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manim learning-by-doing - generalized polygons

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manimoffersUniversal Polygonmodule to draw arbitrary polygons.

There are two types of generic polygon modules.Polygoncap (a poem)Polygram。

Polygonis a geometric term that primarily refers to a plane figure made up of three or more line segments joined end to end.

(indicates contrast)PolygramThe meaning is a little broader, it can draw traditional polygons, but also non-closed polygons, polygons that are not connected to each other, and so on.

For general geometric problems, usePolygonwill suffice, and will only be used when some combination or sequence of shapes needs to be expressed.Polygram。

manimconsultations onPolygoncap (a poem)PolygramThere are four main modules of the

  1. Polygon: Arbitrary polygon
  2. RegularPolygon: Anygreater than zeropolygonal
  3. Polygram: generalized polygons
  4. RegularPolygram: Generalizedgreater than zeropolygonal

Polygoncap (a poem)PolygramIt is actually possible to drawgreater than zeropolygon, except that withRegularPolygoncap (a poem)RegularPolygramIt will be more convenient.

The inheritance relationship of these 4 modules is shown above.

1. Main parameters

Polygon's argument is simple: provide a series of vertex coordinates.

When drawing, the vertices are connected in the order provided, with the last point connecting to the first to form a closed polygon.

Parameter name typology clarification
vertices Point3D List of vertices of a polygon

RegularPolygonThe parameters are also simple:

Parameter name typology clarification
n int Number of sides of a regular polygon

Polygramis parameterized by a multigroup of vertices with multiple vertices in each group, as opposed to thePolygonwhich is parameterized by a single set of vertices.

Parameter name typology clarification
vertex_groups Point3D A list of multiple sets of vertices, if there is only one set of vertices, then the graph and thePolygonequal to

RegularPolygramThe parameters are:

Parameter name typology clarification
num_vertices int Number of vertices
radius float Radius of the outer circle of the graph
density int How many vertices to jump to connect
start_angle float Angle of the first vertex

RegularPolygonIt is relatively simple to connect the vertices in sequence to form a polygon.

(indicates contrast)RegularPolygramhave andensityparameter, which controls jumping several vertices to connect.

set updensity=1words.RegularPolygramcap (a poem)RegularPolygonThe graphics are the same, as demonstrated in detail later in the example.

2. Main approaches

PolygramAs the most generalized polygon, 3 methods are provided.

name (of a thing) clarification
get_vertex_groups Get the coordinates of all vertices of the polytope in a grouped form
get_vertices Get the coordinates of all vertices of the polytope
round_corners Adjusting the curvature of polygon corners

get_vertex_groupscap (a poem)get_verticesThe main difference is:

get_vertex_groupsReturns the vertex coordinates as a group, which is useful for thePolygrammodule is more useful because thePolygramMultiple sets of vertices can be passed as arguments to the module;

get_verticesThen it returns all the coordinates as a list.

round_cornersUsed to adjust the curvature of polygonal sharp corners.

# Create 3 generalized positive hexagons
p1 = RegularPolygram(6)
p2 = RegularPolygram(6)
p3 = RegularPolygram(6)

# p2's sharp corner curvature is set to 0.1
p2.round_corners(radius=0.1)

# p3's sharp corner curvature is set to 0.3
p3.round_corners(radius=0.3)

The other 3 modules don't have any significant methods.

3. Examples of use

3.1 Examples of polygons

A polytope is a closed graph that is connected one by one in the order of the incoming vertices.

# convex polygon
points = [
    LEFT * 2.5,
    LEFT * 1.5 + UP,
    LEFT * 0.5,
    LEFT * 0.5 + DOWN * 1.5,
    LEFT * 2.5 + DOWN * 1.5,
]
Polygon(*points)

# concave polygon
points = [
    RIGHT * 0.5 + UP,
    RIGHT * 1.5 + DOWN,
    RIGHT * 2.5 + UP,
    RIGHT * 2.5 + DOWN * 1.5,
    RIGHT * 0.5 + DOWN * 1.5,
]
Polygon(*points)

3.2 Positive polygons

The square polygon is the easiest, just pass in the number of edges.

RegularPolygon(n=6)
RegularPolygon(n=8)
RegularPolygon(n=12)

3.3 Generalized polygons

A generalized polygon is more like a combination of polygons; it can be passed multiple groups of vertices, and then the graph is constructed based on the vertices of each group.

In the following example, the first graph has 3 group vertices and the second graph has 2 group vertices.

group_points = [
    [[-2.5,0,0], [-1.5,1,0], [-0.5,0,0]],
    [[-2,0,0], [-2,-1.5,0]],
    [[-1,0,0], [-1,-1.5,0]],
]
Polygram(*group_points)

group_points = [
    [[0.5,0,0], [1.5,1,0], [2.5,0,0]],
    [[0.5,-1,0], [1.5,0,0], [2.5,-1,0]],
]
Polygram(*group_points)

3.4. Generalized orthogonal polygons

Generalized orthogonal polygons can adjust the order in which vertices are connected (via the attributedensity), when connected one by one, is the same as a normal square polygon.

# Positive Nine-sided Shape, connecting vertices one by one
RegularPolygram(9, density=1)

# Positive hexagon, connect vertices one at a time
RegularPolygram(9, density=2)

# Positive hexagon, two vertices apart
RegularPolygram(9, density=3)

4. Annexes

The complete code for the article is on a web disk (），

Download at.Full Code (Access code: 6872)

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