 0.1, 'N', rotation=45, url=f'{test_url}')
+
+    with io.BytesIO() as fd:
+        fig.savefig(fd, format='pdf')
+
+        with pikepdf.Pdf.open(fd) as pdf:
+            annots = pdf.pages[0].Annots
+
+            # Iteration over Annots must occur within the context manager,
+            # otherwise it may fail depending on the pdf structure.
+            annot = next(
+                (a for a in annots if a.A.URI == f'{test_url}'),
+                None)
+            assert annot is not None
+            assert getattr(annot, 'QuadPoints', None) is not None
+            # Positions in points (72 per inch)
+            assert annot.Rect[0] == \
+               annot.QuadPoints[6] - decimal.Decimal('0.00001')
+
+
 @needs_usetex
 def test_text_urls_tex():
     pikepdf = pytest.importorskip('pikepdf')