Shapes

All shapes inherit from VObject and share its full set of animation methods.

Ellipse

../_images/ellipse_params.svg

Example: Ellipse

"""Ellipse shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

e = Ellipse(rx=200, ry=100, fill='#58C4DD', fill_opacity=0.6, stroke='#58C4DD')
v.add(e)

v.show(end=0)
class Ellipse(rx=120, ry=60, cx=960, cy=540, **styling)

Ellipse centred at (cx, cy) with radii rx and ry.

Parameters:

  • rx (float) – Horizontal radius.

  • ry (float) – Vertical radius.

  • cx (float) – Centre x.

  • cy (float) – Centre y.

c: Coor

Centre coordinate (time-varying).

rx: Real
ry: Real

Geometry methods

get_area(time=0)

Return the area π·rx·ry.

get_perimeter(time=0)

Approximate perimeter (Ramanujan’s formula).

eccentricity(time=0)

Return the eccentricity e = √(1 - (min/max)²).

get_foci(time=0)

Return a list of two (x, y) foci points.

point_at_angle(degrees, time=0)

Return (x, y) on the ellipse boundary at the given angle.

get_point_at_parameter(t, time=0)

Return (x, y) at parametric value t ∈ [0, 1] (full revolution).

contains_point(px, py, time=0)

Return True if the point lies inside the ellipse.

Mutation methods

set_center(cx, cy, start=0, end=None, easing=smooth)

Animate the centre to a new position.

set_rx(value, start=0, end=None, easing=smooth)
set_ry(value, start=0, end=None, easing=smooth)

Animate radius changes.

get_rx(time=0)
get_ry(time=0)

Return current radii values.

Tangent / Normal

tangent_at_angle(angle_deg, length=200, time=0, **kwargs)

Return a Line tangent to the ellipse at the given angle.

normal_at_angle(angle_deg, length=200, time=0, **kwargs)

Return a Line normal to the ellipse at the given angle.

get_tangent_line(angle_deg, length=100, time=0, **kwargs)

Alias for tangent_at_angle().

Circle

../_images/circle_params.svg

Example: Circle

"""Circle shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

c = Circle(r=120, fill='#58C4DD', fill_opacity=0.6, stroke='#58C4DD')
v.add(c)

v.show(end=0)
class Circle(r=120, cx=960, cy=540, **styling)

Bases: Ellipse

Circle (Ellipse with rx == ry).

Parameters:

  • r (float) – Radius.

  • cx (float) – Centre x.

  • cy (float) – Centre y.

r: Real

Radius (property that gets/sets both rx and ry).

Geometry

point_at_angle(degrees, time=0)

Return (x, y) on the circumference at the given angle.

get_area(time=0)

Return πr².

get_perimeter(time=0)

Return 2πr.

get_radius(time=0)
set_radius(value, start=0, end=None, easing=smooth)

Get / animate the radius.

contains_point(px, py, time=0)

Return True if the point lies inside the circle.

sector_area(start_angle, end_angle, time=0)

Area of the sector between two angles (degrees).

arc_length(start_angle, end_angle, time=0)

Arc length between two angles (degrees).

segment_area(start_angle, end_angle, time=0)

Area of the circular segment between two angles.

chord_length(distance, time=0)

Chord length at given distance from center.

power_of_point(px, py, time=0)

Return the power of a point with respect to the circle.

Construction

chord(angle1, angle2, time=0, **kwargs)

Return a Line chord between two angles.

diameter_line(angle_deg=0, time=0, **kwargs)

Return a Line through the center at the given angle.

get_arc(start_angle=0, end_angle=180, time=0, **kwargs)

Return an Arc on this circle.

arc_between(start_angle, end_angle, time=0, **kwargs)

Same as get_arc().

inscribed_polygon(n, angle=0, time=0, **kwargs)

Return a RegularPolygon inscribed in this circle.

circumscribed_polygon(n, angle=0, time=0, **kwargs)

Return a RegularPolygon circumscribed around this circle.

get_annulus(inner_ratio=0.5, time=0, **kwargs)

Return an Annulus with inner radius as a fraction of r.

annular_sector(inner_ratio=0.5, start_angle=0, end_angle=360, **kwargs)

Return an AnnularSector based on this circle.

get_sectors(n, **kwargs)

Return a list of n equal Wedge sectors.

Tangent lines

tangent_line(angle_degrees, length=100, time=0, **kwargs)

Return a Line tangent at the given angle on the circle.

tangent_at_point(px, py, length=200, time=0, **kwargs)

Return a tangent line at the closest point on the circle.

tangent_line_from_point(px, py, time=0, length=200, **kwargs)

Return tangent lines from an external point.

get_tangent_lines(px, py, time=0, length=200, **kwargs)

Return both tangent lines from external point as a list.

tangent_points(px, py, time=0)

Return the two tangent contact points from an external point.

Intersections

intersect_line(line, time=0)

Return list of (x, y) intersection points with a Line.

intersect_circle(other, time=0)

Return list of (x, y) intersection points with another circle.

Class methods

classmethod from_diameter(p1, p2, **kwargs)

Create a circle from two diameter endpoints.

classmethod from_center_and_point(center, point, **kwargs)

Create from center and a point on the circumference.

classmethod from_bounding_box(vobject, padding=0, time=0, **kwargs)

Create the smallest enclosing circle for a VObject’s bounding box.

classmethod from_three_points(p1, p2, p3, **kwargs)

Create the unique circle through three non-collinear points.

Example: Circle

Circle with grow_from_center animation.

"""Circle with grow_from_center."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

c1 = Circle(r=80, cx=480, cy=540, fill='#58C4DD', fill_opacity=0.8, stroke_width=3)
c2 = Circle(r=60, cx=960, cy=540, fill='#E74C3C', fill_opacity=0.8, stroke_width=3)
c3 = Circle(r=100, cx=1440, cy=540, fill='#83C167', fill_opacity=0.6, stroke_width=3)

v.add(c1, c2, c3)

v.show(end=2)

Dot

Example: Dot & AnnotationDot

"""Dot: small filled circle."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

dots = VCollection(
    Dot(fill='#FFFFFF'),
    Dot(r=20, fill='#58C4DD'),
    Dot(r=30, fill='#FF6B6B'),
    AnnotationDot(fill='#83C167'),
)
dots.arrange(direction='right', buff=80)
dots.center_to_pos()

v.add(dots)

v.show(end=0)
class Dot(r=11, cx=960, cy=540, **styling)

Bases: Circle

Small filled circle with no stroke. Default: white fill (#fff), fill_opacity=1, stroke_width=0.

Parameters:

r (float) – Radius (default 11).

c: Coor

Centre coordinate.

AnnotationDot

class AnnotationDot(r=14.3, cx=960, cy=540, **styling)

Bases: Dot

Slightly larger dot with an outline stroke, designed for annotations. Default styling: white stroke (#fff), stroke_width=5.

Square

Example: Square

"""Square shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

squares = VCollection(
    Square(side=120, fill='#58C4DD', fill_opacity=0.7, stroke='#58C4DD'),
    Square(side=160, fill='#FF6B6B', fill_opacity=0.7, stroke='#FF6B6B'),
    Square(side=200, fill='#83C167', fill_opacity=0.7, stroke='#83C167'),
)
squares.arrange(direction='right', buff=60)
squares.center_to_pos()

v.add(squares)

v.show(end=0)
class Square(side=200, x=960, y=540, **styling)

Bases: Rectangle

Square (rectangle with equal width and height).

Parameters:

side (float) – Side length.

Rectangle

../_images/rectangle_params.svg

Example: Rectangle

"""Rectangle shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

r = Rectangle(300, 180, fill='#E74C3C', fill_opacity=0.6, stroke='#E74C3C')
v.add(r)

v.show(end=0)
class Rectangle(width, height, x=960, y=540, rx=0, ry=0, **styling)

Rectangle positioned at (x, y) (top-left corner).

Parameters:

  • width (float) – Width.

  • height (float) – Height.

  • x (float) – Top-left x.

  • y (float) – Top-left y.

  • rx (float) – Corner radius x.

  • ry (float) – Corner radius y.

x: Real
y: Real
width: Real
height: Real

Geometry

get_size(time=0)

Return (width, height) tuple.

is_square(time=0, tol=1e-3)

Return True if width ≈ height.

aspect_ratio(time=0)

Return width / height.

contains_point(px, py, time=0)

Return True if the point lies inside the rectangle.

sample_border(t, time=0)

Return (x, y) at parameter t ∈ [0, 1] around the border.

Mutation

set_size(width, height, start=0, end=None, easing=smooth)

Animate to new dimensions.

grow_width(amount, start=0, end=1, easing=smooth)
grow_height(amount, start=0, end=1, easing=smooth)

Add amount to width or height over the interval.

expand(amount=20, start=0, end=1, easing=smooth)

Expand width and height by amount simultaneously.

Subdivision

split(direction='horizontal', count=2, time=0, **kwargs)

Split into count sub-rectangles. Direction is 'horizontal' or 'vertical'.

split_horizontal(n=2, time=0, **kwargs)
split_vertical(n=2, time=0, **kwargs)

Convenience methods for split().

quadrants(time=0, **kwargs)

Split into 4 equal sub-rectangles.

subdivide(rows=2, cols=2, time=0, **kwargs)

Split into a grid of rows × cols sub-rectangles.

Construction

inset(amount, time=0, **kwargs)

Return a smaller rectangle inset by amount on all sides.

round_corners(radius=10, time=0, **kwargs)

Return a RoundedRectangle copy with rounded corners.

to_polygon(time=0, **kwargs)

Convert to a Polygon with four vertices.

to_lines(time=0, **kwargs)

Convert to four Line objects (the edges).

diagonal_lines(time=0, **kwargs)

Return the two diagonal Line objects.

chamfer(size=10, time=0, **kwargs)

Return a Polygon with chamfered (cut) corners.

get_grid_lines(rows, cols, time=0, **kwargs)

Return a list of Line objects forming a grid.

Class methods

classmethod square(side, **kwargs)

Create a square rectangle.

classmethod from_center(cx, cy, width, height, **kwargs)

Create a rectangle centered at (cx, cy).

classmethod from_corners(x1, y1, x2, y2, **kwargs)

Create from opposite corner coordinates.

classmethod from_bounding_box(vobject, padding=0, time=0, **kwargs)

Create the bounding rectangle for a VObject.

classmethod from_two_objects(obj_a, obj_b, padding=0, **kwargs)

Create the bounding rectangle that encloses two VObjects.

Example — animated subdivision

r = Rectangle(400, 300, x=780, y=390, fill='#2C3E50', stroke='#ECF0F1')
r.fadein(start=0, end=1)

# Split into a 3×3 grid
cells = r.subdivide(rows=3, cols=3)
for i, cell in enumerate(cells):
    cell.fadein(start=1 + i * 0.2, end=1.5 + i * 0.2)
    v.add(cell)

RoundedRectangle

Example: RoundedRectangle

"""RoundedRectangle shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

r = RoundedRectangle(300, 180, corner_radius=20, fill='#9B59B6', fill_opacity=0.6, stroke='#9B59B6')
v.add(r)

v.show(end=0)
class RoundedRectangle(width, height, x=960, y=540, corner_radius=12, **styling)

Bases: Rectangle

Rectangle with rounded corners.

get_corner_radius(time=0)

Return the corner radius.

set_corner_radius(value, start=0, end=None, easing=smooth)

Animate the corner radius.

Line

../_images/line_params.svg

Example: Line

"""Line shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

l = Line(x1=560, y1=640, x2=1360, y2=440, stroke='#2ECC71', stroke_width=5)
v.add(l)

v.show(end=0)
class Line(x1=0, y1=0, x2=100, y2=100, **styling)

Line segment from (x1, y1) to (x2, y2).

Parameters:

  • x1 (float) – Start x.

  • y1 (float) – Start y.

  • x2 (float) – End x.

  • y2 (float) – End y.

p1: Coor

Start point (time-varying).

p2: Coor

End point (time-varying).

Query methods

get_start(time=0)
get_end(time=0)

Return (x, y) of start / end points.

get_midpoint(time=0)

Return (x, y) midpoint.

get_length(time=0)

Return the length of the line segment.

get_angle(time=0)

Return the angle in degrees.

get_slope(time=0)

Return the slope (dy/dx), or float('inf') for vertical lines.

get_direction(time=0)

Return (dx, dy) unit direction vector.

get_vector(time=0)

Return (dx, dy) (not normalized).

get_normal(time=0)

Return (-dy, dx) unit normal vector.

lerp(t, time=0)

Return (x, y) at parameter t ∈ [0, 1] along the line.

Boolean checks

is_horizontal(time=0, tol=1e-3)
is_vertical(time=0, tol=1e-3)
is_parallel(other, time=0, tol=1e-6)
is_perpendicular(other, time=0, tol=1e-6)
contains_point(px, py, time=0, tol=2)

Mutation

set_start(point, start=0, end=None, easing=smooth)
set_end(point, start=0, end=None, easing=smooth)

Animate start or end point.

set_points(p1, p2, start=0)

Set both points at once (instant).

set_length(length, start=0, end=None, easing=smooth)

Animate to a new length, keeping the midpoint fixed.

set_angle(angle_deg, about='midpoint', start=0, end=None, easing=smooth)

Animate to a new angle. about can be 'midpoint', 'start', or 'end'.

put_start_and_end_on(p1, p2, start=0, end=None, easing=smooth)

Animate both endpoints simultaneously.

extend_to(length, anchor='start', start=0, end=None, easing=smooth)

Extend to a given total length from an anchor.

extend(factor=1.5, start=0, end=None, easing=smooth)

Multiply the length by factor.

scale_length(factor=2.0, time=0)

Instantly scale the length by factor.

add_tip(end=True, start=False, tip_length=None, tip_width=None)

Add arrowhead tips to one or both ends.

Construction

split_at(t=0.5, time=0)

Return two new Line segments split at parameter t.

subdivide_into(n=2, time=0, **kwargs)

Return n equal sub-segments as Line objects.

divide(n=2, time=0)

Return n+1 evenly spaced points along the line.

perpendicular(at_proportion=0.5, length=None, time=0, **kwargs)

Return a Line perpendicular at the given proportion.

parallel(offset=50, time=0, **kwargs)

Return a parallel Line at given offset distance.

parallel_through(point, time=0, **kwargs)

Return a parallel Line through a point.

bisector(time=0, length=None, **kwargs)

Return the perpendicular bisector line.

Intersections and projections

intersect_line(other, time=0)

Return (x, y) intersection with another infinite line, or None.

intersect_segment(other, time=0)

Return (x, y) only if both segments actually overlap.

intersection(other, time=0)

Alias for intersect_line().

project_point(px, py, time=0)

Orthogonal projection of a point onto the infinite line.

closest_point_on_segment(px, py, time=0)

Closest point clamped to the segment.

distance_to_point(px, py, time=0)

Shortest distance from a point to the segment.

angle_to(other, time=0)

Angle between this line and another (degrees).

reflect_over(other, time=0, **kwargs)

Return a Line reflected over another line.

project_onto(other, time=0, **kwargs)

Return the projection of this segment onto another line.

Class methods

classmethod between(p1, p2, **kwargs)

Create a line between two (x, y) points.

classmethod vertical(x, y1, y2, **kwargs)
classmethod horizontal(y, x1, x2, **kwargs)

Create vertical or horizontal lines.

classmethod from_direction(origin, direction, length=100, **kwargs)

Create from an origin point and direction tuple.

classmethod from_angle(origin, angle_deg, length=100, **kwargs)

Create from an origin point and angle.

classmethod from_slope_point(slope, point, length=200, **kwargs)

Create from a slope and a point on the line.

classmethod from_objects(obj_a, obj_b, buff=0, **kwargs)

Create a line connecting two VObjects’ centres.

Example — line geometry

l1 = Line(200, 300, 800, 600, stroke='#3498DB')
l2 = Line(200, 600, 800, 200, stroke='#E74C3C')

# Find intersection
pt = l1.intersect_line(l2)
if pt:
    dot = Dot(cx=pt[0], cy=pt[1])
    dot.fadein(start=1, end=2)

# Perpendicular bisector
bisector = l1.bisector(length=300, stroke='#2ECC71')

DashedLine

Example: DashedLine

"""DashedLine shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

l = DashedLine(x1=560, y1=640, x2=1360, y2=440, dash='12,6', stroke='#F39C12', stroke_width=4)
v.add(l)

v.show(end=0)
class DashedLine(x1=0, y1=0, x2=100, y2=100, dash='10,5', **styling)

Bases: Line

Line with a dashed pattern.

Parameters:

dash (str) – SVG dash-array string.

set_dash_pattern(dash, gap=None, start=0)

Change the dash pattern.

Polygon

Example: Polygon

"""Polygon shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

pts = [(760, 640), (860, 400), (1060, 380), (1160, 600), (960, 700)]
p = Polygon(*pts, fill='#3498DB', fill_opacity=0.5, stroke='#3498DB', stroke_width=3)
v.add(p)

v.show(end=0)
class Polygon(*vertices, closed=True, **styling)

Closed polygon from (x, y) vertex tuples.

Parameters:

  • vertices – Sequence of (x, y) tuples.

  • closed (bool) – False for an open polyline.

vertices: list[Coor]

Vertex coordinates (time-varying).

Geometry

get_vertices(time=0)

Return list of (x, y) tuples.

get_center(time=0)

Return the bounding-box center.

centroid(time=0)

Return the geometric centroid (average of vertices).

area(time=0)

Return the polygon area (shoelace formula, always positive).

signed_area(time=0)

Return signed area (positive for counter-clockwise).

perimeter(time=0)

Return the polygon perimeter.

edge_lengths(time=0)

Return a list of edge lengths.

contains_point(px, py, time=0)

Return True if the point lies inside (winding number algorithm).

winding_number(px, py, time=0)

Return the winding number of a point with respect to the polygon.

is_convex(time=0)

Return True if the polygon is convex.

is_clockwise(time=0)

Return True if vertices are ordered clockwise.

is_regular(tol=1e-3, time=0)

Return True if all edges and angles are equal.

interior_angles(time=0)

Return a list of interior angles in degrees.

Edges and diagonals

get_edges(time=0)

Return a list of ((x1,y1), (x2,y2)) edge tuples.

get_edge_midpoints(time=0)

Return list of (x, y) midpoints of each edge.

get_longest_edge(time=0)
get_shortest_edge(time=0)

Return ((x1,y1), (x2,y2)) for the longest / shortest edge.

get_diagonals(time=0, **kwargs)

Return all diagonals as Line objects.

Mutation

move_vertex(index, x, y, start=0, end=None, easing=smooth)

Animate a single vertex to a new position.

translate(dx, dy)

Translate all vertices by (dx, dy) instantly.

scale_vertices(factor, time=0)

Scale all vertices relative to the centroid.

rotate_vertices(angle_deg, cx=None, cy=None, time=0)

Rotate all vertices around a point (defaults to centroid).

mirror_x(cx=None, time=0)
mirror_y(cy=None, time=0)

Mirror vertices across a vertical / horizontal axis.

apply_pointwise(func, time=0)

Apply a function f(x, y) → (x', y') to each vertex.

Derived shapes

offset(distance, time=0)

Return a new Polygon offset outward by distance.

buffer(distance, time=0)

Alias for offset().

inset(distance, time=0, **kwargs)

Return a new polygon inset by distance.

to_path(time=0)

Convert to a Path.

get_convex_hull(time=0, **kwargs)

Return the convex hull as a new Polygon.

bounding_circle(time=0, **kwargs)

Return the smallest enclosing Circle.

triangulate(time=0, **kwargs)

Return a list of Polygon triangles via ear clipping.

explode_edges(gap=10, **kwargs)

Return individual Line objects with a gap between each.

get_subcurve(a, b, time=0, **kwargs)

Extract the portion of the polyline between parameters a and b (floats in [0, 1] representing fraction of total path length). Returns a new Lines object.

subdivide_edges(iterations=1, time=0, **kwargs)

Subdivide each edge into two, refining the polygon.

smooth_corners(radius=10, time=0, **kwargs)

Return a new polygon with rounded corners.

label_vertices(labels=None, offset=20, font_size=24, time=0, **kwargs)

Return Text labels positioned near each vertex.

Class methods

classmethod from_points(points, **kwargs)

Create from a list of (x, y) points.

classmethod convex_hull(*points, **kwargs)

Create the convex hull of a set of points.

classmethod from_svg_path(path_d, **kwargs)

Create from an SVG path d string.

Example: Polygon gallery

Regular polygons: triangle, pentagon, hexagon.

"""Regular polygon gallery: triangle, pentagon, hexagon."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

tri = RegularPolygon(3, radius=80, cx=380, cy=540, fill='#E74C3C', fill_opacity=0.7)
pent = RegularPolygon(5, radius=80, cx=960, cy=540, fill='#58C4DD', fill_opacity=0.7)
hexa = RegularPolygon(6, radius=80, cx=1540, cy=540, fill='#83C167', fill_opacity=0.7)

l1 = Text('Triangle', x=380, y=680, font_size=24, fill='#aaa', text_anchor='middle')
l2 = Text('Pentagon', x=960, y=680, font_size=24, fill='#aaa', text_anchor='middle')
l3 = Text('Hexagon', x=1540, y=680, font_size=24, fill='#aaa', text_anchor='middle')

v.add(tri, pent, hexa, l1, l2, l3)

v.show(end=2)

Lines

Example: Lines (open polyline)

"""Lines: open polyline through vertices."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

zigzag = Lines(
    (400, 700), (600, 380), (800, 700), (1000, 380), (1200, 700), (1400, 380), (1600, 700),
    stroke='#58C4DD', stroke_width=4, fill_opacity=0,
)

v.add(zigzag)

v.show(end=0)
class Lines(*vertices, **styling)

Bases: Polygon (with closed=False)

Open polyline.

RegularPolygon

Example: RegularPolygon

"""RegularPolygon shapes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

colors = ['#E74C3C', '#F39C12', '#2ECC71', '#3498DB', '#9B59B6']
for i, (n, color) in enumerate(zip([3, 5, 6, 7, 8], colors)):
    cx = 300 + i * 330
    p = RegularPolygon(n, radius=100, cx=cx, cy=540, fill=color, fill_opacity=0.5, stroke=color)
    v.add(p)

v.show(end=0)
../_images/regular_polygon_params.svg
class RegularPolygon(n, radius=120, cx=960, cy=540, angle=0, **styling)

Bases: Polygon

N-sided regular polygon inscribed in a circle of given radius.

Parameters:

  • n (int) – Number of sides.

  • radius (float) – Circumscribed radius.

  • angle (float) – Starting rotation angle in degrees.

get_side_length(time=0)

Return the side length.

get_inradius(time=0)
get_apothem(time=0)

Return the inradius (distance from center to edge midpoint). Both are equivalent.

get_circumradius(time=0)

Return the circumscribed radius.

EquilateralTriangle

class EquilateralTriangle(side_length, angle=0, cx=960, cy=540, **styling)

Bases: RegularPolygon (n=3). Triangle is an alias.

Star

Example: Star

"""Star shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

s = Star(5, outer_radius=140, inner_radius=60, cx=960, cy=540,
         fill='#F1C40F', fill_opacity=0.7, stroke='#F1C40F')
v.add(s)

v.show(end=0)
../_images/star_params.svg
class Star(n=5, outer_radius=120, inner_radius=None, cx=960, cy=540, angle=90, **styling)

Bases: Polygon

N-pointed star.

Parameters:

  • n (int) – Number of points.

  • outer_radius (float) – Outer radius.

  • inner_radius (float) – Inner radius (defaults to outer_radius * 0.4, i.e. 48).

get_outer_radius()
get_inner_radius()

Return the stored radius values.

Example: Star

Stars with varying point counts.

"""Star creation."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

s5 = Star(5, outer_radius=90, inner_radius=40, cx=480, cy=540,
          fill='#F1C40F', fill_opacity=0.8, stroke_width=2)
s6 = Star(6, outer_radius=90, inner_radius=50, cx=960, cy=540,
          fill='#E74C3C', fill_opacity=0.8, stroke_width=2)
s8 = Star(8, outer_radius=90, inner_radius=55, cx=1440, cy=540,
          fill='#9B59B6', fill_opacity=0.8, stroke_width=2)

v.add(s5, s6, s8)

v.show(end=2)

Arc

Example: Arc

"""Arc shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

a = Arc(r=140, start_angle=0, end_angle=270, cx=960, cy=540,
        stroke='#1ABC9C', stroke_width=6, fill_opacity=0)
v.add(a)

v.show(end=0)
../_images/arc_params.svg
class Arc(cx=960, cy=540, r=120, start_angle=0, end_angle=90, **styling)

SVG arc from start_angle to end_angle (in degrees, counterclockwise).

Parameters:

  • cx (float) – Centre x.

  • cy (float) – Centre y.

  • r (float) – Radius.

  • start_angle (float) – Start angle in degrees.

  • end_angle (float) – End angle in degrees.

cx: Real
cy: Real
r: Real
start_angle: Real
end_angle: Real

Methods

get_start_point(time=0)
get_end_point(time=0)

Return (x, y) at the start / end of the arc.

get_arc_length(time=0)

Return the arc length.

point_at_angle(angle_deg, time=0)

Return (x, y) at a specific angle on the arc’s circle.

set_angles(start_angle, end_angle, start=0, end_time=None, easing=smooth)

Animate the arc angles.

Example: Arc & Wedge

Arc sweeps and pie-wedge shapes.

"""Arc and wedge drawing."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

a = Arc(r=100, start_angle=0, end_angle=270, cx=600, cy=540,
        stroke='#58C4DD', stroke_width=5, fill_opacity=0)
w = Wedge(r=100, start_angle=30, end_angle=300, cx=1320, cy=540,
          fill='#E74C3C', fill_opacity=0.6, stroke_width=2)

l1 = Text('Arc', x=600, y=700, font_size=24, fill='#aaa', text_anchor='middle')
l2 = Text('Wedge', x=1320, y=700, font_size=24, fill='#aaa', text_anchor='middle')

v.add(a, w, l1, l2)

v.show(end=2)

Wedge / Sector

../_images/wedge_params.svg

Example: Wedge

"""Wedge (Sector) shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

w = Wedge(r=160, start_angle=30, end_angle=150, cx=960, cy=540,
          fill='#E67E22', fill_opacity=0.7, stroke='#E67E22')
v.add(w)

v.show(end=0)
class Wedge(cx=960, cy=540, r=120, start_angle=0, end_angle=90, **styling)

Bases: Arc

Pie-wedge shape (arc closing through the centre). Sector is an alias.

to_arc(time=0, **kwargs)

Convert to a separate Arc.

Annulus

../_images/annulus_params.svg

Example: Annulus

"""Annulus shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

a = Annulus(inner_radius=80, outer_radius=160, cx=960, cy=540,
            fill='#E74C3C', fill_opacity=0.6, stroke='#E74C3C')
v.add(a)

v.show(end=0)
class Annulus(inner_radius=60, outer_radius=120, cx=960, cy=540, **styling)

Ring (donut) shape.

Parameters:

  • inner_radius (float) – Inner radius.

  • outer_radius (float) – Outer radius.

c: Coor

Centre coordinate.

inner_r: Real
outer_r: Real
get_inner_radius(time=0)
get_outer_radius(time=0)
set_inner_radius(value, start=0, end=None, easing=smooth)
set_outer_radius(value, start=0, end=None, easing=smooth)
set_radii(inner=None, outer=None, start=0, end=None, easing=smooth)

Get, set, or animate both radii at once.

get_area(time=0)

Return π(R² - r²).

AnnularSector

class AnnularSector(inner_radius=60, outer_radius=120, cx=960, cy=540, start_angle=0, end_angle=90, **styling)

Bases: Arc

Sector of an annulus (ring wedge). Like a Wedge but with an inner radius cut out.

Parameters:

  • inner_radius (float) – Inner radius.

  • outer_radius (float) – Outer radius.

set_inner_radius(value, start=0, end=None, easing=smooth)
get_area(time=0)

ArcBetweenPoints

class ArcBetweenPoints(start, end, angle=60, **styling)

Bases: Arc

Arc connecting two points, bulging by a given angle.

Parameters:

  • start (tuple) – Start (x, y) point.

  • end (tuple) – End (x, y) point.

  • angle (float) – Bulge angle in degrees (positive = left of start→end).

ArcPolygon

class ArcPolygon(*vertices, arc_angles=30, **styling)

Polygon whose edges are arcs instead of straight lines.

Parameters:

  • vertices – At least 3 (x, y) tuples.

  • arc_angles – Bulge angle for each edge (scalar for all, or list per edge). Positive = left of travel, negative = right, 0 = straight.

Example

# Triangle with curved edges
ap = ArcPolygon((860, 400), (1060, 400), (960, 250),
                arc_angles=30, fill='#3498DB', fill_opacity=0.3)

Angle

../_images/angle_params.svg

Example: Angle

"""Angle shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

vertex = (960, 540)
p1 = (1260, 540)
p2 = (1160, 340)
l1 = Line(x1=vertex[0], y1=vertex[1], x2=p1[0], y2=p1[1], stroke='#aaa', stroke_width=3)
l2 = Line(x1=vertex[0], y1=vertex[1], x2=p2[0], y2=p2[1], stroke='#aaa', stroke_width=3)
angle = Angle(vertex, p1, p2, radius=60, stroke='#58C4DD', stroke_width=3)
v.add(l1, l2, angle)

v.show(end=0)
class Angle(vertex, p1, p2, radius=36, label=None, label_radius=None, label_font_size=36, **styling)

Bases: VCollection

Angle indicator arc between two points meeting at a vertex. All three position parameters accept (x, y) tuples or Coor objects for time-varying angles.

Parameters:

  • vertex – Vertex point.

  • p1 – First ray endpoint.

  • p2 – Second ray endpoint.

  • radius (float) – Arc radius.

  • label (str) – Optional text label displayed inside the arc (e.g. 'θ').

  • label_radius (float) – Distance from vertex to label (defaults to radius).

  • label_font_size (float) – Font size for the label.

RightAngle

class RightAngle(vertex, p1, p2, size=18, **styling)

Right angle square indicator.

Cross

Example: Cross

"""Cross shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

c = Cross(cx=960, cy=540, size=200, stroke='#E74C3C', stroke_width=6)
v.add(c)

v.show(end=0)
class Cross(size=36, cx=960, cy=540, **styling)

X-mark shape (two crossing lines).

Text

Example: Text

"""Text shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

t = Text('Hello, World!', x=960, y=540, font_size=72,
         fill='#fff', stroke_width=0, text_anchor='middle')
v.add(t)

v.show(end=0)
class Text(text='', x=960, y=540, font_size=48, text_anchor=None, font_family=None, **styling)

SVG <text> element with animation support.

Parameters:

  • text (str) – Text content.

  • x (float) – X position.

  • y (float) – Y position.

  • font_size (float) – Font size in pixels.

  • text_anchor (str) – SVG text-anchor ('start', 'middle', 'end').

  • font_family (str) – Font family name.

text: String

The text content (time-varying).

font_size: Real

Font size (time-varying, animatable).

Query

get_text(time=0)

Return the current text string.

get_font_size(time=0)

Return the current font size.

starts_with(prefix, time=0)
ends_with(suffix, time=0)

String checks on the current text.

Text animations

typing(start=0, end=1, change_existence=True)

Typewriter effect — reveals the text character by character.

reveal_by_word(start=0, end=1, change_existence=True, easing=None)

Reveal text word by word. Alias: word_by_word.

typewrite(start=0, end=1, cursor='|', cursor_blink=0.5)

Typewriter with a blinking cursor character.

untype(start=0, end=1)

Reverse typewriter — removes characters one by one.

scramble(start=0, end=1, chars=None)

Scramble text with random characters before settling to the final text.

set_text(start, end, new_text)

Change the text content over the interval.

highlight(start=0, end=1, color='#FFFF00')

Briefly highlight the text with a color flash.

highlight_substring(substring, color='#FFFF00', start=0, end=None)

Highlight occurrences of a substring with a different color.

Example — typewriter effect

t = Text("Hello, World!", x=960, y=540, font_size=64, fill='#fff')
t.typing(start=0, end=3)  # Reveals over 3 seconds

CountAnimation

class CountAnimation(start_val=0, end_val=100, start=0, end=1, fmt='{:.0f}', easing=smooth, x=960, y=540, font_size=60, **styling)

Bases: Text

Animated counter that interpolates between two numeric values.

Parameters:

  • start_val (float) – Starting number.

  • end_val (float) – Ending number.

  • start (float) – Animation start time.

  • end (float) – Animation end time.

  • fmt (str) – Format string (e.g. '{:.2f}' or '${:,.0f}').

  • easing – Easing function (default smooth).

Example

counter = CountAnimation(0, 1000, fmt='${:,.0f}',
                         x=960, y=540, font_size=72, fill='#2ECC71')
counter.fadein(start=0, end=0.5)
# Counts from $0 to $1,000 over 3 seconds

Integer

class Integer(value=0, x=960, y=540, font_size=48, **styling)

Bases: DecimalNumber

Like DecimalNumber but formats as an integer (no decimal places).

ComplexValueTracker

class ComplexValueTracker(value=0 + 0j, creation=0)

Like ValueTracker but tracks a complex number (two Reals for real/imaginary parts).

set_value(val, start=0)
animate_value(target, start, end, easing=smooth)
at_time(time)

Get, set, or animate the complex value.

Path

Example: Path

"""Path shape."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

d = 'M 560,640 C 660,300 1260,300 1360,640'
p = Path(d, stroke='#E74C3C', stroke_width=5, fill_opacity=0)
v.add(p)

v.show(end=0)
class Path(path, x=0, y=0, **styling)

Raw SVG <path> element.

Parameters:

path (str) – SVG path data (d attribute).

d: String

Path data (time-varying).

Image

class Image(href, x=0, y=0, width=1, height=1, **styling)

SVG <image> element.

Parameters:

href (str) – Image URL or path.

x: Real
y: Real
width: Real
height: Real

Trace

class Trace(point, start=0, end=None, dt=1 / 60, **styling)

Follows a Coor attribute and renders its trajectory as a polyline.

Parameters:

  • point (Coor) – The coordinate to trace.

  • start (float) – Start time.

  • end (float) – End time.

  • dt (float) – Time step between samples.

vertices(time)

Return the list of (x, y) vertices traced up to time.

to_polygon(time)

Convert the trace to a Polygon.

CubicBezier

class CubicBezier(p0=(860, 540), p1=(910, 440), p2=(1010, 440), p3=(1060, 540), **styling)

Cubic Bezier curve from four control points.

p0: Coor
p1: Coor
p2: Coor
p3: Coor
point_at(t, time=0)

Return (x, y) at parameter t ∈ [0, 1].

tangent_at(t, time=0)

Return (dx, dy) tangent vector at parameter t.

Elbow

class Elbow(cx=960, cy=540, width=40, height=40, **styling)

Bases: Lines

Right-angle connector (L-shape).

Parameters:

  • width (float) – Horizontal arm size.

  • height (float) – Vertical arm size.

Fractals & Spirals

class KochSnowflake(cx=960, cy=540, size=400, depth=3, **styling)

Bases: Polygon

Koch snowflake fractal polygon. Each recursion depth subdivides edges with triangular bumps, creating the classic fractal boundary.

Parameters:

  • cx (float) – Center x.

  • cy (float) – Center y.

  • size (float) – Side length of the initial equilateral triangle.

  • depth (int) – Recursion depth (0 = triangle, 3 is typical).

class SierpinskiTriangle(cx=960, cy=540, size=500, depth=4, **styling)

Bases: VCollection

Sierpinski triangle fractal composed of many small filled triangles.

Parameters:

  • cx (float) – Center x.

  • cy (float) – Center y.

  • size (float) – Side length of the outer triangle.

  • depth (int) – Recursion depth (0 = solid triangle, 4–5 is typical).

class Spiral(cx=960, cy=540, a=0, b=15, turns=5, num_points=500, log_spiral=False, **styling)

Bases: Lines

Archimedean (r = a + b·θ) or logarithmic (r = a·e^{b·θ}) spiral.

Parameters:

  • a (float) – Initial radius (distance from center at θ=0).

  • b (float) – Growth rate per radian.

  • turns (float) – Number of full turns.

  • num_points (int) – Number of sample points.

  • log_spiral (bool) – If True, use logarithmic spiral.

Example

# Archimedean spiral
s = Spiral(a=0, b=12, turns=6, stroke='#3498DB', stroke_width=2)
s.create(start=0, end=3)

# Logarithmic spiral
ls = Spiral(a=5, b=0.15, turns=4, log_spiral=True,
            stroke='#E74C3C', stroke_width=2)

SurroundingRectangle

class SurroundingRectangle(target, buff=14, corner_radius=6, follow=True, **styling)

Bases: RoundedRectangle

Rectangle that surrounds a target object with padding. If follow=True (default), tracks the target as it moves.

Parameters:

  • target (VObject) – Object to surround.

  • buff (float) – Padding around the target.

  • follow (bool) – Track target position dynamically.

Example

SurroundingRectangle — highlight an object with a border.

from vectormation.objects import *
text = Text('Important', font_size=60)
text.center_to_pos()
sr = SurroundingRectangle(text, buff=15, stroke='#FF6B6B', rx=8, ry=8)
sr.create(start=0, end=1)

SurroundingCircle

class SurroundingCircle(target, buff=14, follow=True, **styling)

Bases: Circle

Circle that surrounds a target object with padding.

Parameters:

  • target (VObject) – Object to surround.

  • buff (float) – Padding around the target.

  • follow (bool) – Track target position dynamically.

BackgroundRectangle

class BackgroundRectangle(target, buff=14, z=-1, **styling)

Bases: Rectangle

Semi-transparent rectangle behind a target object (useful for text backgrounds). Default fill is black at 75% opacity.

Parameters:

  • target (VObject) – Object to put background behind.

  • buff (float) – Padding around the target.

ScreenRectangle

class ScreenRectangle(width=480, **styling)

Bases: Rectangle

Rectangle with the canvas aspect ratio (16:9). Height is derived from width.

Parameters:

width (float) – Width in pixels.

ValueTracker

class ValueTracker(value=0, creation=0)

Convenience wrapper around a time-varying Real attribute. Use to drive reactive animations (e.g. link a label’s position to a value).

Parameters:

value (float) – Initial value.

set_value(val, start=0)

Set the value from start onward.

animate_value(target, start, end, easing=smooth)

Animate to a new value over [start, end].

at_time(time)

Return the value at a given time.

DecimalNumber

class DecimalNumber(value=0, fmt='{:.2f}', x=960, y=540, font_size=48, **styling)

Bases: Text

Text that dynamically displays a numeric value, updating each frame.

Parameters:

  • value – Initial value, or a Real / ValueTracker to track.

  • fmt (str) – Format string for display.

tracker: Real

The underlying tracked value.

Paragraph

class Paragraph(*lines, x=960, y=540, font_size=36, alignment='left', line_spacing=1.4, **styling)

Multi-line text with configurable alignment and line spacing.

Parameters:

  • lines – Text strings, one per line.

  • alignment (str) – 'left', 'center', or 'right'.

  • line_spacing (float) – Vertical spacing multiplier.

p = Paragraph('First line of text.',
              'Second line here.',
              'And a third.',
              alignment='center', font_size=32)

BulletedList

class BulletedList(*items, x=200, y=200, font_size=36, bullet='•', indent=40, line_spacing=1.6, **styling)

List of items with bullet characters.

Parameters:

  • items – Text strings for each list item.

  • bullet (str) – Bullet character (default '•').

  • indent (float) – Horizontal indent for the text after the bullet.

bl = BulletedList('First point',
                  'Second point',
                  'Third point')

NumberedList

class NumberedList(*items, x=200, y=200, font_size=36, indent=50, line_spacing=1.6, start_number=1, **styling)

List of items with numeric labels (1. 2. 3. …).

Parameters:

  • items – Text strings for each list item.

  • indent (float) – Horizontal indent for text after the number.

  • start_number (int) – First number in the sequence.

nl = NumberedList('Install the package',
                  'Import the module',
                  'Create your animation')