matplotlib · WeatherGod · Jan 20, 2022 · Dec 23, 2021 · Jan 4, 2022 · Jan 5, 2022
diff --git a/doc/users/next_whats_new/3d_plot_focal_length.rst b/doc/users/next_whats_new/3d_plot_focal_length.rst
@@ -0,0 +1,31 @@
+Give the 3D camera a custom focal length
+----------------------------------------
+
+Users can now better mimic real-world cameras by specifying the focal length of
+the virtual camera in 3D plots. The default focal length of 1 corresponds to a
+Field of View (FOV) of 90 deg, and is backwards-compatible with existing 3D
+plots. An increased focal length between 1 and infinity "flattens" the image,
+while a decreased focal length between 1 and 0 exaggerates the perspective and
+gives the image more apparent depth.
+
+The focal length can be calculated from a desired FOV via the equation:
+
+.. mathmpl::
+
+    focal\_length = 1/\tan(FOV/2)
+
+.. plot::
+    :include-source: true
+
+    from mpl_toolkits.mplot3d import axes3d
+    import matplotlib.pyplot as plt
+    fig, axs = plt.subplots(1, 3, subplot_kw={'projection': '3d'},
+                            constrained_layout=True)
+    X, Y, Z = axes3d.get_test_data(0.05)
+    focal_lengths = [0.25, 1, 4]
+    for ax, fl in zip(axs, focal_lengths):
+        ax.plot_wireframe(X, Y, Z, rstride=10, cstride=10)
+        ax.set_proj_type('persp', focal_length=fl)
+        ax.set_title(f"focal_length = {fl}")
+    plt.tight_layout()
+    plt.show()
diff --git a/examples/mplot3d/projections.py b/examples/mplot3d/projections.py
@@ -0,0 +1,55 @@
+"""
+========================
+3D plot projection types
+========================
+
+Demonstrates the different camera projections for 3D plots, and the effects of
+changing the focal length for a perspective projection. Note that Matplotlib
+corrects for the 'zoom' effect of changing the focal length.
+
+The default focal length of 1 corresponds to a Field of View (FOV) of 90 deg.
+An increased focal length between 1 and infinity "flattens" the image, while a
+decreased focal length between 1 and 0 exaggerates the perspective and gives
+the image more apparent depth. In the limiting case, a focal length of
+infinity corresponds to an orthographic projection after correction of the
+zoom effect.
+
+You can calculate focal length from a FOV via the equation:
+
+.. mathmpl::
+
+    1 / \tan (FOV / 2)
+
+Or vice versa:
+
+.. mathmpl::
+
+    FOV = 2 * \atan (1 / focal length)
+
+"""
+
+from mpl_toolkits.mplot3d import axes3d
+import matplotlib.pyplot as plt
+
+
+fig, axs = plt.subplots(1, 3, subplot_kw={'projection': '3d'})
+
+# Get the test data
+X, Y, Z = axes3d.get_test_data(0.05)
+
+# Plot the data
+for ax in axs:
+    ax.plot_wireframe(X, Y, Z, rstride=10, cstride=10)
+
+# Set the orthographic projection.
+axs[0].set_proj_type('ortho')  # FOV = 0 deg
+axs[0].set_title("'ortho'\nfocal_length = ∞", fontsize=10)
+
+# Set the perspective projections
+axs[1].set_proj_type('persp')  # FOV = 90 deg
+axs[1].set_title("'persp'\nfocal_length = 1 (default)", fontsize=10)
+
+axs[2].set_proj_type('persp', focal_length=0.2)  # FOV = 157.4 deg
+axs[2].set_title("'persp'\nfocal_length = 0.2", fontsize=10)
+
+plt.show()
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -57,7 +57,7 @@ class Axes3D(Axes):
     def __init__(
             self, fig, rect=None, *args,
             elev=30, azim=-60, roll=0, sharez=None, proj_type='persp',
-            box_aspect=None, computed_zorder=True,
+            box_aspect=None, computed_zorder=True, focal_length=None,
             **kwargs):
         """
         Parameters
@@ -104,6 +104,13 @@ def __init__(
             This behavior is deprecated in 3.4, the default will
             change to False in 3.5.  The keyword will be undocumented
             and a non-False value will be an error in 3.6.
+        focal_length : float, default: None
+            For a projection type of 'persp', the focal length of the virtual
+            camera. Must be > 0. If None, defaults to 1.
+            For a projection type of 'ortho', must be set to either None
+            or infinity (numpy.inf). If None, defaults to infinity.
+            The focal length can be computed from a desired Field Of View via
+            the equation: focal_length = 1/tan(FOV/2)
 
         **kwargs
             Other optional keyword arguments:
@@ -117,7 +124,7 @@ def __init__(
         self.initial_azim = azim
         self.initial_elev = elev
         self.initial_roll = roll
-        self.set_proj_type(proj_type)
+        self.set_proj_type(proj_type, focal_length)
         self.computed_zorder = computed_zorder
 
         self.xy_viewLim = Bbox.unit()
@@ -989,18 +996,33 @@ def view_init(self, elev=None, azim=None, roll=None, vertical_axis="z"):
             dict(x=0, y=1, z=2), vertical_axis=vertical_axis
         )
 
-    def set_proj_type(self, proj_type):
+    def set_proj_type(self, proj_type, focal_length=None):
         """
         Set the projection type.
 
         Parameters
         ----------
         proj_type : {'persp', 'ortho'}
-        """
-        self._projection = _api.check_getitem({
-            'persp': proj3d.persp_transformation,
-            'ortho': proj3d.ortho_transformation,
-        }, proj_type=proj_type)
+            The projection type.
+        focal_length : float, default: None
+            For a projection type of 'persp', the focal length of the virtual
+            camera. Must be > 0. If None, defaults to 1.
+            The focal length can be computed from a desired Field Of View via
+            the equation: focal_length = 1/tan(FOV/2)
+        """
+        _api.check_in_list(['persp', 'ortho'], proj_type=proj_type)
+        if proj_type == 'persp':
+            if focal_length is None:
+                focal_length = 1
+            elif focal_length <= 0:
+                raise ValueError(f"focal_length = {focal_length} must be "
+                                 "greater than 0")
+            self._focal_length = focal_length
+        elif proj_type == 'ortho':
+            if focal_length not in (None, np.inf):
+                raise ValueError(f"focal_length = {focal_length} must be "
+                                 f"None for proj_type = {proj_type}")
+            self._focal_length = np.inf
 
     def _roll_to_vertical(self, arr):
         """Roll arrays to match the different vertical axis."""
@@ -1056,8 +1078,21 @@ def get_proj(self):
         V = np.zeros(3)
         V[self._vertical_axis] = -1 if abs(elev_rad) > 0.5 * np.pi else 1
 
-        viewM = proj3d.view_transformation(eye, R, V, roll_rad)
-        projM = self._projection(-self._dist, self._dist)
+        # Generate the view and projection transformation matrices
+        if self._focal_length == np.inf:
+            # Orthographic projection
+            viewM = proj3d.view_transformation(eye, R, V, roll_rad)
+            projM = proj3d.ortho_transformation(-self._dist, self._dist)
+        else:
+            # Perspective projection
+            # Scale the eye dist to compensate for the focal length zoom effect
+            eye_focal = R + self._dist * ps * self._focal_length
+            viewM = proj3d.view_transformation(eye_focal, R, V, roll_rad)
+            projM = proj3d.persp_transformation(-self._dist,
+                                                self._dist,
+                                                self._focal_length)
+
+        # Combine all the transformation matrices to get the final projection
         M0 = np.dot(viewM, worldM)
         M = np.dot(projM, M0)
         return M
@@ -1120,7 +1155,7 @@ def cla(self):
                 pass
 
         self._autoscaleZon = True
-        if self._projection is proj3d.ortho_transformation:
+        if self._focal_length == np.inf:
             self._zmargin = rcParams['axes.zmargin']
         else:
             self._zmargin = 0.

diff --git a/lib/mpl_toolkits/mplot3d/proj3d.py b/lib/mpl_toolkits/mplot3d/proj3d.py
@@ -90,23 +90,27 @@ def view_transformation(E, R, V, roll):
     return np.dot(Mr, Mt)
 
 
-def persp_transformation(zfront, zback):
-    a = (zfront+zback)/(zfront-zback)
-    b = -2*(zfront*zback)/(zfront-zback)
-    return np.array([[1, 0, 0, 0],
-                     [0, 1, 0, 0],
-                     [0, 0, a, b],
-                     [0, 0, -1, 0]])
+def persp_transformation(zfront, zback, focal_length):
+    e = focal_length
+    a = 1  # aspect ratio
+    b = (zfront+zback)/(zfront-zback)
+    c = -2*(zfront*zback)/(zfront-zback)
+    proj_matrix = np.array([[e,   0,  0, 0],
+                            [0, e/a,  0, 0],
+                            [0,   0,  b, c],
+                            [0,   0, -1, 0]])
+    return proj_matrix
 
 
 def ortho_transformation(zfront, zback):
     # note: w component in the resulting vector will be (zback-zfront), not 1
     a = -(zfront + zback)
     b = -(zfront - zback)
-    return np.array([[2, 0, 0, 0],
-                     [0, 2, 0, 0],
-                     [0, 0, -2, 0],
-                     [0, 0, a, b]])
+    proj_matrix = np.array([[2, 0,  0, 0],
+                            [0, 2,  0, 0],
+                            [0, 0, -2, 0],
+                            [0, 0,  a, b]])
+    return proj_matrix
 
 
 def _proj_transform_vec(vec, M):

diff --git a/lib/mpl_toolkits/tests/baseline_images/test_mplot3d/axes3d_focal_length.png b/lib/mpl_toolkits/tests/baseline_images/test_mplot3d/axes3d_focal_length.png
diff --git a/lib/mpl_toolkits/tests/test_mplot3d.py b/lib/mpl_toolkits/tests/test_mplot3d.py
@@ -871,7 +871,7 @@ def _test_proj_make_M():
     V = np.array([0, 0, 1])
     roll = 0
     viewM = proj3d.view_transformation(E, R, V, roll)
-    perspM = proj3d.persp_transformation(100, -100)
+    perspM = proj3d.persp_transformation(100, -100, 1)
     M = np.dot(perspM, viewM)
     return M
 
@@ -1036,6 +1036,22 @@ def test_unautoscale(axis, auto):
     np.testing.assert_array_equal(get_lim(), (-0.5, 0.5))
 
 
+def test_axes3d_focal_length_checks():
+    fig = plt.figure()
+    ax = fig.add_subplot(projection='3d')
+    with pytest.raises(ValueError):
+        ax.set_proj_type('persp', focal_length=0)
+    with pytest.raises(ValueError):
+        ax.set_proj_type('ortho', focal_length=1)
+
+
+@mpl3d_image_comparison(['axes3d_focal_length.png'], remove_text=False)
+def test_axes3d_focal_length():
+    fig, axs = plt.subplots(1, 2, subplot_kw={'projection': '3d'})
+    axs[0].set_proj_type('persp', focal_length=np.inf)
+    axs[1].set_proj_type('persp', focal_length=0.15)
+
+
 @mpl3d_image_comparison(['axes3d_ortho.png'], remove_text=False)
 def test_axes3d_ortho():
     fig = plt.figure()