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manim learning by doing - right angle plane

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a plane with right anglesNumberPlanebeManimObjects in the library for creating 2D coordinate planes, which help the user to visualize axes and gridlines in the scene.

With axes, gridlines, and scales, it dynamically displays function curves, geometric shapes, and their transformations, making complex mathematical concepts intuitive and easy to understand.

NumberPlaneoffersx-axiscap (a poem)y-axiswhich is usually centrosymmetric.

By default, theNumberPlaneA background grid will be displayed, which is very helpful for displaying math functions, geometric shapes, and so on.

We can define the extent of the coordinate plane, add labels to the axes, and place other shapes, functions, or animations on theNumberPlaneon, thus demonstrating math concepts in an animation.

As described belowManimhit the nail on the headNumberPlaneobjects as well as some common usage examples.

1. Main parameters

NumberPlaneThe main parameters are:

Parameter name typology clarification
x_range Sequence[float] the plane of right angleshorizontal coordinate axisRange, Interval
y_range Sequence[float] the plane of right anglesvertical coordinate axisRange, Interval
x_length float Right Angle Plane Width
y_length float Right Angle Plane Height
background_line_style dict Right Angle Plane Background Gridline Style
faded_line_style dict Fade gridline style for secondary background gridlines
faded_line_ratio int Define the ratio of the fade gridlines to the background gridlines
make_smooth_after_applying_functions bool Whether smoothing is performed after applying the function

In the right-angled plane, it is common to have coordinate axes and background grid lines whose styles are passed through thebackground_line_styleparameter to set.

In addition.NumberPlaneThere's another one in there.faded_line_styleparameter, which defines the style of the faded grid lines.

These faded gridlines are often used to supplement the background gridlines to provide a more detailed visual effect or to help distinguish between different coordinate areas.

In general, there is no need to usefaded_line_stylecap (a poem)faded_line_ratio。

2. Main approaches

ManimThe coordinate system in theCoordinateSystemClasses provide a number of methods, including:

  1. Methods for getting and setting coordinate system properties
  2. Method of converting coordinates in a coordinate system to on-screen coordinates
  3. Methods of drawing shapes (points, lines, surfaces, etc.) in the coordinate system

The following introduction to the various coordinate systems will be used in the example used in the method, here will not be introduced one by one.

(indicates contrast)NumberPlaneinherited fromCoordinateSystemclass, so you can use its various methods directly.

3. Examples of use

Here are a few examples to showNumberPlaneThe function of the

3.1 Basic two-dimensional coordinate plane

By default, theNumberPlaneDisplays axes and background gridlines to help users clearly see the division of the coordinate system.

The coordinate axes are white by default and the background gridlines are blue by default.

The following example shows a standard two-dimensional coordinate plane, containing thex-axiscap (a poem)y-axis，

x-axiscap (a poem)y-axisThe range of each is set to-7~7cap (a poem)-4~4The grid lines are spaced1。

plane = NumberPlane(
    x_range=[-7, 7],
    y_range=[-4, 4],
    x_length=6,
    y_length=4,
)

3.2. Customizing grid line styles

NumberPlaneThe styles of the background gridlines and the fade gridlines of the

The following example provides an overview of theBackground gridlinescap (a poem)Fade gridlinesThe color, width and transparency are set.

The background gridlines are cyan and the fade gridlines are gray.

plane = NumberPlane(
    x_range=[-7, 7],
    y_range=[-4, 4],
    x_length=6,
    y_length=4,
    background_line_style={
        "stroke_color": TEAL,
        "stroke_width": 4,
        "stroke_opacity": 0.6,
    },
    faded_line_style={
        "stroke_color": GREY,
        "stroke_opacity": 0.3,
    },
    faded_line_ratio=2,
)

Note that this also sets thefaded_line_ratio=2It means that every 1 frameBackground gridlinesEquivalent to 2 compartments ofFade gridlines。

3.3 Axes of different scales

By default, theNumberPlane(used form a nominal expression)X-axiscap (a poem)Y-axisThe intervals of the

In fact, by setting different coordinate ranges and display ranges, you can create axes with different scales.

That is, the Y-axis interval can be greater than the X-axis interval or less than the X-axis interval.

# Y-axis spacing is greater than X-axis spacing
plane1 = NumberPlane(
    
    
    
    y_length=3, )
)

# y_range is less than x_range
plane2 = NumberPlane(
    x_range=[-3, 3], y_range=[-7, 7], x_length=3, )
    
    x_length=3,
    y_length=3, )
)

3.4. Plotting function images

utilizationNumberPlaneThe greatest use lies in the ability to plot the image of a function in it, an image or a geometric figure in a coordinate system, the

It can be easier to locate their positions and adjust the transformation relationship between them.

The following example plots 2 functions in a coordinate system, using the plotting methods provided by the coordinate system base class:plot_parametric_curve。

plane = NumberPlane(
    x_range=[-4, 4],
    y_range=[-16, 16],
    x_length=6,
    y_length=4,
)

g1 = plane.plot_parametric_curve(
    lambda x: [x, x**2],
    t_range=[-3.5, 3.5, 0.01],
)
g2 = plane.plot_parametric_curve(
    lambda x: [x, x**3],
    t_range=[-2.5, 2.5, 0.01],
)

4. Annexes

The code in the article is just an extract of the key parts, the complete code is shared on a web disk (number_plane.py），

Download at.Full Code (Access code: 6872)

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