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manim learning-by-doing - points and lines in 3D

Popularity：398 ℃/2024-11-06 10:16:38

Manim Provides a range of objects designed for 3D space, making it easier to create 3D math animations.

This post begins with the simplest of these point and line related objects, theDot3D(points in three dimensions).Line3D(lines in three dimensions) andArrow3D(three-dimensional arrow).

  • Dot3DUsed to represent points in three-dimensional space, it is the basis for constructing other complex three-dimensional shapes, and it is suitable for labeling key points, positions, vector starting points, etc.
  • Line3DIt is used to draw line segments in three-dimensional space and can represent vectors, paths, trajectories, etc. It is suitable for showing the trajectory of an object, the direction of a force, etc.
  • Arrow3DexistLine3DThe arrowhead is added to the base of the line segment for explicitly indicating direction. It is suitable for representing vectors, directions of forces, velocities, etc.

1. Main parameters

Dot3DThe main parameters of the

Parameter name typology clarification
point Position of the point, contains 3 values x, y, z.
radius float radius of a point
color Color Dot color
resolution tuple[int, int] Point resolution

Dot3Dis essentially a sphere, so there isradiusparameter that controls the size of the point;

resolutionThe parameter sets the resolution of the point of this sphere, the larger the value, the more rounded the point looks, generally do not need to set this parameter, the default value will be fine.

Line3DThe main parameters of the

Parameter name typology clarification
start Coordinates of the starting point of the line segment, containing x, y, and z values.
end The endpoint coordinates of the line segment, containing x, y, and z values.
thickness float Thickness of the line segment
color Color Color of line segments

Arrow3DThe main parameters of the

Parameter name typology clarification
start Coordinates of the starting point of the arrow, containing x, y, and z values.
end Coordinates of the end point of the arrow, containing x, y, and z values.
thickness float Thickness of the arrow body
height float Height of arrow tip
base_radius float Bottom radius of arrow tip
color Color Color of arrows

2. Main approaches

Dot3Dcap (a poem)Arrow3DThere are no special methods, just the usual Manim object scaling, panning and so on.

But.Line3DThere are several methods unique to yourself.

name (of a thing) clarification
parallel_to Create a line segment parallel to the given line segment
perpendicular_to Creates a line segment perpendicular to the given line segment
pointify Get the point that represents the center of the object

3. Examples of use

Finally, it is better to demonstrate the important parameters and methods of the above objects through examples.

3.1. Position and color of Dot3D

In this example, we'll create aDot3DObject.

The first point has a default radius and color; while for the second point, we will customize its radius and color.

By adjusting these parameters, we can clearly see the position and color difference between two points in 3D space.

# Use default parameters
dot1 = Dot3D(point=axes.c2p(1, 2, 3))

# Customize the radius and color
dot2 = Dot3D(
    
    radius=0.2, color=RED, # Customize radius and color.
    color=RED, )
)

3.2. Length and direction of Line3D

This example will show how to draw a line segment in 3D space using the Line3D object.

First set up a line segment based on the start and end points, and at the same time, adjust the thickness and color of the line segment to make it more eye-catching.

Then, through the functionparallel_tocap (a poem)perpendicular_toPlot the parallel (yellow) and perpendicular (red) lines of this segment, respectively.

# Specify the start and end points and the line thickness.
line = Line3D(
    start=LEFT + DOWN * 2 + IN, end=RIGHT + UP * 2 + OUT * 2, line = Line3D(
    end=RIGHT + UP * 2 + OUT * 2, thickness=0.02, line3D = Line3D(
    thickness=0.02, color=BLUE,
    color=BLUE, )
)

# Draw parallel lines to line
Line3D.parallel_to(line, color=YELLOW)

# Draw a perpendicular line to line
Line3D.perpendicular_to(line, color=RED)

3.3. Arrow3D Orientation and Style

In this example, we use theArrow3Dobject to represent a line segment with an arrow to emphasize direction.

First set the start and end points of the arrows, and to emphasize the arrows, the

Then adjust the thickness (thicknessparameter), the height of the arrow tip (heightparameter) and the bottom radius (base_radius(Parameters).

# Specify the start and end points and arrow style parameters.
arrow = Arrow3D(
    start=[-1, -1, -2], end=[1, 2, 2], # Specify the start and end points and arrow style parameters.
    start=[-1, -1, -2], end=[1, 2, 2], thickness=0.05,
    thickness=0.05, height=0.2,
    base_radius=0.1
    base_radius=0.1, color=GREEN,
    color=GREEN.
)

3.4. Combined Use of Dot3D, Line3D and Arrow3D

In this synthesized example, we combine the use of theDot3D、Line3Dcap (a poem)Arrow3Dto create a more complex 3D scene.

First, place aDot3Dobject as a starting point.

We will then use theLine3Dobject draws a line segment from that point to another location, representing a path or trajectory.

Finally, we'll add a line segment at the end of theArrow3DObject.

By adjusting the parameters of these objects (e.g., position, color, thickness, etc.), it is possible to create a 3D graphic that is both clear and expressive for a variety of purposes such as presentations, teaching, or scientific research.

# Create a Dot3D object as the starting point
dot = Dot3D(point=[-1, -1, -1], color=BLUE)

# Create a Line3D object to connect the starting point to another point
line = Line3D(
    start=[-1, -1, -1], end=[2, 2, 2, 2], color=BLUE
    start=[-1, -1, -1], end=[2, 2, 2], thickness=0.05, color=BLUE
    thickness=0.05, color=YELLOW,
    color=YELLOW, )
)

# Create an Arrow3D object to indicate the direction at the end point
arrow = Arrow3D(
    start=[2, 2, 2], end=[1, 2, -1], # Create an Arrow3D object to indicate the direction at the end.
    start=[2, 2, 2], end=[1, 2, -1],
    start=[2, 2], end=[1, 2, -1], thickness=0.05,
    base_radius=0.1
    base_radius=0.1, color=RED,
    color=RED.
)

4. Annexes

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

Download at.Full Code (Access code: 6872)

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