video/.agents/skills/manimce-best-practices/rules/axes.md

name, description, metadata

name	description	metadata
axes	Axes, NumberPlane, and coordinate systems in Manim	tags axes, numberplane, coordinate, grid, numberline

Coordinate Systems

Create axes, grids, and number lines for mathematical visualizations.

Axes

Basic 2D coordinate axes.

from manim import *

class AxesExample(Scene):
    def construct(self):
        # Default axes
        axes = Axes()
        self.add(axes)

Customizing Axes

class CustomAxes(Scene):
    def construct(self):
        axes = Axes(
            x_range=[-5, 5, 1],      # [min, max, step]
            y_range=[-3, 3, 1],
            x_length=10,              # Physical length on screen
            y_length=6,
            axis_config={
                "color": BLUE,
                "include_tip": True,
                "include_numbers": True,
            },
            x_axis_config={
                "numbers_to_include": [-4, -2, 0, 2, 4],
            },
            y_axis_config={
                "numbers_to_include": [-2, 0, 2],
            },
        )
        self.add(axes)

Adding Labels

class AxesLabels(Scene):
    def construct(self):
        axes = Axes(x_range=[-5, 5], y_range=[-3, 3])

        # Add axis labels
        x_label = axes.get_x_axis_label("x")
        y_label = axes.get_y_axis_label("y")

        # Custom labels
        x_label = axes.get_x_axis_label(MathTex(r"\theta"))
        y_label = axes.get_y_axis_label(MathTex(r"f(\theta)"))

        self.add(axes, x_label, y_label)

NumberPlane

Grid with axes - shows coordinate lines.

class NumberPlaneExample(Scene):
    def construct(self):
        # Default plane
        plane = NumberPlane()
        self.add(plane)

Customizing NumberPlane

class CustomPlane(Scene):
    def construct(self):
        plane = NumberPlane(
            x_range=[-4, 4, 1],
            y_range=[-3, 3, 1],
            x_length=8,
            y_length=6,
            background_line_style={
                "stroke_color": BLUE_D,
                "stroke_width": 1,
                "stroke_opacity": 0.5,
            },
            axis_config={
                "color": WHITE,
            },
        )
        self.add(plane)

ComplexPlane

For visualizing complex numbers.

class ComplexPlaneExample(Scene):
    def construct(self):
        plane = ComplexPlane()

        # Plot complex number
        z = complex(2, 1)  # 2 + i
        dot = Dot(plane.n2p(z), color=YELLOW)
        label = MathTex("2+i").next_to(dot, UR)

        self.add(plane, dot, label)

NumberLine

Single axis line.

class NumberLineExample(Scene):
    def construct(self):
        line = NumberLine(
            x_range=[-5, 5, 1],
            length=10,
            include_numbers=True,
            include_tip=True,
        )
        self.add(line)

Coordinate Conversions

class CoordinateConversion(Scene):
    def construct(self):
        axes = Axes(x_range=[-5, 5], y_range=[-3, 3])

        # Convert coordinates to screen position
        point = axes.c2p(2, 1)  # coords_to_point: (2, 1) -> screen position

        # Convert screen position to coordinates
        coords = axes.p2c(point)  # point_to_coords: screen -> (x, y)

        dot = Dot(point, color=RED)
        self.add(axes, dot)

Shorthand Methods

axes = Axes()

# c2p = coords_to_point
axes.c2p(x, y)

# p2c = point_to_coords
axes.p2c(point)

# i2gp = input_to_graph_point (for graphs)
axes.i2gp(x, graph)

# For NumberPlane/ComplexPlane
plane.n2p(complex_number)  # number_to_point
plane.p2n(point)           # point_to_number

ThreeDAxes

For 3D visualizations.

class ThreeDAxesExample(ThreeDScene):
    def construct(self):
        axes = ThreeDAxes(
            x_range=[-4, 4, 1],
            y_range=[-4, 4, 1],
            z_range=[-4, 4, 1],
            x_length=8,
            y_length=8,
            z_length=6,
        )

        self.set_camera_orientation(phi=75 * DEGREES, theta=-45 * DEGREES)
        self.add(axes)

Plotting Points

class PlotPoints(Scene):
    def construct(self):
        axes = Axes(x_range=[-5, 5], y_range=[-3, 3])

        points = [(1, 2), (-2, 1), (3, -1), (0, 2)]
        dots = VGroup(*[
            Dot(axes.c2p(x, y), color=YELLOW)
            for x, y in points
        ])

        self.add(axes, dots)

Best Practices

1. Set appropriate ranges - Don't include unnecessary empty space
2. Match x_length/y_length to range ratio - Prevents distortion
3. Use NumberPlane for transformations - Grid shows distortion clearly
4. Use c2p for all coordinate work - Don't manually convert
5. Include numbers sparingly - Too many numbers clutter the display