Coordinate

By default, the scene in manim is made up by 8 x 14 grid. The grid is addressed using a numpy array in the form of [x, y, z]. For 2D animations only the x and y axes are used.

class DotMap(Scene):
    def construct(self):
        dots = dict()
        annos = dict()
        var_index = 0
        for x in range(-7, 8):
            for y in range(-4, 5):
                annos[f"{x}{y}"] = TexMobject(f"({x}, {y})")
                dots[f"{var_index}"] = Dot(np.array([x, y, 0]))
                var_index = var_index + 1
        for anno, dot in zip(annos.values(), dots.values()):
            self.add(anno)
            self.add(dot)
            self.wait(0.2)
            self.remove(anno)

Note

You can place objects outside this boundary, but it won’t show up in the render.

Using Coordinates

Coordinates are used for creating geometries (VMobject in manim) and animations.

Here coordinates are used to create this Polygon

class CoorPolygon(Scene):
    def construct(self):
        for x in range(-7, 8):
            for y in range(-4, 5):
                self.add(Dot(np.array([x, y, 0]), color=DARK_GREY))
        polygon = Polygon(
            np.array([3, 2, 0]),
            np.array([1, -1, 0]),
            np.array([-5, -4, 0]),
            np.array([-4, 4, 0]))
        self.add(polygon)

Coordinate Aliasing

From some animations typing a np.array everytime you need a coordinate can be tedious. Manim provides aliases to the most common coordinates:

UP == np.array([0, 1, 0])
DOWN == np.array([0, -1, 0])
LEFT ==  np.array([-1, 0, 0])
RIGHT == np.array([1, 0, 0])
UL == np.array([-1, 1, 0])
DL == np.array([-1, -1, 0])
UR == np.array([1, 1, 0])
DR == np.array([1, -1, 0])

Here coordinates are used for animations

class CoorAlias(Scene):
    def construct(self):
        for x in range(-7, 8):
            for y in range(-4, 5):
                self.add(Dot(np.array([x, y, 0]), color=DARK_GREY))

        aliases = {
            "UP": UP,
            "np.array([0,1,0])": np.array([0, 1, 0]),
            "DOWN": DOWN,
            "np.array([0,-1,0])": np.array([0, -1, 0]),
            "LEFT": LEFT,
            "np.array([-1,0,0])": np.array([-1, 0, 0]),
            "RIGHT": RIGHT,
            "np.array([1,0,0])": np.array([1, 0, 0]),
            "UL": UL,
            "np.array([-1,1,0])": np.array([-1, 1, 0]),
            "DL": DL,
            "np.array([-1,-1,0])": np.array([-1, -1, 0]),
            "UR": UR,
            "np.array([1,1,0])": np.array([1, 1, 0]),
            "DR": DR,
            "np.array([1,-1,0])": np.array([1, -1, 0])}
        circle = Circle(color=RED, radius=0.5)
        self.add(circle)
        self.wait(0.5)

        for text, aliase in aliases.items():
            anno = TexMobject(f"\\texttt{{{text}}}")
            self.play(Write(anno, run_time=0.2))
            self.play(ApplyMethod(circle.shift, aliase))
            self.wait(0.2)
            self.play(FadeOut(anno, run_time=0.2))

Coordinate Arithmetic

Numpy array allows arithmetic operations:

>>> numpy.array([2,2,0]) + 4
array([6, 6, 4])

>>> np.array([1, -3, 0]) + np.array([-4, 2, 0])
array([-3, -1,  0])

>>> np.array([2, 2, 0]) - np.array([3,6, 0])
array([-1, -4,  0])

>>> numpy.array([2,2,0]) - 3
array([-1, -1, -3])

>>> np.array([1, -3, 0]) * 3
array([ 3, -9,  0])

>>> numpy.array([2,2,0]) / 2
array([1., 1., 0.])

>>> numpy.array([2,2,0]) / numpy.array([1, 4, 0])
__main__:1: RuntimeWarning: invalid value encountered in true_divide
array([2. , 0.5, nan])

class CoorArithmetic(Scene):
    def construct(self):
        for x in range(-7, 8):
            for y in range(-4, 5):
                self.add(Dot(np.array([x, y, 0]), color=DARK_GREY))

        circle = Circle(color=RED, radius=0.5)
        self.add(circle)
        self.wait(0.5)

        aliases = {
            "LEFT * 3": LEFT * 3,
            "UP + RIGHT / 2": UP + RIGHT / 2,
            "DOWN + LEFT * 2": DOWN + LEFT * 2,
            "RIGHT * 3.75 * DOWN": RIGHT * 3.75 * DOWN,
            # certain arithmetic won't work as you expected
            # In [4]: RIGHT * 3.75 * DOWN
            # Out[4]: array([ 0., -0.,  0.])
            "RIGHT * 3.75 + DOWN": RIGHT * 3.75 + DOWN}

        for text, aliase in aliases.items():
            anno = TexMobject(f"\\texttt{{{text}}}")
            self.play(Write(anno, run_time=0.2))
            self.play(ApplyMethod(circle.shift, aliase))
            self.wait(0.2)
            self.play(FadeOut(anno, run_time=0.2))