Rewrote ParametricFunction to have less buggy interpolation

manimlib/mobject/functions.py

@@ -7,22 +7,54 @@ class ParametricFunction(VMobject):
     CONFIG = {
         "t_min": 0,
         "t_max": 1,
-        "num_anchor_points": 100,
+        # TODO, be smarter about choosing this number
+        "step_size": 0.01,
+        "dt": 1e-8,
+        # TODO, be smar about figuring these out?
+        "discontinuities": [],
     }
 
     def __init__(self, function, **kwargs):
         self.function = function
         VMobject.__init__(self, **kwargs)
 
+    def get_function(self):
+        return self.function
+
+    def get_point_from_function(self, t):
+        return self.function(t)
+
     def generate_points(self):
-        n_points = 3 * self.num_anchor_points - 2
-        self.points = np.zeros((n_points, self.dim))
-        self.points[:, 0] = np.linspace(
-            self.t_min, self.t_max, n_points
+        t_min, t_max = self.t_min, self.t_max
+        dt = self.dt
+        step_size = self.step_size
+
+        discontinuities = filter(
+            lambda t: t_min <= t <= t_max,
+            self.discontinuities
         )
-        # VMobject.apply_function takes care of preserving
-        # desirable tangent line properties at anchor points
-        self.apply_function(lambda p: self.function(p[0]))
+        discontinuities = np.array(list(discontinuities))
+        boundary_times = [
+            self.t_min, self.t_max,
+            *(discontinuities - dt),
+            *(discontinuities + dt),
+        ]
+        boundary_times.sort()
+        print(boundary_times)
+        for t1, t2 in zip(boundary_times[0::2], boundary_times[1::2]):
+            t_range = list(np.arange(t1, t2, step_size))
+            if t_range[-1] != t2:
+                t_range.append(t2)
+            points = np.array([self.function(t) for t in t_range])
+            valid_indices = np.apply_along_axis(
+                np.all, 1, np.isfinite(points)
+            )
+            points = points[valid_indices]
+            if len(points) > 0:
+                self.start_new_path(points[0])
+                self.add_points_as_corners(points[1:])
+        self.make_smooth()
+        return self
 
 
 class FunctionGraph(ParametricFunction):
@@ -34,12 +66,11 @@ class FunctionGraph(ParametricFunction):
 
     def __init__(self, function, **kwargs):
         digest_config(self, kwargs)
-
-        def parametric_function(t):
-            return t * RIGHT + function(t) * UP
+        self.parametric_function = \
+            lambda t: np.array([t, function(t), 0])
         ParametricFunction.__init__(
             self,
-            parametric_function,
+            self.parametric_function,
             t_min=self.x_min,
             t_max=self.x_max,
             **kwargs
@@ -48,3 +79,6 @@ class FunctionGraph(ParametricFunction):
 
     def get_function(self):
         return self.function
+
+    def get_point_from_function(self, x):
+        return self.parametric_function(x)