API 参考：几何图形（geometry）¶

共 57 个类，按字母排序。每个类含中文说明、继承链、参数表与上手示例，API 文档由 autodoc 从 manim v0.21.0 源码自动生成；带完整中文精讲的类见 API 索引。

Angle¶

两条线的夹角图形：自动找交点、按半径画出夹角弧，可标注度数，几何作图必备。

继承关系¶

参数¶

`line1`	—，Line
`line2`	—，Line
`radius`	None，float \| None
`quadrant`	(1, 1)，AngleQuadrant
`other_angle`	False，bool
`dot`	False，bool
`dot_radius`	None，float \| None
`dot_distance`	0.55，float
`dot_color`	ManimColor('#FFFFFF')，ParsableManimColor
`elbow`	False，bool

快速上手¶

angle = Angle(line1, line2, radius=0.5)

API 文档¶

class manim.Angle(line1: Line, line2: Line, radius: float | None = None, quadrant: AngleQuadrant = (1, 1), other_angle: bool = False, dot: bool = False, dot_radius: float | None = None, dot_distance: float = 0.55, dot_color: ParsableManimColor = ManimColor('#FFFFFF'), elbow: bool = False, **kwargs: Any)¶

基类：VMobject

A circular arc or elbow-type mobject representing an angle of two lines.

Parameters¶

line1 :: The first line.
line2 :: The second line.
radius :: The radius of the Arc.
quadrant: A sequence of two int numbers determining which of the 4 quadrants should be used. The first value indicates whether to anchor the arc on the first line closer to the end point (1) or start point (-1), and the second value functions similarly for the end (1) or start (-1) of the second line. Possibilities: (1,1), (-1,1), (1,-1), (-1,-1).
other_angle :: Toggles between the two possible angles defined by two points and an arc center. If set to False (default), the arc will always go counterclockwise from the point on line1 until the point on line2 is reached. If set to True, the angle will go clockwise from line1 to line2.
dot: Allows for a Dot in the arc. Mainly used as an convention to indicate a right angle. The dot can be customized in the next three parameters.
dot_radius: The radius of the Dot. If not specified otherwise, this radius will be 1/10 of the arc radius.
dot_distance: Relative distance from the center to the arc: 0 puts the dot in the center and 1 on the arc itself.
dot_color: The color of the Dot.
elbow: Produces an elbow-type mobject indicating a right angle, see RightAngle for more information and a shorthand.
**kwargs: Further keyword arguments that are passed to the constructor of Arc or Elbow.

Examples¶

The first example shows some right angles with a dot in the middle while the second example shows all 8 possible angles defined by two lines.

class RightArcAngleExample(Scene):
    def construct(self):
        line1 = Line( LEFT, RIGHT )
        line2 = Line( DOWN, UP )
        rightarcangles = [
            Angle(line1, line2, dot=True),
            Angle(line1, line2, radius=0.4, quadrant=(1,-1), dot=True, other_angle=True),
            Angle(line1, line2, radius=0.5, quadrant=(-1,1), stroke_width=8, dot=True, dot_color=YELLOW, dot_radius=0.04, other_angle=True),
            Angle(line1, line2, radius=0.7, quadrant=(-1,-1), color=RED, dot=True, dot_color=GREEN, dot_radius=0.08),
        ]
        plots = VGroup()
        for angle in rightarcangles:
            plot=VGroup(line1.copy(),line2.copy(), angle)
            plots.add(plot)
        plots.arrange(buff=1.5)
        self.add(plots)

class AngleExample(Scene):
    def construct(self):
        line1 = Line( LEFT + (1/3) * UP, RIGHT + (1/3) * DOWN )
        line2 = Line( DOWN + (1/3) * RIGHT, UP + (1/3) * LEFT )
        angles = [
            Angle(line1, line2),
            Angle(line1, line2, radius=0.4, quadrant=(1,-1), other_angle=True),
            Angle(line1, line2, radius=0.5, quadrant=(-1,1), stroke_width=8, other_angle=True),
            Angle(line1, line2, radius=0.7, quadrant=(-1,-1), color=RED),
            Angle(line1, line2, other_angle=True),
            Angle(line1, line2, radius=0.4, quadrant=(1,-1)),
            Angle(line1, line2, radius=0.5, quadrant=(-1,1), stroke_width=8),
            Angle(line1, line2, radius=0.7, quadrant=(-1,-1), color=RED, other_angle=True),
        ]
        plots = VGroup()
        for angle in angles:
            plot=VGroup(line1.copy(),line2.copy(), angle)
            plots.add(VGroup(plot,SurroundingRectangle(plot, buff=0.3)))
        plots.arrange_in_grid(rows=2,buff=1)
        self.add(plots)

class FilledAngle(Scene):
    def construct(self):
        l1 = Line(ORIGIN, 2 * UP + RIGHT).set_color(GREEN)
        l2 = (
            Line(ORIGIN, 2 * UP + RIGHT)
            .set_color(GREEN)
            .rotate(-20 * DEGREES, about_point=ORIGIN)
        )
        norm = l1.get_length()
        a1 = Angle(l1, l2, other_angle=True, radius=norm - 0.5).set_color(GREEN)
        a2 = Angle(l1, l2, other_angle=True, radius=norm).set_color(GREEN)
        q1 = a1.points #  save all coordinates of points of angle a1
        q2 = a2.reverse_direction().points  #  save all coordinates of points of angle a1 (in reversed direction)
        pnts = np.concatenate([q1, q2, q1[0].reshape(1, 3)])  # adds points and ensures that path starts and ends at same point
        mfill = VMobject().set_color(ORANGE)
        mfill.set_points_as_corners(pnts).set_fill(GREEN, opacity=1)
        self.add(l1, l2)
        self.add(mfill)

static from_three_points(A: Point3DLike, B: Point3DLike, C: Point3DLike, **kwargs: Any) → Angle¶

The angle between the lines AB and BC.

This constructs the angle \(\\angle ABC\).

Parameters¶

A: The endpoint of the first angle leg
B: The vertex of the angle
C: The endpoint of the second angle leg
**kwargs: Further keyword arguments are passed to Angle

Returns¶

The Angle calculated from the three points

Angle(line1, line2, radius=0.5, quadrant=(-1,1), stroke_width=8), Angle(line1, line2, radius=0.7, quadrant=(-1,-1), color=RED, other_angle=True),

Examples¶

class AngleFromThreePointsExample(Scene):
    def construct(self):
        sample_angle = Angle.from_three_points(UP, ORIGIN, LEFT)
        red_angle = Angle.from_three_points(LEFT + UP, ORIGIN, RIGHT, radius=.8, quadrant=(-1,-1), color=RED, stroke_width=8, other_angle=True)
        self.add(red_angle, sample_angle)

get_lines() → VGroup¶

Get the lines forming an angle of the Angle class.

Returns¶

VGroup: A VGroup containing the lines that form the angle of the Angle class.

Examples¶

>>> line_1, line_2 = Line(ORIGIN, RIGHT), Line(ORIGIN, UR)
>>> angle = Angle(line_1, line_2)
>>> angle.get_lines()
VGroup(Line, Line)

get_value(degrees: bool = False) → float¶

Get the value of an angle of the Angle class.

Parameters¶

degrees: A boolean to decide the unit (deg/rad) in which the value of the angle is returned.

Returns¶

float: The value in degrees/radians of an angle of the Angle class.

Examples¶

class GetValueExample(Scene):
    def construct(self):
        line1 = Line(LEFT+(1/3)*UP, RIGHT+(1/3)*DOWN)
        line2 = Line(DOWN+(1/3)*RIGHT, UP+(1/3)*LEFT)

        angle = Angle(line1, line2, radius=0.4)

        value = DecimalNumber(angle.get_value(degrees=True), unit=r"^{\circ}")
        value.next_to(angle, UR)

        self.add(line1, line2, angle, value)

AnnotationDot¶

带描边强调的小圆点，比普通 Dot 在复杂背景上更醒目，常用于标记点。

继承关系¶

参数¶

`radius`	0.10400000000000001，float
`stroke_width`	5，float
`stroke_color`	ManimColor('#FFFFFF')，ParsableManimColor
`fill_color`	ManimColor('#58C4DD')，ParsableManimColor

API 文档¶

基类：Dot

A dot with bigger radius and bold stroke to annotate scenes.

AnnularSector¶

扇环（圆环的一段）：内外半径 + 起止角度，饼图环图的基础件。

继承关系¶

参数¶

`inner_radius`	1，float
`outer_radius`	2，float
`angle`	1.5707963267948966，float
`start_angle`	0，float
`fill_opacity`	1，float
`stroke_width`	0，float
`color`	ManimColor('#FFFFFF')，ParsableManimColor

快速上手¶

s = AnnularSector(inner_radius=1, outer_radius=2, angle=PI/2)

API 文档¶

class manim.AnnularSector(inner_radius: float = 1, outer_radius: float = 2, angle: float = 1.5707963267948966, start_angle: float = 0, fill_opacity: float = 1, stroke_width: float = 0, color: ManimColor | int | str | NDArray[int64] | tuple[int, int, int] | NDArray[float64] | tuple[float, float, float] | tuple[int, int, int, int] | tuple[float, float, float, float] = ManimColor('#FFFFFF'), **kwargs: Any)¶

基类：Arc

A sector of an annulus.

Parameters¶

inner_radius: The inside radius of the Annular Sector.
outer_radius: The outside radius of the Annular Sector.
angle: The clockwise angle of the Annular Sector.
start_angle: The starting clockwise angle of the Annular Sector.
fill_opacity: The opacity of the color filled in the Annular Sector.
stroke_width: The stroke width of the Annular Sector.
color: The color filled into the Annular Sector.

Examples¶

class AnnularSectorExample(Scene):
    def construct(self):
        # Changes background color to clearly visualize changes in fill_opacity.
        self.camera.background_color = WHITE

        # The default parameter start_angle is 0, so the AnnularSector starts from the +x-axis.
        s1 = AnnularSector(color=YELLOW).move_to(2 * UL)

        # Different inner_radius and outer_radius than the default.
        s2 = AnnularSector(inner_radius=1.5, outer_radius=2, angle=45 * DEGREES, color=RED).move_to(2 * UR)

        # fill_opacity is typically a number > 0 and <= 1. If fill_opacity=0, the AnnularSector is transparent.
        s3 = AnnularSector(inner_radius=1, outer_radius=1.5, angle=PI, fill_opacity=0.25, color=BLUE).move_to(2 * DL)

        # With a negative value for the angle, the AnnularSector is drawn clockwise from the start value.
        s4 = AnnularSector(inner_radius=1, outer_radius=1.5, angle=-3 * PI / 2, color=GREEN).move_to(2 * DR)

        self.add(s1, s2, s3, s4)

generate_points() → Self¶

Initializes points and therefore the shape.

Gets called upon creation. This is an empty method that can be implemented by subclasses.

Annulus¶

完整圆环：内半径 + 外半径，甜甜圈形状。

继承关系¶

参数¶

`inner_radius`	1，float
`outer_radius`	2，float
`fill_opacity`	1，float
`stroke_width`	0，float
`color`	ManimColor('#FFFFFF')，ParsableManimColor
`mark_paths_closed`	False，bool

API 文档¶

基类：Circle

Region between two concentric Circles.

Parameters¶

inner_radius: The radius of the inner Circle.
outer_radius: The radius of the outer Circle.
kwargs: Additional arguments to be passed to Annulus

Examples¶

class AnnulusExample(Scene):
    def construct(self):
        annulus_1 = Annulus(inner_radius=0.5, outer_radius=1).shift(UP)
        annulus_2 = Annulus(inner_radius=0.3, outer_radius=0.6, color=RED).next_to(annulus_1, DOWN)
        self.add(annulus_1, annulus_2)

generate_points() → Self¶

Initializes points and therefore the shape.

Gets called upon creation. This is an empty method that can be implemented by subclasses.

Arc¶

圆弧：半径 + 起始角 + 张角，所有曲线类图形（Circle、Sector……）的祖宗。

继承关系¶

参数¶

`radius`	1.0，float \| None
`start_angle`	0，float
`angle`	1.5707963267948966，float
`num_components`	9，int
`arc_center`	array([0., 0., 0.])，Point3DLike

快速上手¶

arc = Arc(radius=2, start_angle=0, angle=PI)

API 文档¶

class manim.Arc(radius: float | None = 1.0, start_angle: float = 0, angle: float = 1.5707963267948966, num_components: int = 9, arc_center: Point3DLike = array([0., 0., 0.]), **kwargs: Any)¶

基类：TipableVMobject

A circular arc.

Examples¶

A simple arc of angle Pi.

class ArcExample(Scene):
    def construct(self):
        self.add(Arc(angle=PI))

generate_points() → Self¶

Initializes points and therefore the shape.

Gets called upon creation. This is an empty method that can be implemented by subclasses.

get_arc_center(warning: bool = True) → Point3D¶: Looks at the normals to the first two anchors, and finds their intersection points

ArcBetweenPoints¶

过两点的一段圆弧：自动选半径让弧经过两点，画「连接箭头」或「跳跃路径」常用。

继承关系¶

参数¶

`start`	—，Point3DLike
`end`	—，Point3DLike
`angle`	1.5707963267948966，float
`radius`	None，float \| None

快速上手¶

arc = ArcBetweenPoints(a.get_center(), b.get_center())

API 文档¶

class manim.ArcBetweenPoints(start: Point3DLike, end: Point3DLike, angle: float = 1.5707963267948966, radius: float | None = None, **kwargs: Any)¶

基类：Arc

Inherits from Arc and additionally takes 2 points between which the arc is spanned.

Example¶

class ArcBetweenPointsExample(Scene):
    def construct(self):
        circle = Circle(radius=2, stroke_color=GREY)
        dot_1 = Dot(color=GREEN).move_to([2, 0, 0]).scale(0.5)
        dot_1_text = Tex("(2,0)").scale(0.5).next_to(dot_1, RIGHT).set_color(BLUE)
        dot_2 = Dot(color=GREEN).move_to([0, 2, 0]).scale(0.5)
        dot_2_text = Tex("(0,2)").scale(0.5).next_to(dot_2, UP).set_color(BLUE)
        arc= ArcBetweenPoints(start=2 * RIGHT, end=2 * UP, stroke_color=YELLOW)
        self.add(circle, dot_1, dot_2, dot_1_text, dot_2_text)
        self.play(Create(arc))

ArcPolygon¶

边为圆弧的多边形：顶点之间用弧连接而非直线，呈现「鼓包」轮廓。

继承关系¶

参数¶

`angle`	0.7853981633974483，float
`radius`	None，float \| None
`arc_config`	None，list[dict] \| None

API 文档¶

class manim.ArcPolygon(*vertices: Point3DLike, angle: float = 0.7853981633974483, radius: float | None = None, arc_config: list[dict] | None = None, **kwargs: Any)¶

基类：VMobject

A generalized polygon allowing for points to be connected with arcs.

This version tries to stick close to the way Polygon is used. Points can be passed to it directly which are used to generate the according arcs (using ArcBetweenPoints). An angle or radius can be passed to it to use across all arcs, but to configure arcs individually an arc_config list has to be passed with the syntax explained below.

Parameters¶

vertices: A list of vertices, start and end points for the arc segments.
angle: The angle used for constructing the arcs. If no other parameters are set, this angle is used to construct all arcs.
radius: The circle radius used to construct the arcs. If specified, overrides the specified angle.
arc_config: When passing a dict, its content will be passed as keyword arguments to ArcBetweenPoints. Otherwise, a list of dictionaries containing values that are passed as keyword arguments for every individual arc can be passed.
kwargs: Further keyword arguments that are passed to the constructor of VMobject.

Attributes¶

arcslist

The arcs created from the input parameters:

>>> from manim import ArcPolygon
>>> ap = ArcPolygon([0, 0, 0], [2, 0, 0], [0, 2, 0])
>>> ap.arcs
[ArcBetweenPoints, ArcBetweenPoints, ArcBetweenPoints]

小技巧

Two instances of ArcPolygon can be transformed properly into one another as well. Be advised that any arc initialized with angle=0 will actually be a straight line, so if a straight section should seamlessly transform into an arced section or vice versa, initialize the straight section with a negligible angle instead (such as angle=0.0001).

备注

There is an alternative version (ArcPolygonFromArcs) that is instantiated with pre-defined arcs.

Examples¶

class SeveralArcPolygons(Scene):
    def construct(self):
        a = [0, 0, 0]
        b = [2, 0, 0]
        c = [0, 2, 0]
        ap1 = ArcPolygon(a, b, c, radius=2)
        ap2 = ArcPolygon(a, b, c, angle=45*DEGREES)
        ap3 = ArcPolygon(a, b, c, arc_config={'radius': 1.7, 'color': RED})
        ap4 = ArcPolygon(a, b, c, color=RED, fill_opacity=1,
                                    arc_config=[{'radius': 1.7, 'color': RED},
                                    {'angle': 20*DEGREES, 'color': BLUE},
                                    {'radius': 1}])
        ap_group = VGroup(ap1, ap2, ap3, ap4).arrange()
        self.play(*[Create(ap) for ap in [ap1, ap2, ap3, ap4]])
        self.wait()

For further examples see ArcPolygonFromArcs.

ArcPolygonFromArcs¶

用现成 Arc 对象拼成多边形，边完全由你给的弧决定。

继承关系¶

API 文档¶

class manim.ArcPolygonFromArcs(*arcs: Arc | ArcBetweenPoints, **kwargs: Any)¶

基类：VMobject

A generalized polygon allowing for points to be connected with arcs.

This version takes in pre-defined arcs to generate the arcpolygon and introduces little new syntax. However unlike Polygon it can't be created with points directly.

For proper appearance the passed arcs should connect seamlessly: [a,b][b,c][c,a]

If there are any gaps between the arcs, those will be filled in with straight lines, which can be used deliberately for any straight sections. Arcs can also be passed as straight lines such as an arc initialized with angle=0.

Parameters¶

arcs: These are the arcs from which the arcpolygon is assembled.
kwargs: Keyword arguments that are passed to the constructor of VMobject. Affects how the ArcPolygon itself is drawn, but doesn't affect passed arcs.

Attributes¶

arcs

The arcs used to initialize the ArcPolygonFromArcs:

>>> from manim import ArcPolygonFromArcs, Arc, ArcBetweenPoints
>>> ap = ArcPolygonFromArcs(Arc(), ArcBetweenPoints([1,0,0], [0,1,0]), Arc())
>>> ap.arcs
[Arc, ArcBetweenPoints, Arc]

小技巧

备注

There is an alternative version (ArcPolygon) that can be instantiated with points.

参见

ArcPolygon

Examples¶

One example of an arcpolygon is the Reuleaux triangle. Instead of 3 straight lines connecting the outer points, a Reuleaux triangle has 3 arcs connecting those points, making a shape with constant width.

Passed arcs are stored as submobjects in the arcpolygon. This means that the arcs are changed along with the arcpolygon, for example when it's shifted, and these arcs can be manipulated after the arcpolygon has been initialized.

Also both the arcs contained in an ArcPolygonFromArcs, as well as the arcpolygon itself are drawn, which affects draw time in Create for example. In most cases the arcs themselves don't need to be drawn, in which case they can be passed as invisible.

class ArcPolygonExample(Scene):
    def construct(self):
        arc_conf = {"stroke_width": 0}
        poly_conf = {"stroke_width": 10, "stroke_color": BLUE,
              "fill_opacity": 1, "color": PURPLE}
        a = [-1, 0, 0]
        b = [1, 0, 0]
        c = [0, np.sqrt(3), 0]
        arc0 = ArcBetweenPoints(a, b, radius=2, **arc_conf)
        arc1 = ArcBetweenPoints(b, c, radius=2, **arc_conf)
        arc2 = ArcBetweenPoints(c, a, radius=2, **arc_conf)
        reuleaux_tri = ArcPolygonFromArcs(arc0, arc1, arc2, **poly_conf)
        self.play(FadeIn(reuleaux_tri))
        self.wait(2)

The arcpolygon itself can also be hidden so that instead only the contained arcs are drawn. This can be used to easily debug arcs or to highlight them.

class ArcPolygonExample2(Scene):
    def construct(self):
        arc_conf = {"stroke_width": 3, "stroke_color": BLUE,
            "fill_opacity": 0.5, "color": GREEN}
        poly_conf = {"color": None}
        a = [-1, 0, 0]
        b = [1, 0, 0]
        c = [0, np.sqrt(3), 0]
        arc0 = ArcBetweenPoints(a, b, radius=2, **arc_conf)
        arc1 = ArcBetweenPoints(b, c, radius=2, **arc_conf)
        arc2 = ArcBetweenPoints(c, a, radius=2, stroke_color=RED)
        reuleaux_tri = ArcPolygonFromArcs(arc0, arc1, arc2, **poly_conf)
        self.play(FadeIn(reuleaux_tri))
        self.wait(2)

Arrow¶

带箭头的直线：start/end + 箭尖样式 buff 可调，是最常用的指向性图形。

继承关系¶

参数¶

`stroke_width`	6，float
`buff`	0.25，float
`max_tip_length_to_length_ratio`	0.25，float
`max_stroke_width_to_length_ratio`	5，float

快速上手¶

arrow = Arrow(LEFT, RIGHT, buff=0.1)

API 文档¶

class manim.Arrow(*args: Any, stroke_width: float = 6, buff: float = 0.25, max_tip_length_to_length_ratio: float = 0.25, max_stroke_width_to_length_ratio: float = 5, **kwargs: Any)¶

基类：Line

An arrow.

Parameters¶

args: Arguments to be passed to Line.
stroke_width: The thickness of the arrow. Influenced by max_stroke_width_to_length_ratio.
buff: The distance of the arrow from its start and end points.
max_tip_length_to_length_ratio: tip_length scales with the length of the arrow. Increasing this ratio raises the max value of tip_length.
max_stroke_width_to_length_ratio: stroke_width scales with the length of the arrow. Increasing this ratio ratios the max value of stroke_width.
kwargs: Additional arguments to be passed to Line.

参见

ArrowTip CurvedArrow

Examples¶

from manim.mobject.geometry.tips import ArrowSquareTip
class ArrowExample(Scene):
    def construct(self):
        arrow_1 = Arrow(start=RIGHT, end=LEFT, color=GOLD)
        arrow_2 = Arrow(start=RIGHT, end=LEFT, color=GOLD, tip_shape=ArrowSquareTip).shift(DOWN)
        g1 = Group(arrow_1, arrow_2)

        # the effect of buff
        square = Square(color=MAROON_A)
        arrow_3 = Arrow(start=LEFT, end=RIGHT)
        arrow_4 = Arrow(start=LEFT, end=RIGHT, buff=0).next_to(arrow_1, UP)
        g2 = Group(arrow_3, arrow_4, square)

        # a shorter arrow has a shorter tip and smaller stroke width
        arrow_5 = Arrow(start=ORIGIN, end=config.top).shift(LEFT * 4)
        arrow_6 = Arrow(start=config.top + DOWN, end=config.top).shift(LEFT * 3)
        g3 = Group(arrow_5, arrow_6)

        self.add(Group(g1, g2, g3).arrange(buff=2))

class ArrowExample(Scene):
    def construct(self):
        left_group = VGroup()
        # As buff increases, the size of the arrow decreases.
        for buff in np.arange(0, 2.2, 0.45):
            left_group += Arrow(buff=buff, start=2 * LEFT, end=2 * RIGHT)
        # Required to arrange arrows.
        left_group.arrange(DOWN)
        left_group.move_to(4 * LEFT)

        middle_group = VGroup()
        # As max_stroke_width_to_length_ratio gets bigger,
        # the width of stroke increases.
        for i in np.arange(0, 5, 0.5):
            middle_group += Arrow(max_stroke_width_to_length_ratio=i)
        middle_group.arrange(DOWN)

        UR_group = VGroup()
        # As max_tip_length_to_length_ratio increases,
        # the length of the tip increases.
        for i in np.arange(0, 0.3, 0.1):
            UR_group += Arrow(max_tip_length_to_length_ratio=i)
        UR_group.arrange(DOWN)
        UR_group.move_to(4 * RIGHT + 2 * UP)

        DR_group = VGroup()
        DR_group += Arrow(start=LEFT, end=RIGHT, color=BLUE, tip_shape=ArrowSquareTip)
        DR_group += Arrow(start=LEFT, end=RIGHT, color=BLUE, tip_shape=ArrowSquareFilledTip)
        DR_group += Arrow(start=LEFT, end=RIGHT, color=YELLOW, tip_shape=ArrowCircleTip)
        DR_group += Arrow(start=LEFT, end=RIGHT, color=YELLOW, tip_shape=ArrowCircleFilledTip)
        DR_group.arrange(DOWN)
        DR_group.move_to(4 * RIGHT + 2 * DOWN)

        self.add(left_group, middle_group, UR_group, DR_group)

get_default_tip_length() → float¶

Returns the default tip_length of the arrow.

Examples¶

>>> Arrow().get_default_tip_length()
0.35

get_normal_vector() → Vector3D¶

Returns the normal of a vector.

Examples¶

>>> np.round(Arrow().get_normal_vector()) + 0. # add 0. to avoid negative 0 in output
array([ 0.,  0., -1.])

reset_normal_vector() → Self¶: Resets the normal of a vector

scale(factor: float, scale_tips: bool = False, **kwargs: Any) → Self¶

Scale an arrow, but keep stroke width and arrow tip size fixed.

参见

scale()

Examples¶

>>> arrow = Arrow(np.array([-1, -1, 0]), np.array([1, 1, 0]), buff=0)
>>> scaled_arrow = arrow.scale(2)
>>> np.round(scaled_arrow.get_start_and_end(), 8) + 0
array([[-2., -2.,  0.],
       [ 2.,  2.,  0.]])
>>> arrow.tip.length == scaled_arrow.tip.length
True

Manually scaling the object using the default method scale() does not have the same properties:

>>> new_arrow = Arrow(np.array([-1, -1, 0]), np.array([1, 1, 0]), buff=0)
>>> another_scaled_arrow = VMobject.scale(new_arrow, 2)
>>> another_scaled_arrow.tip.length == arrow.tip.length
False

ArrowCircleFilledTip¶

圆形实心箭尖样式类：配合 Arrow 的 tip_shape 使用（ArrowCircleTip 的实心版）。

继承关系¶

参数¶

`fill_opacity`	1，float
`stroke_width`	0，float

API 文档¶

class manim.ArrowCircleFilledTip(fill_opacity: float = 1, stroke_width: float = 0, **kwargs: Any)¶

基类：ArrowCircleTip

Circular arrow tip with filled tip.

ArrowCircleTip¶

空心圆形箭尖样式类：把箭头末端换成小圆圈，思维导图风。

继承关系¶

参数¶

`fill_opacity`	0，float
`stroke_width`	3，float
`length`	0.35，float
`start_angle`	3.141592653589793，float

API 文档¶

class manim.ArrowCircleTip(fill_opacity: float = 0, stroke_width: float = 3, length: float = 0.35, start_angle: float = 3.141592653589793, **kwargs: Any)¶

基类：ArrowTip, Circle

Circular arrow tip.

ArrowSquareFilledTip¶

方形实心箭尖样式类。

继承关系¶

参数¶

`fill_opacity`	1，float
`stroke_width`	0，float

API 文档¶

class manim.ArrowSquareFilledTip(fill_opacity: float = 1, stroke_width: float = 0, **kwargs: Any)¶

基类：ArrowSquareTip

Square arrow tip with filled tip.

ArrowSquareTip¶

空心方形箭尖样式类。

继承关系¶

参数¶

`fill_opacity`	0，float
`stroke_width`	3，float
`length`	0.35，float
`start_angle`	3.141592653589793，float

API 文档¶

class manim.ArrowSquareTip(fill_opacity: float = 0, stroke_width: float = 3, length: float = 0.35, start_angle: float = 3.141592653589793, **kwargs: Any)¶

基类：ArrowTip, Square

Square arrow tip.

ArrowTip¶

所有箭尖样式的基类：自定义箭尖就继承它实现 set_points()，length/width 属性定义尺寸。

继承关系¶

API 文档¶

class manim.ArrowTip(*args: Any, **kwargs: Any)¶

基类：VMobject

Base class for arrow tips.

参见

ArrowTriangleTip ArrowTriangleFilledTip ArrowCircleTip ArrowCircleFilledTip ArrowSquareTip ArrowSquareFilledTip StealthTip

Examples¶

Cannot be used directly, only intended for inheritance:

>>> tip = ArrowTip()
Traceback (most recent call last):
...
NotImplementedError: Has to be implemented in inheriting subclasses.

Instead, use one of the pre-defined ones, or make a custom one like this:

>>> from manim import RegularPolygon, Arrow
>>> class MyCustomArrowTip(ArrowTip, RegularPolygon):
...     def __init__(self, length=0.35, **kwargs):
...         RegularPolygon.__init__(self, n=5, **kwargs)
...         self.width = length
...         self.stretch_to_fit_height(length)
>>> arr = Arrow(
...     np.array([-2, -2, 0]), np.array([2, 2, 0]), tip_shape=MyCustomArrowTip
... )
>>> isinstance(arr.tip, RegularPolygon)
True
>>> from manim import Scene, Create
>>> class CustomTipExample(Scene):
...     def construct(self):
...         self.play(Create(arr))

Using a class inherited from ArrowTip to get a non-filled tip is a shorthand to manually specifying the arrow tip style as follows:

>>> arrow = Arrow(np.array([0, 0, 0]), np.array([1, 1, 0]),
...               tip_style={'fill_opacity': 0, 'stroke_width': 3})

The following example illustrates the usage of all of the predefined arrow tips.

class ArrowTipsShowcase(Scene):
    def construct(self):
        tip_names = [
            'Default (YELLOW)', 'ArrowTriangleTip', 'Default', 'ArrowSquareTip',
            'ArrowSquareFilledTip', 'ArrowCircleTip', 'ArrowCircleFilledTip', 'StealthTip'
        ]

        big_arrows = [
            Arrow(start=[-4, 3.5, 0], end=[2, 3.5, 0], color=YELLOW),
            Arrow(start=[-4, 2.5, 0], end=[2, 2.5, 0], tip_shape=ArrowTriangleTip),
            Arrow(start=[-4, 1.5, 0], end=[2, 1.5, 0]),
            Arrow(start=[-4, 0.5, 0], end=[2, 0.5, 0], tip_shape=ArrowSquareTip),

            Arrow([-4, -0.5, 0], [2, -0.5, 0], tip_shape=ArrowSquareFilledTip),
            Arrow([-4, -1.5, 0], [2, -1.5, 0], tip_shape=ArrowCircleTip),
            Arrow([-4, -2.5, 0], [2, -2.5, 0], tip_shape=ArrowCircleFilledTip),
            Arrow([-4, -3.5, 0], [2, -3.5, 0], tip_shape=StealthTip)
        ]

        small_arrows = (
            arrow.copy().scale(0.5, scale_tips=True).next_to(arrow, RIGHT) for arrow in big_arrows
        )

        labels = (
            Text(tip_names[i], font='monospace', font_size=20, color=BLUE).next_to(big_arrows[i], LEFT) for i in range(len(big_arrows))
        )

        self.add(*big_arrows, *small_arrows, *labels)

property base: Point3D¶

The base point of the arrow tip.

This is the point connecting to the arrow line.

Examples¶

>>> from manim import Arrow
>>> arrow = Arrow(np.array([0, 0, 0]), np.array([2, 0, 0]), buff=0)
>>> arrow.tip.base.round(2) + 0.  # add 0. to avoid negative 0 in output
array([1.65, 0.  , 0.  ])

property length: float¶

The length of the arrow tip.

Examples¶

>>> from manim import Arrow
>>> arrow = Arrow(np.array([0, 0, 0]), np.array([1, 2, 0]))
>>> round(arrow.tip.length, 3)
0.35

property tip_angle: float¶

The angle of the arrow tip.

Examples¶

>>> from manim import Arrow
>>> arrow = Arrow(np.array([0, 0, 0]), np.array([1, 1, 0]), buff=0)
>>> bool(round(arrow.tip.tip_angle, 5) == round(PI/4, 5))
True

property tip_point: Point3D¶

The tip point of the arrow tip.

Examples¶

>>> from manim import Arrow
>>> arrow = Arrow(np.array([0, 0, 0]), np.array([2, 0, 0]), buff=0)
>>> arrow.tip.tip_point.round(2) + 0.
array([2., 0., 0.])

property vector: Vector3D¶

The vector pointing from the base point to the tip point.

Examples¶

>>> from manim import Arrow
>>> arrow = Arrow(np.array([0, 0, 0]), np.array([2, 2, 0]), buff=0)
>>> arrow.tip.vector.round(2) + 0.
array([0.25, 0.25, 0.  ])

ArrowTriangleFilledTip¶

三角实心箭尖（默认样式），一般不直接实例化。

继承关系¶

参数¶

`fill_opacity`	1，float
`stroke_width`	0，float

API 文档¶

class manim.ArrowTriangleFilledTip(fill_opacity: float = 1, stroke_width: float = 0, **kwargs: Any)¶

基类：ArrowTriangleTip

Triangular arrow tip with filled tip.

This is the default arrow tip shape.

ArrowTriangleTip¶

空心三角箭尖样式类。

继承关系¶

参数¶

`fill_opacity`	0，float
`stroke_width`	3，float
`length`	0.35，float
`width`	0.35，float
`start_angle`	3.141592653589793，float

API 文档¶

class manim.ArrowTriangleTip(fill_opacity: float = 0, stroke_width: float = 3, length: float = 0.35, width: float = 0.35, start_angle: float = 3.141592653589793, **kwargs: Any)¶

基类：ArrowTip, Triangle

Triangular arrow tip.

BackgroundRectangle¶

自动包裹目标对象的背景色矩形：给文字图形加底色衬垫，防止与背景混淆。

继承关系¶

参数¶

`color`	None
`stroke_width`	0，float
`stroke_opacity`	0，float
`fill_opacity`	0.75，float
`buff`	0

快速上手¶

bg = BackgroundRectangle(label, fill_opacity=0.7)

API 文档¶

基类：SurroundingRectangle

A background rectangle. Its default color is the background color of the scene.

Examples¶

class ExampleBackgroundRectangle(Scene):
    def construct(self):
        circle = Circle().shift(LEFT)
        circle.set_stroke(color=GREEN, width=20)
        triangle = Triangle().shift(2 * RIGHT)
        triangle.set_fill(PINK, opacity=0.5)
        backgroundRectangle1 = BackgroundRectangle(circle, color=WHITE, fill_opacity=0.15)
        backgroundRectangle2 = BackgroundRectangle(triangle, color=WHITE, fill_opacity=0.15)
        self.add(backgroundRectangle1)
        self.add(backgroundRectangle2)
        self.add(circle)
        self.add(triangle)
        self.play(Rotate(backgroundRectangle1, PI / 4))
        self.play(Rotate(backgroundRectangle2, PI / 2))

pointwise_become_partial(mobject: Mobject, a: Any, b: float) → Self¶

Given a 2nd VMobject vmobject, a lower bound a and an upper bound b, modify this VMobject's points to match the portion of the Bézier spline described by vmobject.points with the parameter t between a and b.

Parameters¶

vmobject: The VMobject that will serve as a model.
a: The lower bound for t.
b: The upper bound for t

Returns¶

VMobject: The VMobject itself, after the transformation.

Raises¶

TypeError: If vmobject is not an instance of VMobject.

Circle¶

圆：radius 或 diameter 指定大小，提供 from_three_points、point_at_angle、surround 等几何工厂方法。

继承关系¶

参数¶

`radius`	None，float \| None
`color`	ManimColor('#FC6255')，ParsableManimColor

快速上手¶

c = Circle(radius=2, color=BLUE)

API 文档¶

基类：Arc

A circle.

Parameters¶

color: The color of the shape.
kwargs: Additional arguments to be passed to Arc

Examples¶

class CircleExample(Scene):
    def construct(self):
        circle_1 = Circle(radius=1.0)
        circle_2 = Circle(radius=1.5, color=GREEN)
        circle_3 = Circle(radius=1.0, color=BLUE_B, fill_opacity=1)

        circle_group = Group(circle_1, circle_2, circle_3).arrange(buff=1)
        self.add(circle_group)

static from_three_points(p1: Point3DLike, p2: Point3DLike, p3: Point3DLike, **kwargs: Any) → Circle¶

Returns a circle passing through the specified three points.

Example¶

class CircleFromPointsExample(Scene):
    def construct(self):
        circle = Circle.from_three_points(LEFT, LEFT + UP, UP * 2, color=RED)
        dots = VGroup(
            Dot(LEFT),
            Dot(LEFT + UP),
            Dot(UP * 2),
        )
        self.add(NumberPlane(), circle, dots)

point_at_angle(angle: float) → Point3D¶

Returns the position of a point on the circle.

Parameters¶

angle: The angle of the point along the circle in radians.

Returns¶

numpy.ndarray: The location of the point along the circle's circumference.

Examples¶

class PointAtAngleExample(Scene):
    def construct(self):
        circle = Circle(radius=2.0)
        p1 = circle.point_at_angle(PI/2)
        p2 = circle.point_at_angle(270*DEGREES)

        s1 = Square(side_length=0.25).move_to(p1)
        s2 = Square(side_length=0.25).move_to(p2)
        self.add(circle, s1, s2)

surround(mobject: Mobject, dim_to_match: int = 0, stretch: bool = False, buffer_factor: float = 1.2) → Self¶

Modifies a circle so that it surrounds a given mobject.

Parameters¶

mobject: The mobject that the circle will be surrounding.

dim_to_match buffer_factor

Scales the circle with respect to the mobject. A buffer_factor < 1 makes the circle smaller than the mobject.

stretch: Stretches the circle to fit more tightly around the mobject. Note: Does not work with Line

Examples¶

class CircleSurround(Scene):
    def construct(self):
        triangle1 = Triangle()
        circle1 = Circle().surround(triangle1)
        group1 = Group(triangle1,circle1) # treat the two mobjects as one

        line2 = Line()
        circle2 = Circle().surround(line2, buffer_factor=2.0)
        group2 = Group(line2,circle2)

        # buffer_factor < 1, so the circle is smaller than the square
        square3 = Square()
        circle3 = Circle().surround(square3, buffer_factor=0.5)
        group3 = Group(square3, circle3)

        group = Group(group1, group2, group3).arrange(buff=1)
        self.add(group)

ConvexHull¶

一组点的凸包多边形：自动计算外轮廓，计算几何可视化。

继承关系¶

参数¶

API 文档¶

class manim.ConvexHull(*points: Point3DLike, tolerance: float = 1e-05, **kwargs: Any)¶

基类：Polygram

Constructs a convex hull for a set of points in no particular order.

Parameters¶

points: The points to consider.
tolerance: The tolerance used by quickhull.
kwargs: Forwarded to the parent constructor.

Examples¶

class ConvexHullExample(Scene):
    def construct(self):
        points = [
            [-2.35, -2.25, 0],
            [1.65, -2.25, 0],
            [2.65, -0.25, 0],
            [1.65, 1.75, 0],
            [-0.35, 2.75, 0],
            [-2.35, 0.75, 0],
            [-0.35, -1.25, 0],
            [0.65, -0.25, 0],
            [-1.35, 0.25, 0],
            [0.15, 0.75, 0]
        ]
        hull = ConvexHull(*points, color=BLUE)
        dots = VGroup(*[Dot(point) for point in points])
        self.add(hull)
        self.add(dots)

Cross¶

叉号（×）图形：stroke_width 和比例可调，标记错误或否定语义。

继承关系¶

参数¶

`mobject`	None，Mobject \| None
`stroke_color`	ManimColor('#FC6255')，ParsableManimColor
`stroke_width`	6.0，float
`scale_factor`	1.0，float

快速上手¶

cross = Cross(mob)

API 文档¶

基类：VGroup

Creates a cross.

Parameters¶

mobject: The mobject linked to this instance. It fits the mobject when specified. Defaults to None.
stroke_color: Specifies the color of the cross lines. Defaults to RED.
stroke_width: Specifies the width of the cross lines. Defaults to 6.
scale_factor: Scales the cross to the provided units. Defaults to 1.

Examples¶

class ExampleCross(Scene):
    def construct(self):
        cross = Cross()
        self.add(cross)

CubicBezier¶

三次贝塞尔曲线：两个锚点 + 两个控制点，是矢量绘图的最小单元。

继承关系¶

参数¶

`start_anchor`	—，Point3DLike
`start_handle`	—，Point3DLike
`end_handle`	—，Point3DLike
`end_anchor`	—，Point3DLike

快速上手¶

b = CubicBezier(a1, h1, h2, a2)

API 文档¶

class manim.CubicBezier(start_anchor: Point3DLike, start_handle: Point3DLike, end_handle: Point3DLike, end_anchor: Point3DLike, **kwargs: Any)¶

基类：VMobject

A cubic Bézier curve.

Example¶

class BezierSplineExample(Scene):
    def construct(self):
        p1 = np.array([-3, 1, 0])
        p1b = p1 + [1, 0, 0]
        d1 = Dot(point=p1).set_color(BLUE)
        l1 = Line(p1, p1b)
        p2 = np.array([3, -1, 0])
        p2b = p2 - [1, 0, 0]
        d2 = Dot(point=p2).set_color(RED)
        l2 = Line(p2, p2b)
        bezier = CubicBezier(p1b, p1b + 3 * RIGHT, p2b - 3 * RIGHT, p2b)
        self.add(l1, d1, l2, d2, bezier)

CurvedArrow¶

弯曲的箭头：ArcBetweenPoints + 箭尖的组合体，流程图里绕过障碍的连线。

继承关系¶

参数¶

`start_point`	—，Point3DLike
`end_point`	—，Point3DLike

API 文档¶

class manim.CurvedArrow(start_point: Point3DLike, end_point: Point3DLike, **kwargs: Any)¶: 基类：ArcBetweenPoints

CurvedDoubleArrow¶

两端都带箭尖的弯弧，双向关系专用。

继承关系¶

参数¶

`start_point`	—，Point3DLike
`end_point`	—，Point3DLike

API 文档¶

class manim.CurvedDoubleArrow(start_point: Point3DLike, end_point: Point3DLike, **kwargs: Any)¶: 基类：CurvedArrow

Cutout¶

带镂空的多边形：外部轮廓减内部孔洞，fill 模式下孔洞透明。

继承关系¶

参数¶

快速上手¶

c = Cutout(square, circle)

API 文档¶

class manim.Cutout(main_shape: VMobject, *mobjects: VMobject, **kwargs: Any)¶

基类：VMobject

A shape with smaller cutouts.

Parameters¶

main_shape: The primary shape from which cutouts are made.
mobjects: The smaller shapes which are to be cut out of the main_shape.
kwargs: Further keyword arguments that are passed to the constructor of VMobject.

警告

Technically, this class behaves similar to a symmetric difference: if parts of the mobjects are not located within the main_shape, these parts will be added to the resulting VMobject.

Examples¶

class CutoutExample(Scene):
    def construct(self):
        s1 = Square().scale(2.5)
        s2 = Triangle().shift(DOWN + RIGHT).scale(0.5)
        s3 = Square().shift(UP + RIGHT).scale(0.5)
        s4 = RegularPolygon(5).shift(DOWN + LEFT).scale(0.5)
        s5 = RegularPolygon(6).shift(UP + LEFT).scale(0.5)
        c = Cutout(s1, s2, s3, s4, s5, fill_opacity=1, color=BLUE, stroke_color=RED)
        self.play(Write(c), run_time=4)
        self.wait()

DashedLine¶

虚线直线：DashedVMobject 的直线便捷版，辅助线首选。

继承关系¶

参数¶

`dash_length`	0.05，float
`dashed_ratio`	0.5，float

快速上手¶

d = DashedLine(LEFT, RIGHT)

API 文档¶

class manim.DashedLine(*args: Any, dash_length: float = 0.05, dashed_ratio: float = 0.5, **kwargs: Any)¶

基类：Line

A dashed Line.

Parameters¶

args: Arguments to be passed to Line
dash_length: The length of each individual dash of the line.
dashed_ratio: The ratio of dash space to empty space. Range of 0-1.
kwargs: Additional arguments to be passed to Line

参见

DashedVMobject

Examples¶

class DashedLineExample(Scene):
    def construct(self):
        # dash_length increased
        dashed_1 = DashedLine(config.left_side, config.right_side, dash_length=2.0).shift(UP*2)
        # normal
        dashed_2 = DashedLine(config.left_side, config.right_side)
        # dashed_ratio decreased
        dashed_3 = DashedLine(config.left_side, config.right_side, dashed_ratio=0.1).shift(DOWN*2)
        self.add(dashed_1, dashed_2, dashed_3)

get_end() → Point3D¶

Returns the end point of the line.

Examples¶

>>> DashedLine().get_end()
array([1., 0., 0.])

get_first_handle() → Point3D¶

Returns the point of the first handle.

Examples¶

>>> DashedLine().get_first_handle()
array([-0.98333333,  0.        ,  0.        ])

get_last_handle() → Point3D¶

Returns the point of the last handle.

Examples¶

>>> DashedLine().get_last_handle()
array([0.98333333, 0.        , 0.        ])

get_start() → Point3D¶

Returns the start point of the line.

Examples¶

>>> DashedLine().get_start()
array([-1.,  0.,  0.])

Difference¶

布尔差集：从主体图形中挖掉重叠部分，属于 VMobject 布尔运算家族。

继承关系¶

参数¶

`subject`	—，VMobject
`clip`	—，VMobject

快速上手¶

diff = Difference(square, circle)

API 文档¶

class manim.Difference(subject: VMobject, clip: VMobject, **kwargs: Any)¶

基类：_BooleanOps

Subtracts one VMobject from another one.

Parameters¶

subject: The 1st VMobject.
clip: The 2nd VMobject

Example¶

class DifferenceExample(Scene):
    def construct(self):
        sq = Square(color=RED, fill_opacity=1)
        sq.move_to([-2, 0, 0])
        cr = Circle(color=BLUE, fill_opacity=1)
        cr.move_to([-1.3, 0.7, 0])
        un = Difference(sq, cr, color=GREEN, fill_opacity=1)
        un.move_to([1.5, 0, 0])
        self.add(sq, cr, un)

Dot¶

小圆点：radius 很小且 fill 为主，标记坐标、描点画图的基本单元。

继承关系¶

参数¶

`point`	array([0., 0., 0.])，Point3DLike
`radius`	0.08，float
`stroke_width`	0，float
`fill_opacity`	1.0，float
`color`	ManimColor('#FFFFFF')，ParsableManimColor

快速上手¶

dot = Dot(point, color=RED)

API 文档¶

class manim.Dot(point: Point3DLike = array([0., 0., 0.]), radius: float = 0.08, stroke_width: float = 0, fill_opacity: float = 1.0, color: ParsableManimColor = ManimColor('#FFFFFF'), **kwargs: Any)¶

基类：Circle

A circle with a very small radius.

Parameters¶

point: The location of the dot.
radius: The radius of the dot.
stroke_width: The thickness of the outline of the dot.
fill_opacity: The opacity of the dot's fill_colour
color: The color of the dot.
kwargs: Additional arguments to be passed to Circle

Examples¶

class DotExample(Scene):
    def construct(self):
        dot1 = Dot(point=LEFT, radius=0.08)
        dot2 = Dot(point=ORIGIN)
        dot3 = Dot(point=RIGHT)
        self.add(dot1,dot2,dot3)

DoubleArrow¶

两端都有箭头的直线，表示双向映射或区间。

继承关系¶

快速上手¶

d = DoubleArrow(LEFT, RIGHT)

API 文档¶

class manim.DoubleArrow(*args: Any, **kwargs: Any)¶

基类：Arrow

An arrow with tips on both ends.

Parameters¶

args: Arguments to be passed to Arrow
kwargs: Additional arguments to be passed to Arrow

参见

ArrowTip CurvedDoubleArrow

Examples¶

from manim.mobject.geometry.tips import ArrowCircleFilledTip
class DoubleArrowExample(Scene):
    def construct(self):
        circle = Circle(radius=2.0)
        d_arrow = DoubleArrow(start=circle.get_left(), end=circle.get_right())
        d_arrow_2 = DoubleArrow(tip_shape_end=ArrowCircleFilledTip, tip_shape_start=ArrowCircleFilledTip)
        group = Group(Group(circle, d_arrow), d_arrow_2).arrange(UP, buff=1)
        self.add(group)

class DoubleArrowExample2(Scene):
    def construct(self):
        box = Square()
        p1 = box.get_left()
        p2 = box.get_right()
        d1 = DoubleArrow(p1, p2, buff=0)
        d2 = DoubleArrow(p1, p2, buff=0, tip_length=0.2, color=YELLOW)
        d3 = DoubleArrow(p1, p2, buff=0, tip_length=0.4, color=BLUE)
        Group(d1, d2, d3).arrange(DOWN)
        self.add(box, d1, d2, d3)

Elbow¶

直角弯头线：两条垂直短线段，管道图、直角坐标标记用。

继承关系¶

参数¶

`width`	0.2，float
`angle`	0，float

API 文档¶

class manim.Elbow(width: float = 0.2, angle: float = 0, **kwargs: Any)¶

基类：VMobject

Two lines that create a right angle about each other: L-shape.

Parameters¶

width: The length of the elbow's sides.
angle: The rotation of the elbow.
kwargs: Additional arguments to be passed to VMobject

参见

RightAngle

Examples¶

class ElbowExample(Scene):
    def construct(self):
        elbow_1 = Elbow()
        elbow_2 = Elbow(width=2.0)
        elbow_3 = Elbow(width=2.0, angle=5*PI/4)

        elbow_group = Group(elbow_1, elbow_2, elbow_3).arrange(buff=1)
        self.add(elbow_group)

Ellipse¶

椭圆：width/height 分别指定两轴，圆形的长轴版。

继承关系¶

参数¶

`width`	2，float
`height`	1，float

快速上手¶

e = Ellipse(width=4, height=2)

API 文档¶

class manim.Ellipse(width: float = 2, height: float = 1, **kwargs: Any)¶

基类：Circle

A circular shape; oval, circle.

Parameters¶

width: The horizontal width of the ellipse.
height: The vertical height of the ellipse.
kwargs: Additional arguments to be passed to Circle.

Examples¶

class EllipseExample(Scene):
    def construct(self):
        ellipse_1 = Ellipse(width=2.0, height=4.0, color=BLUE_B)
        ellipse_2 = Ellipse(width=4.0, height=1.0, color=BLUE_D)
        ellipse_group = Group(ellipse_1,ellipse_2).arrange(buff=1)
        self.add(ellipse_group)

Exclusion¶

布尔异或：只保留两个图形不重叠的部分。

继承关系¶

参数¶

`subject`	—，VMobject
`clip`	—，VMobject

API 文档¶

class manim.Exclusion(subject: VMobject, clip: VMobject, **kwargs: Any)¶

基类：_BooleanOps

Find the XOR between two VMobject. This creates a new VMobject consisting of the region covered by exactly one of them.

Parameters¶

subject: The 1st VMobject.
clip: The 2nd VMobject

Example¶

class IntersectionExample(Scene):
    def construct(self):
        sq = Square(color=RED, fill_opacity=1)
        sq.move_to([-2, 0, 0])
        cr = Circle(color=BLUE, fill_opacity=1)
        cr.move_to([-1.3, 0.7, 0])
        un = Exclusion(sq, cr, color=GREEN, fill_opacity=1)
        un.move_to([1.5, 0.4, 0])
        self.add(sq, cr, un)

Intersection¶

布尔交集：只保留两个图形重叠的区域。

继承关系¶

快速上手¶

i = Intersection(square, circle)

API 文档¶

class manim.Intersection(*vmobjects: VMobject, **kwargs: Any)¶

基类：_BooleanOps

Find the intersection of two VMobject s. This keeps the parts covered by both VMobject s.

Parameters¶

vmobjects: The VMobject to find the intersection.

Raises¶

ValueError: If less the 2 VMobject are passed.

Example¶

class IntersectionExample(Scene):
    def construct(self):
        sq = Square(color=RED, fill_opacity=1)
        sq.move_to([-2, 0, 0])
        cr = Circle(color=BLUE, fill_opacity=1)
        cr.move_to([-1.3, 0.7, 0])
        un = Intersection(sq, cr, color=GREEN, fill_opacity=1)
        un.move_to([1.5, 0, 0])
        self.add(sq, cr, un)

Label¶

几何图形上的标签：自带背景框的小文本，跟随目标位置摆放。

继承关系¶

参数¶

`label`	—，str \| ManimTextLabel
`label_config`	None，dict[str, Any] \| None
`box_config`	None，dict[str, Any] \| None
`frame_config`	None，dict[str, Any] \| None

API 文档¶

class manim.Label(label: str | ManimTextLabel, label_config: dict[str, Any] | None = None, box_config: dict[str, Any] | None = None, frame_config: dict[str, Any] | None = None, **kwargs: Any)¶

基类：VGroup

A Label consisting of text surrounded by a frame.

Parameters¶

label: Label that will be displayed.
label_config: A dictionary containing the configuration for the label. This is only applied if label is of type str.
box_config: A dictionary containing the configuration for the background box.
frame_config: A dictionary containing the configuration for the frame.

Examples¶

class LabelExample(Scene):
    def construct(self):
        label = Label(
            label=Text('Label Text', font='sans-serif'),
            box_config = {
                "color" : BLUE,
                "fill_opacity" : 0.75
            }
        )
        label.scale(3)
        self.add(label)

LabeledArrow¶

带文字标签的箭头：label 自动置于箭身中点，省去手动对位。

继承关系¶

API 文档¶

class manim.LabeledArrow(*args: Any, **kwargs: Any)¶

基类：LabeledLine, Arrow

Constructs an arrow containing a label box somewhere along its length. This class inherits its label properties from LabeledLine, so the main parameters controlling it are the same.

Parameters¶

label: Label that will be displayed on the Arrow.
label_position: A ratio in the range [0-1] to indicate the position of the label with respect to the length of the line. Default value is 0.5.
label_config: A dictionary containing the configuration for the label. This is only applied if label is of type str.
box_config: A dictionary containing the configuration for the background box.
frame_config: A dictionary containing the configuration for the frame.

参见

LabeledLine

Examples¶

class LabeledArrowExample(Scene):
    def construct(self):
        l_arrow = LabeledArrow("0.5", start=LEFT*3, end=RIGHT*3 + UP*2, label_position=0.5)

        self.add(l_arrow)

LabeledDot¶

带文字标签的圆点：标签居中于点内，图论顶点标注专用。

继承关系¶

参数¶

`label`	—
`radius`	None，float \| None
`buff`	0.1，float

API 文档¶

class manim.LabeledDot(label: str | SingleStringMathTex | Text | Tex, radius: float | None = None, buff: float = 0.1, **kwargs: Any)¶

基类：Dot

A Dot containing a label in its center.

Parameters¶

label: The label of the Dot. This is rendered as MathTex by default (i.e., when passing a str), but other classes representing rendered strings like Text or Tex can be passed as well.
radius: The radius of the Dot. If provided, the buff is ignored. If None (the default), the radius is calculated based on the size of the label and the buff.

Examples¶

class SeveralLabeledDots(Scene):
    def construct(self):
        sq = Square(fill_color=RED, fill_opacity=1)
        self.add(sq)
        dot1 = LabeledDot(Tex("42", color=RED))
        dot2 = LabeledDot(MathTex("a", color=GREEN))
        dot3 = LabeledDot(Text("ii", color=BLUE))
        dot4 = LabeledDot("3")
        dot1.next_to(sq, UL)
        dot2.next_to(sq, UR)
        dot3.next_to(sq, DL)
        dot4.next_to(sq, DR)
        self.add(dot1, dot2, dot3, dot4)

LabeledLine¶

带标签的直线：标签自动放在线段中点。

继承关系¶

参数¶

`label`	—，str \| ManimTextLabel
`label_position`	0.5，float
`label_config`	None，dict[str, Any] \| None
`box_config`	None，dict[str, Any] \| None
`frame_config`	None，dict[str, Any] \| None

API 文档¶

class manim.LabeledLine(label: str | ManimTextLabel, label_position: float = 0.5, label_config: dict[str, Any] | None = None, box_config: dict[str, Any] | None = None, frame_config: dict[str, Any] | None = None, *args: Any, **kwargs: Any)¶

基类：Line

Constructs a line containing a label box somewhere along its length.

Parameters¶

label: Label that will be displayed on the line.
label_position: A ratio in the range [0-1] to indicate the position of the label with respect to the length of the line. Default value is 0.5.
label_config: A dictionary containing the configuration for the label. This is only applied if label is of type str.
box_config: A dictionary containing the configuration for the background box.
frame_config: A dictionary containing the configuration for the frame.

参见

LabeledArrow

Examples¶

class LabeledLineExample(Scene):
    def construct(self):
        line = LabeledLine(
            label          = '0.5',
            label_position = 0.8,
            label_config = {
                "font_size" : 20
            },
            start=LEFT+DOWN,
            end=RIGHT+UP)

        line.set_length(line.get_length() * 2)
        self.add(line)

LabeledPolygram¶

带顶点标签的折线/多边形：每个顶点自动编号。

继承关系¶

参数¶

`label`	—，str \| ManimTextLabel
`precision`	0.01，float
`label_config`	None，dict[str, Any] \| None
`box_config`	None，dict[str, Any] \| None
`frame_config`	None，dict[str, Any] \| None

API 文档¶

class manim.LabeledPolygram(*vertex_groups: Point3DLike_Array, label: str | ManimTextLabel, precision: float = 0.01, label_config: dict[str, Any] | None = None, box_config: dict[str, Any] | None = None, frame_config: dict[str, Any] | None = None, **kwargs: Any)¶

基类：Polygram

Constructs a polygram containing a label box at its pole of inaccessibility.

Parameters¶

vertex_groups: Vertices passed to the Polygram constructor.
label: Label that will be displayed on the Polygram.
precision: The precision used by the PolyLabel algorithm.
label_config: A dictionary containing the configuration for the label. This is only applied if label is of type str.
box_config: A dictionary containing the configuration for the background box.
frame_config: A dictionary containing the configuration for the frame.

备注

The PolyLabel Algorithm expects each vertex group to form a closed ring. If the input is open, LabeledPolygram will attempt to close it. This may cause the polygon to intersect itself leading to unexpected results.

小技巧

Make sure the precision corresponds to the scale of your inputs! For instance, if the bounding box of your polygon stretches from 0 to 10,000, a precision of 1.0 or 10.0 should be sufficient.

Examples¶

class LabeledPolygramExample(Scene):
    def construct(self):
        # Define Rings
        ring1 = [
            [-3.8, -2.4, 0], [-2.4, -2.5, 0], [-1.3, -1.6, 0], [-0.2, -1.7, 0],
            [1.7, -2.5, 0], [2.9, -2.6, 0], [3.5, -1.5, 0], [4.9, -1.4, 0],
            [4.5, 0.2, 0], [4.7, 1.6, 0], [3.5, 2.4, 0], [1.1, 2.5, 0],
            [-0.1, 0.9, 0], [-1.2, 0.5, 0], [-1.6, 0.7, 0], [-1.4, 1.9, 0],
            [-2.6, 2.6, 0], [-4.4, 1.2, 0], [-4.9, -0.8, 0], [-3.8, -2.4, 0]
        ]
        ring2 = [
            [0.2, -1.2, 0], [0.9, -1.2, 0], [1.4, -2.0, 0], [2.1, -1.6, 0],
            [2.2, -0.5, 0], [1.4, 0.0, 0], [0.4, -0.2, 0], [0.2, -1.2, 0]
        ]
        ring3 = [[-2.7, 1.4, 0], [-2.3, 1.7, 0], [-2.8, 1.9, 0], [-2.7, 1.4, 0]]

        # Create Polygons (for reference)
        p1 = Polygon(*ring1, fill_opacity=0.75)
        p2 = Polygon(*ring2, fill_color=BLACK, fill_opacity=1)
        p3 = Polygon(*ring3, fill_color=BLACK, fill_opacity=1)

        # Create Labeled Polygram
        polygram = LabeledPolygram(
            *[ring1, ring2, ring3],
            label=Text('Pole', font='sans-serif'),
            precision=0.01,
        )

        # Display Circle (for reference)
        circle = Circle(radius=polygram.radius, color=WHITE).move_to(polygram.pole)

        self.add(p1, p2, p3)
        self.add(polygram)
        self.add(circle)

import requests
import json

class LabeledCountryExample(Scene):
    def construct(self):
        # Fetch JSON data and process arcs
        data = requests.get('https://cdn.jsdelivr.net/npm/us-atlas@3/nation-10m.json').json()
        arcs, transform = data['arcs'], data['transform']
        sarcs = [np.cumsum(arc, axis=0) * transform['scale'] + transform['translate'] for arc in arcs]
        ssarcs = sorted(sarcs, key=len, reverse=True)[:1]

        # Compute Bounding Box
        points = np.concatenate(ssarcs)
        mins, maxs = np.min(points, axis=0), np.max(points, axis=0)

        # Build Axes
        ax = Axes(
            x_range=[mins[0], maxs[0], maxs[0] - mins[0]], x_length=10,
            y_range=[mins[1], maxs[1], maxs[1] - mins[1]], y_length=7,
            tips=False
        )

        # Adjust Coordinates
        array = [[ax.c2p(*point) for point in sarc] for sarc in ssarcs]

        # Add Polygram
        polygram = LabeledPolygram(
            *array,
            label=Text('USA', font='sans-serif'),
            precision=0.01,
            fill_color=BLUE,
            stroke_width=0,
            fill_opacity=0.75
        )

        # Display Circle (for reference)
        circle = Circle(radius=polygram.radius, color=WHITE).move_to(polygram.pole)

        self.add(ax)
        self.add(polygram)
        self.add(circle)

Line¶

两点之间的直线：buff 让端点留白不压对象，put_start_and_end_on 可动画化，是构图的骨架。

继承关系¶

参数¶

`start`	array([-1., 0., 0.])，Point3DLike \| Mobject
`end`	array([1., 0., 0.])，Point3DLike \| Mobject
`buff`	0，float
`path_arc`	0，float

快速上手¶

line = Line(ORIGIN, RIGHT * 3)

API 文档¶

class manim.Line(start: Point3DLike | Mobject = array([-1., 0., 0.]), end: Point3DLike | Mobject = array([1., 0., 0.]), buff: float = 0, path_arc: float = 0, **kwargs: Any)¶

基类：TipableVMobject

A straight or curved line segment between two points or mobjects.

Parameters¶

start: The starting point or Mobject of the line.
end: The ending point or Mobject of the line.
buff: The distance to shorten the line from both ends.
path_arc: If nonzero, the line will be curved into an arc with this angle (in radians).
kwargs: Additional arguments to be passed to TipableVMobject

Examples¶

class LineExample(Scene):
    def construct(self):
        line1 = Line(LEFT*2, RIGHT*2)
        line2 = Line(LEFT*2, RIGHT*2, buff=0.5)
        line3 = Line(LEFT*2, RIGHT*2, path_arc=PI/2)
        grp = VGroup(line1,line2,line3).arrange(DOWN, buff=2)
        self.add(grp)

generate_points() → Self¶

Initializes points and therefore the shape.

Gets called upon creation. This is an empty method that can be implemented by subclasses.

get_projection(point: Point3DLike) → Point3D¶

Returns the projection of a point onto a line.

Parameters¶

point: The point to which the line is projected.

put_start_and_end_on(start: Point3DLike, end: Point3DLike) → Self¶

Sets starts and end coordinates of a line.

Examples¶

class LineExample(Scene):
    def construct(self):
        d = VGroup()
        for i in range(0,10):
            d.add(Dot())
        d.arrange_in_grid(buff=1)
        self.add(d)
        l= Line(d[0], d[1])
        self.add(l)
        self.wait()
        l.put_start_and_end_on(d[1].get_center(), d[2].get_center())
        self.wait()
        l.put_start_and_end_on(d[4].get_center(), d[7].get_center())
        self.wait()

set_points_by_ends(start: Point3DLike | Mobject, end: Point3DLike | Mobject, buff: float = 0, path_arc: float = 0) → Self¶

Sets the points of the line based on its start and end points. Unlike put_start_and_end_on(), this method respects self.buff and Mobject bounding boxes.

Parameters¶

start: The start point or Mobject of the line.
end: The end point or Mobject of the line.
buff: The empty space between the start and end of the line, by default 0.
path_arc: The angle of a circle spanned by this arc, by default 0 which is a straight line.

Polygon¶

多边形：顶点列表连线闭合，一切直边图形（三角形、矩形……）的基类。

继承关系¶

快速上手¶

p = Polygon(ORIGIN, RIGHT, UP)

API 文档¶

class manim.Polygon(*vertices: Point3DLike, **kwargs: Any)¶

基类：Polygram

A shape consisting of one closed loop of vertices.

Parameters¶

vertices: The vertices of the Polygon.
kwargs: Forwarded to the parent constructor.

Examples¶

class PolygonExample(Scene):
    def construct(self):
        isosceles = Polygon([-5, 1.5, 0], [-2, 1.5, 0], [-3.5, -2, 0])
        position_list = [
            [4, 1, 0],  # middle right
            [4, -2.5, 0],  # bottom right
            [0, -2.5, 0],  # bottom left
            [0, 3, 0],  # top left
            [2, 1, 0],  # middle
            [4, 3, 0],  # top right
        ]
        square_and_triangles = Polygon(*position_list, color=PURPLE_B)
        self.add(isosceles, square_and_triangles)

Polygram¶

折线组：可以含多个不闭合顶点组（组 = 一条折线），比 Polygon 更自由的连点工具。

继承关系¶

参数¶

API 文档¶

class manim.Polygram(*vertex_groups: Point3DLike_Array, color: ParsableManimColor = ManimColor('#58C4DD'), **kwargs: Any)¶

基类：VMobject

A generalized Polygon, allowing for disconnected sets of edges.

Parameters¶

vertex_groups

The groups of vertices making up the Polygram.

The first vertex in each group is repeated to close the shape. Each point must be 3-dimensional: [x,y,z]

color

The color of the Polygram.

kwargs

Forwarded to the parent constructor.

Examples¶

import numpy as np

class PolygramExample(Scene):
    def construct(self):
        hexagram = Polygram(
            [[0, 2, 0], [-np.sqrt(3), -1, 0], [np.sqrt(3), -1, 0]],
            [[-np.sqrt(3), 1, 0], [0, -2, 0], [np.sqrt(3), 1, 0]],
        )
        self.add(hexagram)

        dot = Dot()
        self.play(MoveAlongPath(dot, hexagram), run_time=5, rate_func=linear)
        self.remove(dot)
        self.wait()

get_vertex_groups() → list[Point3D_Array]¶

Gets the vertex groups of the Polygram.

Returns¶

list[Point3D_Array]: The list of vertex groups of the Polygram.

Examples¶

>>> poly = Polygram([ORIGIN, RIGHT, UP, LEFT + UP], [LEFT, LEFT + UP, 2 * LEFT])
>>> groups = poly.get_vertex_groups()
>>> len(groups)
2
>>> groups[0]
array([[ 0.,  0.,  0.],
       [ 1.,  0.,  0.],
       [ 0.,  1.,  0.],
       [-1.,  1.,  0.]])
>>> groups[1]
array([[-1.,  0.,  0.],
       [-1.,  1.,  0.],
       [-2.,  0.,  0.]])

get_vertices() → Point3D_Array¶

Gets the vertices of the Polygram.

Returns¶

numpy.ndarray: The vertices of the Polygram.

Examples¶

>>> sq = Square()
>>> sq.get_vertices()
array([[ 1.,  1.,  0.],
       [-1.,  1.,  0.],
       [-1., -1.,  0.],
       [ 1., -1.,  0.]])

round_corners(radius: float | list[float] = 0.5, evenly_distribute_anchors: bool = False, components_per_rounded_corner: int = 2) → Self¶

Rounds off the corners of the Polygram.

Parameters¶

radius: The curvature of the corners of the Polygram.
evenly_distribute_anchors: Break long line segments into proportionally-sized segments.
components_per_rounded_corner: The number of points used to represent the rounded corner curve.

参见

RoundedRectangle

备注

If radius is supplied as a single value, then the same radius will be applied to all corners. If radius is a list, then the individual values will be applied sequentially, with the first corner receiving radius[0], the second corner receiving radius[1], etc. The radius list will be repeated as necessary.

The components_per_rounded_corner value is provided so that the fidelity of the rounded corner may be fine-tuned as needed. 2 is an appropriate value for most shapes, however a larger value may be need if the rounded corner is particularly large. 2 is the minimum number allowed, representing the start and end of the curve. 3 will result in a start, middle, and end point, meaning 2 curves will be generated.

The option to evenly_distribute_anchors is provided so that the line segments (the part part of each line remaining after rounding off the corners) can be subdivided to a density similar to that of the average density of the rounded corners. This may be desirable in situations in which an even distribution of curves is desired for use in later transformation animations. Be aware, though, that enabling this option can result in an an object containing significantly more points than the original, especially when the rounded corner curves are small.

Examples¶

class PolygramRoundCorners(Scene):
    def construct(self):
        star = Star(outer_radius=2)

        shapes = VGroup(star)
        shapes.add(star.copy().round_corners(radius=0.1))
        shapes.add(star.copy().round_corners(radius=0.25))

        shapes.arrange(RIGHT)
        self.add(shapes)

Rectangle¶

矩形：width/height 与角半径可调，包围、对齐、底衬的主力图形。

继承关系¶

参数¶

`color`	ManimColor('#FFFFFF')，ParsableManimColor
`height`	2.0，float
`width`	4.0，float
`grid_xstep`	None，float \| None
`grid_ystep`	None，float \| None
`mark_paths_closed`	True，bool
`close_new_points`	True，bool

快速上手¶

r = Rectangle(width=4, height=2)

API 文档¶

基类：Polygon

A quadrilateral with two sets of parallel sides.

Parameters¶

color: The color of the rectangle.
height: The vertical height of the rectangle.
width: The horizontal width of the rectangle.
grid_xstep: Space between vertical grid lines.
grid_ystep: Space between horizontal grid lines.
mark_paths_closed: No purpose.
close_new_points: No purpose.
kwargs: Additional arguments to be passed to Polygon

Examples¶

class RectangleExample(Scene):
    def construct(self):
        rect1 = Rectangle(width=4.0, height=2.0, grid_xstep=1.0, grid_ystep=0.5)
        rect2 = Rectangle(width=1.0, height=4.0)
        rect3 = Rectangle(width=2.0, height=2.0, grid_xstep=1.0, grid_ystep=1.0)
        rect3.grid_lines.set_stroke(width=1)

        rects = Group(rect1, rect2, rect3).arrange(buff=1)
        self.add(rects)

RegularPolygon¶

正多边形：n 指定边数，内切圆半径可调。

继承关系¶

参数¶

快速上手¶

hexagon = RegularPolygon(n=6)

API 文档¶

class manim.RegularPolygon(n: int = 6, **kwargs: Any)¶

基类：RegularPolygram

An n-sided regular Polygon.

Parameters¶

n: The number of sides of the RegularPolygon.
kwargs: Forwarded to the parent constructor.

Examples¶

class RegularPolygonExample(Scene):
    def construct(self):
        poly_1 = RegularPolygon(n=6)
        poly_2 = RegularPolygon(n=6, start_angle=30*DEGREES, color=GREEN)
        poly_3 = RegularPolygon(n=10, color=RED)

        poly_group = Group(poly_1, poly_2, poly_3).scale(1.5).arrange(buff=1)
        self.add(poly_group)

RegularPolygram¶

正多角星：n 顶点按密度跳着连线（如五角星 density=2）。

继承关系¶

参数¶

`num_vertices`	—，int
`density`	2，int
`radius`	1，float
`start_angle`	None，float \| None

API 文档¶

class manim.RegularPolygram(num_vertices: int, *, density: int = 2, radius: float = 1, start_angle: float | None = None, **kwargs: Any)¶

基类：Polygram

A Polygram with regularly spaced vertices.

Parameters¶

num_vertices

The number of vertices.

density

The density of the RegularPolygram.

Can be thought of as how many vertices to hop to draw a line between them. Every density-th vertex is connected.

radius

The radius of the circle that the vertices are placed on.

start_angle

The angle the vertices start at; the rotation of the RegularPolygram.

kwargs

Forwarded to the parent constructor.

Examples¶

class RegularPolygramExample(Scene):
    def construct(self):
        pentagram = RegularPolygram(5, radius=2)
        self.add(pentagram)

RightAngle¶

直角标记：两条线垂直时的小方框角标，几何证明标配。

继承关系¶

参数¶

`line1`	—，Line
`line2`	—，Line
`length`	None，float \| None

快速上手¶

ra = RightAngle(line1, line2, length=0.3)

API 文档¶

class manim.RightAngle(line1: Line, line2: Line, length: float | None = None, **kwargs: Any)¶

基类：Angle

An elbow-type mobject representing a right angle between two lines.

Parameters¶

line1: The first line.
line2: The second line.
length: The length of the arms.
**kwargs: Further keyword arguments that are passed to the constructor of Angle.

Examples¶

class RightAngleExample(Scene):
    def construct(self):
        line1 = Line( LEFT, RIGHT )
        line2 = Line( DOWN, UP )
        rightangles = [
            RightAngle(line1, line2),
            RightAngle(line1, line2, length=0.4, quadrant=(1,-1)),
            RightAngle(line1, line2, length=0.5, quadrant=(-1,1), stroke_width=8),
            RightAngle(line1, line2, length=0.7, quadrant=(-1,-1), color=RED),
        ]
        plots = VGroup()
        for rightangle in rightangles:
            plot=VGroup(line1.copy(),line2.copy(), rightangle)
            plots.add(plot)
        plots.arrange(buff=1.5)
        self.add(plots)

RoundedRectangle¶

圆角矩形：corner_radius 控制圆角，卡片式 UI 元素的首选。

继承关系¶

参数¶

快速上手¶

card = RoundedRectangle(corner_radius=0.2, width=4, height=2)

API 文档¶

class manim.RoundedRectangle(corner_radius: float | list[float] = 0.5, **kwargs: Any)¶

基类：Rectangle

A rectangle with rounded corners.

Parameters¶

corner_radius: The curvature of the corners of the rectangle.
kwargs: Additional arguments to be passed to Rectangle

Examples¶

class RoundedRectangleExample(Scene):
    def construct(self):
        rect_1 = RoundedRectangle(corner_radius=0.5)
        rect_2 = RoundedRectangle(corner_radius=1.5, height=4.0, width=4.0)

        rect_group = Group(rect_1, rect_2).arrange(buff=1)
        self.add(rect_group)

Sector¶

扇形：圆 + 张角，饼图的组成单元。

继承关系¶

参数¶

快速上手¶

s = Sector(angle=PI/3)

API 文档¶

class manim.Sector(radius: float = 1, **kwargs: Any)¶

基类：AnnularSector

A sector of a circle.

Examples¶

class ExampleSector(Scene):
    def construct(self):
        sector = Sector(radius=2)
        sector2 = Sector(radius=2.5, angle=60*DEGREES).move_to([-3, 0, 0])
        sector.set_color(RED)
        sector2.set_color(PINK)
        self.add(sector, sector2)

Square¶

正方形：Rectangle 的等边便捷版，边长用 side_length。

继承关系¶

参数¶

快速上手¶

sq = Square(side_length=2)

API 文档¶

class manim.Square(side_length: float = 2.0, **kwargs: Any)¶

基类：Rectangle

A rectangle with equal side lengths.

Parameters¶

side_length: The length of the sides of the square.
kwargs: Additional arguments to be passed to Rectangle.

Examples¶

class SquareExample(Scene):
    def construct(self):
        square_1 = Square(side_length=2.0).shift(DOWN)
        square_2 = Square(side_length=1.0).next_to(square_1, direction=UP)
        square_3 = Square(side_length=0.5).next_to(square_2, direction=UP)
        self.add(square_1, square_2, square_3)

Star¶

五角星样式的正多角星：n 与密度决定角数，外内半径比决定胖瘦。

继承关系¶

参数¶

`n`	5，int
`outer_radius`	1，float
`inner_radius`	None，float \| None
`density`	2，int
`start_angle`	1.5707963267948966，float \| None

快速上手¶

star = Star(n=5, fill_color=YELLOW)

API 文档¶

class manim.Star(n: int = 5, *, outer_radius: float = 1, inner_radius: float | None = None, density: int = 2, start_angle: float | None = 1.5707963267948966, **kwargs: Any)¶

基类：Polygon

A regular polygram without the intersecting lines.

Parameters¶

n

How many points on the Star.

outer_radius

The radius of the circle that the outer vertices are placed on.

inner_radius

The radius of the circle that the inner vertices are placed on.

If unspecified, the inner radius will be calculated such that the edges of the Star perfectly follow the edges of its RegularPolygram counterpart.

density

The density of the Star. Only used if inner_radius is unspecified.

See RegularPolygram for more information.

start_angle

The angle the vertices start at; the rotation of the Star.

kwargs

Forwardeds to the parent constructor.

Raises¶

ValueError: If inner_radius is unspecified and density is not in the range [1, n/2).

Examples¶

class StarExample(Scene):
    def construct(self):
        pentagram = RegularPolygram(5, radius=2)
        star = Star(outer_radius=2, color=RED)

        self.add(pentagram)
        self.play(Create(star), run_time=3)
        self.play(FadeOut(star), run_time=2)

class DifferentDensitiesExample(Scene):
    def construct(self):
        density_2 = Star(7, outer_radius=2, density=2, color=RED)
        density_3 = Star(7, outer_radius=2, density=3, color=PURPLE)

        self.add(VGroup(density_2, density_3).arrange(RIGHT))

StealthTip¶

隐形战斗机风格的箭尖（默认箭尖），一般不直接实例化。

继承关系¶

参数¶

`fill_opacity`	1，float
`stroke_width`	3，float
`length`	0.175，float
`start_angle`	3.141592653589793，float

API 文档¶

class manim.StealthTip(fill_opacity: float = 1, stroke_width: float = 3, length: float = 0.175, start_angle: float = 3.141592653589793, **kwargs: Any)¶

基类：ArrowTip

'Stealth' fighter / kite arrow shape.

Naming is inspired by the corresponding TikZ arrow shape.

property length: float¶

The length of the arrow tip.

In this case, the length is computed as the height of the triangle encompassing the stealth tip (otherwise, the tip is scaled too large).

SurroundingRectangle¶

围绕目标的矩形框：自动留边距包围对象，强调、圈选必备。

继承关系¶

参数¶

`color`	ManimColor('#FFFF00')，ParsableManimColor
`buff`	0.1
`corner_radius`	0.0，float

快速上手¶

box = SurroundingRectangle(formula, color=YELLOW)

API 文档¶

基类：RoundedRectangle

A rectangle surrounding a Mobject

Examples¶

class SurroundingRectExample(Scene):
    def construct(self):
        title = Title("A Quote from Newton")
        quote = Text(
            "If I have seen further than others, \n"
            "it is by standing upon the shoulders of giants.",
            color=BLUE,
        ).scale(0.75)
        box = SurroundingRectangle(quote, color=YELLOW, buff=MED_LARGE_BUFF)

        t2 = Tex(r"Hello World").scale(1.5)
        box2 = SurroundingRectangle(t2, corner_radius=0.2)
        mobjects = VGroup(VGroup(box, quote), VGroup(t2, box2)).arrange(DOWN)
        self.add(title, mobjects)

TangentLine¶

曲线在指定参数处的切线：微分几何可视化直接可用。

继承关系¶

参数¶

`vmob`	—，VMobject
`alpha`	—，float
`length`	1，float
`d_alpha`	1e-06，float

快速上手¶

t = TangentLine(circle, alpha=0.3)

API 文档¶

class manim.TangentLine(vmob: VMobject, alpha: float, length: float = 1, d_alpha: float = 1e-06, **kwargs: Any)¶

基类：Line

Constructs a line tangent to a VMobject at a specific point.

Parameters¶

vmob: The VMobject on which the tangent line is drawn.
alpha: How far along the shape that the line will be constructed. range: 0-1.
length: Length of the tangent line.
d_alpha: The dx value
kwargs: Additional arguments to be passed to Line

参见

point_from_proportion()

Examples¶

class TangentLineExample(Scene):
    def construct(self):
        circle = Circle(radius=2)
        line_1 = TangentLine(circle, alpha=0.0, length=4, color=BLUE_D) # right
        line_2 = TangentLine(circle, alpha=0.4, length=4, color=GREEN) # top left
        self.add(circle, line_1, line_2)

TangentialArc¶

以一点为端点、与曲线相切的弧：强调方向变化的小装饰。

继承关系¶

参数¶

`line1`	—，Line
`line2`	—，Line
`radius`	—，float
`corner`	(1, 1)，Any

API 文档¶

class manim.TangentialArc(line1: Line, line2: Line, radius: float, corner: Any = (1, 1), **kwargs: Any)¶

基类：ArcBetweenPoints

Construct an arc that is tangent to two intersecting lines. You can choose any of the 4 possible corner arcs via the corner tuple. corner = (s1, s2) where each si is ±1 to control direction along each line.

Examples¶

class TangentialArcExample(Scene):
    def construct(self):
        line1 = DashedLine(start=3 * LEFT, end=3 * RIGHT)
        line1.rotate(angle=31 * DEGREES, about_point=ORIGIN)
        line2 = DashedLine(start=3 * UP, end=3 * DOWN)
        line2.rotate(angle=12 * DEGREES, about_point=ORIGIN)

        arc = TangentialArc(line1, line2, radius=2.25, corner=(1, 1), color=TEAL)
        self.add(arc, line1, line2)

The following example shows all four possible corner configurations:

class TangentialArcCorners(Scene):
    def construct(self):
        # Create two intersecting lines
        line1 = DashedLine(start=3 * LEFT, end=3 * RIGHT, color=GREY)
        line2 = DashedLine(start=3 * UP, end=3 * DOWN, color=GREY)

        # All four corner configurations with different colors
        arc_pp = TangentialArc(line1, line2, radius=1.5, corner=(1, 1), color=RED)
        arc_pn = TangentialArc(line1, line2, radius=1.5, corner=(1, -1), color=GREEN)
        arc_np = TangentialArc(line1, line2, radius=1.5, corner=(-1, 1), color=BLUE)
        arc_nn = TangentialArc(line1, line2, radius=1.5, corner=(-1, -1), color=YELLOW)

        # Labels for each arc
        label_pp = Text("(1,1)", font_size=24, color=RED).next_to(arc_pp, UR, buff=0.1)
        label_pn = Text("(1,-1)", font_size=24, color=GREEN).next_to(arc_pn, DR, buff=0.1)
        label_np = Text("(-1,1)", font_size=24, color=BLUE).next_to(arc_np, UL, buff=0.1)
        label_nn = Text("(-1,-1)", font_size=24, color=YELLOW).next_to(arc_nn, DL, buff=0.1)

        self.add(line1, line2, arc_pp, arc_pn, arc_np, arc_nn)
        self.add(label_pp, label_pn, label_np, label_nn)

TipableVMobject¶

「可装箭尖」线段的基类：Arrow、Line 继承它获得 add_tip/tip 配置能力。

继承关系¶

参数¶

`tip_length`	0.35，float
`normal_vector`	array([0., 0., 1.])，Vector3DLike
`tip_style`	None，dict \| None

API 文档¶

class manim.TipableVMobject(tip_length: float = 0.35, normal_vector: Vector3DLike = array([0., 0., 1.]), tip_style: dict | None = None, **kwargs: Any)¶

基类：VMobject

Meant for shared functionality between Arc and Line. Functionality can be classified broadly into these groups:

Adding, Creating, Modifying tips

add_tip calls create_tip, before pushing the new tip
into the TipableVMobject's list of submobjects

stylistic and positional configuration

Checking for tips

Boolean checks for whether the TipableVMobject has a tip
and a starting tip

Getters

Straightforward accessors, returning information pertaining
to the TipableVMobject instance's tip(s), its length etc

add_tip(tip: tips.ArrowTip | None = None, tip_shape: type[tips.ArrowTip] | None = None, tip_length: float | None = None, tip_width: float | None = None, at_start: bool = False) → Self¶: Adds a tip to the TipableVMobject instance, recognising that the endpoints might need to be switched if it's a 'starting tip' or not.

create_tip(tip_shape: type[tips.ArrowTip] | None = None, tip_length: float | None = None, tip_width: float | None = None, at_start: bool = False) → tips.ArrowTip¶: Stylises the tip, positions it spatially, and returns the newly instantiated tip to the caller.

get_end() → Point3D¶: Returns the point, where the stroke that surrounds the Mobject ends.

get_start() → Point3D¶: Returns the point, where the stroke that surrounds the Mobject starts.

get_tip() → VMobject¶: Returns the TipableVMobject instance's (first) tip, otherwise throws an exception.

get_tips() → VGroup¶: Returns a VGroup (collection of VMobjects) containing the TipableVMObject instance's tips.

get_unpositioned_tip(tip_shape: type[tips.ArrowTip] | None = None, tip_length: float | None = None, tip_width: float | None = None) → tips.ArrowTip | tips.ArrowTriangleFilledTip¶: Returns a tip that has been stylistically configured, but has not yet been given a position in space.

Triangle¶

等边三角形：RegularPolygon(n=3) 的便捷版。

继承关系¶

快速上手¶

tri = Triangle()

API 文档¶

class manim.Triangle(**kwargs: Any)¶

基类：RegularPolygon

An equilateral triangle.

Parameters¶

kwargs: Additional arguments to be passed to RegularPolygon

Examples¶

class TriangleExample(Scene):
    def construct(self):
        triangle_1 = Triangle()
        triangle_2 = Triangle().scale(2).rotate(60*DEGREES)
        tri_group = Group(triangle_1, triangle_2).arrange(buff=1)
        self.add(tri_group)

Underline¶

下划线：贴住目标底部的横线，强调文本用。

继承关系¶

参数¶

`mobject`	—，Mobject
`buff`	0.1，float

快速上手¶

u = Underline(text)

API 文档¶

class manim.Underline(mobject: Mobject, buff: float = 0.1, **kwargs: Any)¶

基类：Line

Creates an underline.

Examples¶

class UnderLine(Scene):
    def construct(self):
        man = Tex("Manim")  # Full Word
        ul = Underline(man)  # Underlining the word
        self.add(man, ul)

Union¶

布尔并集：合并两个图形为一个轮廓。

继承关系¶

快速上手¶

u = Union(square, circle)

API 文档¶

class manim.Union(*vmobjects: VMobject, **kwargs: Any)¶

基类：_BooleanOps

Union of two or more VMobject s. This returns the common region of the VMobject s.

Parameters¶

vmobjects: The VMobject s to find the union of.

Raises¶

ValueError: If less than 2 VMobject s are passed.

Example¶

class UnionExample(Scene):
    def construct(self):
        sq = Square(color=RED, fill_opacity=1)
        sq.move_to([-2, 0, 0])
        cr = Circle(color=BLUE, fill_opacity=1)
        cr.move_to([-1.3, 0.7, 0])
        un = Union(sq, cr, color=GREEN, fill_opacity=1)
        un.move_to([1.5, 0.3, 0])
        self.add(sq, cr, un)

Vector¶

从原点出发的箭头（向量）：direction 与长度构造，线性代数可视化核心对象。

继承关系¶

参数¶

`direction`	array([1., 0., 0.])
`buff`	0，float

快速上手¶

v = Vector(RIGHT * 2, color=RED)

API 文档¶

class manim.Vector(direction: Vector2DLike | Vector3DLike = array([1., 0., 0.]), buff: float = 0, **kwargs: Any)¶

基类：Arrow

A vector specialized for use in graphs.

小心

Do not confuse with the Vector2D, Vector3D or VectorND type aliases, which are not Mobjects!

Parameters¶

direction: The direction of the arrow.
buff: The distance of the vector from its endpoints.
kwargs: Additional arguments to be passed to Arrow

Examples¶

class VectorExample(Scene):
    def construct(self):
        plane = NumberPlane()
        vector_1 = Vector([1,2])
        vector_2 = Vector([-5,-2])
        self.add(plane, vector_1, vector_2)

coordinate_label(integer_labels: bool = True, n_dim: int = 2, color: ParsableManimColor | None = None, **kwargs: Any) → Matrix¶

Creates a label based on the coordinates of the vector.

Parameters¶

integer_labels: Whether or not to round the coordinates to integers.
n_dim: The number of dimensions of the vector.
color: Sets the color of label, optional.
kwargs: Additional arguments to be passed to Matrix.

Returns¶

Matrix: The label.

Examples¶

class VectorCoordinateLabel(Scene):
    def construct(self):
        plane = NumberPlane()

        vec_1 = Vector([1, 2])
        vec_2 = Vector([-3, -2])
        label_1 = vec_1.coordinate_label()
        label_2 = vec_2.coordinate_label(color=YELLOW)

        self.add(plane, vec_1, vec_2, label_1, label_2)

API 参考：几何图形（geometry）¶

Angle¶

继承关系¶

参数¶

快速上手¶

API 文档¶

Parameters¶

Examples¶

Parameters¶

Returns¶

Examples¶

Returns¶

Examples¶

Parameters¶

Returns¶

Examples¶

AnnotationDot¶

继承关系¶

参数¶

API 文档¶

AnnularSector¶

继承关系¶

参数¶

快速上手¶

API 文档¶

Parameters¶

Examples¶

Annulus¶

继承关系¶

参数¶

API 文档¶

Parameters¶

Examples¶

Arc¶

继承关系¶

参数¶

快速上手¶

API 文档¶

Examples¶

ArcBetweenPoints¶

继承关系¶

参数¶

快速上手¶

API 文档¶

Example¶

ArcPolygon¶

继承关系¶

参数¶

API 文档¶

Parameters¶

Attributes¶

See Also¶

Examples¶

ArcPolygonFromArcs¶

继承关系¶

API 文档¶

Parameters¶

Attributes¶

Examples¶

Arrow¶

继承关系¶

参数¶

快速上手¶

API 文档¶

Parameters¶

Examples¶

Examples¶

Examples¶

Examples¶

ArrowCircleFilledTip¶

继承关系¶

参数¶

API 文档¶

ArrowCircleTip¶

继承关系¶

参数¶

API 文档¶

ArrowSquareFilledTip¶

继承关系¶

参数¶