Rewrote ParametricFunction to have less buggy interpolation

manimlib/mobject/coordinate_systems.py

@@ -31,7 +31,6 @@ class Axes(VGroup):
         "x_max": FRAME_X_RADIUS,
         "y_min": -FRAME_Y_RADIUS,
         "y_max": FRAME_Y_RADIUS,
-        "default_num_graph_points": 100,
     }
 
     def __init__(self, **kwargs):
@@ -68,14 +67,12 @@ class Axes(VGroup):
         ])
 
     def get_graph(
-        self, function, num_graph_points=None,
+        self, function,
         x_min=None,
         x_max=None,
         **kwargs
     ):
         kwargs["fill_opacity"] = kwargs.get("fill_opacity", 0)
-        kwargs["num_anchor_points"] = \
-            num_graph_points or self.default_num_graph_points
         x_min = x_min or self.x_min
         x_max = x_max or self.x_max
         graph = ParametricFunction(

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
+        t_min, t_max = self.t_min, self.t_max
-        self.points = np.zeros((n_points, self.dim))
+        dt = self.dt
-        self.points[:, 0] = np.linspace(
+        step_size = self.step_size
-            self.t_min, self.t_max, n_points
+
+        discontinuities = filter(
+            lambda t: t_min <= t <= t_max,
+            self.discontinuities
         )
-        # VMobject.apply_function takes care of preserving
+        discontinuities = np.array(list(discontinuities))
-        # desirable tangent line properties at anchor points
+        boundary_times = [
-        self.apply_function(lambda p: self.function(p[0]))
+            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)
-
+        self.parametric_function = \
-        def parametric_function(t):
+            lambda t: np.array([t, function(t), 0])
-            return t * RIGHT + function(t) * UP
         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)

manimlib/mobject/types/vectorized_mobject.py

@@ -485,11 +485,12 @@ class VMobject(Mobject):
         return points
 
     def set_points_as_corners(self, points):
-        if len(points) == 0:
+        nppcc = self.n_points_per_cubic_curve
-            return  # TODO, raise warning?
+        points = np.array(points)
-        self.clear_points()
+        self.set_anchors_and_handles(*[
-        self.start_new_path(points[0])
+            interpolate(points[:-1], points[1:], a)
-        self.add_points_as_corners(points[1:])
+            for a in np.linspace(0, 1, nppcc)
+        ])
         return self
 
     def set_points_smoothly(self, points):

manimlib/scene/graph_scene.py

@@ -44,7 +44,6 @@ class GraphScene(Scene):
         "axes_color": GREY,
         "graph_origin": 2.5 * DOWN + 4 * LEFT,
         "exclude_zero_label": True,
-        "num_graph_anchor_points": 25,
         "default_graph_colors": [BLUE, GREEN, YELLOW],
         "default_derivative_color": GREEN,
         "default_input_color": YELLOW,
@@ -149,6 +148,7 @@ class GraphScene(Scene):
         color=None,
         x_min=None,
         x_max=None,
+        **kwargs
     ):
         if color is None:
             color = next(self.default_graph_colors_cycle)
@@ -167,7 +167,7 @@ class GraphScene(Scene):
         graph = ParametricFunction(
             parameterized_function,
             color=color,
-            num_anchor_points=self.num_graph_anchor_points,
+            **kwargs
         )
         graph.underlying_function = func
         return graph

old_projects/eoc/chapter3.py

@@ -97,7 +97,6 @@ class ContrastAbstractAndConcrete(Scene):
             ParametricFunction(
                 lambda t : (t/denom)*RIGHT+np.sin(t)*UP+np.cos(t)*OUT,
                 t_max = 12*np.pi,
-                num_anchor_points = 100,
             )
             for denom in (12.0, 4.0)
         ]

old_projects/eoc/chapter4.py

@@ -208,7 +208,6 @@ class DampenedSpring(Scene):
             ParametricFunction(
                 lambda t : (t/denom)*RIGHT+np.sin(t)*UP+np.cos(t)*OUT,
                 t_max = 12*np.pi,
-                num_anchor_points = 100,
                 color = GREY,
             ).shift(3*LEFT)
             for denom in (12.0, 2.0)

old_projects/fourier.py

@@ -3911,7 +3911,6 @@ class BoundsAtInfinity(SummarizeFormula):
             number_line_config = {
                 "include_tip" : False,
             },
-            default_num_graph_points = 1000,
         )
         axes.x_axis.add_numbers(*list(filter(
             lambda x : x != 0,

old_projects/uncertainty.py

@@ -525,7 +525,7 @@ class ShowPlan(PiCreatureScene):
         wave = FunctionGraph(
             lambda x : 0.3*np.sin(15*x)*np.sin(0.5*x),
             x_min = 0, x_max = 30,
-            num_anchor_points = 500,
+            step_size = 0.001,
         )
         wave.next_to(word, RIGHT)
         rect = BackgroundRectangle(wave, fill_opacity = 1)
@@ -965,7 +965,7 @@ class VariousMusicalNotes(Scene):
             a = graph_width_tracker.get_value()
             return FunctionGraph(
                 lambda x : np.exp(-a*x**2)*np.sin(freq*x)-0.5,
-                num_anchor_points = 500,
+                step_size = 0.001,
             )
         graph = get_graph()
         def graph_update(graph):
@@ -1044,7 +1044,7 @@ class VariousMusicalNotes(Scene):
             lambda x : 0.5*np.sin(freq*x),
             x_min = -FRAME_WIDTH,
             x_max = FRAME_WIDTH,
-            num_anchor_points = 1000
+            n_components = 0.001
         )
         long_graph.set_color(BLUE)
         long_graph.next_to(graph, UP, MED_LARGE_BUFF)