Fixed :meth:.CoordinateSystem.get_area when using few plot points and a boundary graph (#2244)

* make sure left and right endpoint of area are vertically above a, b

* fix border when bounded_graph is passed

* added test

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* update get_area test, also affected by changes

* fix test data

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: behackl

manim/mobject/coordinate_systems.py

@@ -1293,14 +1293,18 @@ def construct(self):
 
         if bounded_graph is None:
             points = (
-                [self.c2p(a)]
+                [self.c2p(a), graph.function(a)]
                 + [p for p in graph.points if a <= self.p2c(p)[0] <= b]
-                + [self.c2p(b)]
+                + [graph.function(b), self.c2p(b)]
             )
         else:
-            points = [p for p in graph.points if a <= self.p2c(p)[0] <= b] + [
-                p for p in bounded_graph.points if a <= self.p2c(p)[0] <= b
-            ][::-1]
+            graph_points, bounded_graph_points = (
+                [g.function(a)]
+                + [p for p in g.points if a <= self.p2c(p)[0] <= b]
+                + [g.function(b)]
+                for g in (graph, bounded_graph)
+            )
+            points = graph_points + bounded_graph_points[::-1]
         return Polygon(*points, **kwargs).set_opacity(opacity).set_color(color)
 
     def angle_of_tangent(

tests/control_data/graphical_units_data/plot/get_area.npz

@@ -199,6 +199,17 @@ def test_get_area(scene):
     scene.add(ax, curve1, curve2, area1, area2)
 
 
+@frames_comparison
+def test_get_area_with_boundary_and_few_plot_points(scene):
+    ax = Axes(x_range=[-2, 2], y_range=[-2, 2], color=WHITE)
+    f1 = ax.plot(lambda t: t, [-1, 1, 0.5])
+    f2 = ax.plot(lambda t: 1, [-1, 1, 0.5])
+    a1 = ax.get_area(f1, [-1, 0.75], color=RED)
+    a2 = ax.get_area(f1, [-0.75, 1], bounded_graph=f2, color=GREEN)
+
+    scene.add(ax, f1, f2, a1, a2)
+
+
 @frames_comparison
 def test_get_riemann_rectangles(scene):
     ax = Axes(y_range=[-2, 10])