3D Objects¶

VectorMation includes a lightweight 3D module for rendering three-dimensional scenes as SVG. Objects are projected orthographically and depth-sorted each frame, so surfaces, primitives, and axis lines correctly occlude one another.

All 3D content lives inside a ThreeDAxes instance, which acts as both the coordinate system and the renderer. Surfaces are registered with add_surface(), primitives with add_3d().

Example: Creating 3D axes

from vectormation.objects import *
import math

canvas = VectorMathAnim()
canvas.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
canvas.add_objects(axes)

Example: ThreeDAxes

"""ThreeDAxes: basic 3D coordinate system."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))

v.add(axes)

v.show(end=0)

ThreeDAxes¶

class ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2), cx=960, cy=540, scale=160, phi=75deg, theta=-30deg, show_ticks=True, show_labels=True, show_grid=False, x_label='x', y_label='y', z_label='z', **styling)¶

Three-dimensional coordinate axes with camera control, ticks, labels, and depth-sorted rendering.

Bases: VCollection

Parameters:

x_range (tuple) – (min, max) for the x-axis.
y_range (tuple) – (min, max) for the y-axis.
z_range (tuple) – (min, max) for the z-axis.
cx (float) – Screen centre x (default 960).
cy (float) – Screen centre y (default 540).
scale (float) – Pixels per math unit (default 160).
phi (float) – Camera elevation in radians (default math.radians(75)).
theta (float) – Camera azimuth in radians (default math.radians(-30)).
show_ticks (bool) – Draw tick marks on axes (default True).
show_labels (bool) – Draw numeric tick labels (default True).
show_grid (bool) – Draw ground-plane grid lines (default False).
x_label (str) – Label for x-axis, or None to hide.
y_label (str) – Label for y-axis, or None to hide.
z_label (str) – Label for z-axis, or None to hide.

phi: Real¶: Camera elevation angle in radians (animatable).

theta: Real¶: Camera azimuth angle in radians (animatable).

Camera Methods

set_camera_orientation(start, end, phi=None, theta=None, easing=smooth)¶

Animate camera elevation and/or azimuth over [start, end].

Parameters:

phi (float) – Target elevation in radians, or None to keep current.
theta (float) – Target azimuth in radians, or None to keep current.

Example: Rotating camera to top-down view

# Rotate camera to a top-down view over 3 seconds
axes.set_camera_orientation(0, 3, phi=0, theta=0)

Example: Camera Rotation

"""Animated camera rotation with set_camera_orientation."""
from vectormation.objects import *
import math

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.plot_surface(lambda x, y: math.sin(x) * math.cos(y),
                  resolution=(20, 20), fill_color='#58C4DD')
axes.set_camera_orientation(0, 3, phi=math.radians(30), theta=math.radians(-120))

v.add(axes)

v.show(end=3)

begin_ambient_camera_rotation(start=0, end=None, rate=0.1)¶

Continuously rotate the camera theta at rate radians per second. If end is None, the rotation continues indefinitely.

Parameters:: rate (float) – Angular velocity in radians/second.

Example: Ambient camera rotation

# Slowly orbit the scene for the entire animation
axes.begin_ambient_camera_rotation(start=0, rate=0.15)

Example: Ambient Camera Rotation

"""Ambient camera rotation around a 3D scene."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
sphere = Sphere3D(radius=1.5, checkerboard_colors=('#FC6255', '#c44030'))
axes.add_surface(sphere)
axes.begin_ambient_camera_rotation(start=0, rate=0.3)

v.add(axes)

v.show(end=4)

set_camera_preset(name, start=0, end=0.5, easing=smooth)¶

Animate camera to a named preset orientation.

Parameters:: name (str) – One of 'default', 'isometric', 'front', 'top', 'side'.

Preset values:

Name	phi	theta
`default`	75 deg	-30 deg
`isometric`	54.7 deg	-45 deg
`front`	90 deg	0 deg
`top`	0 deg	0 deg
`side`	90 deg	-90 deg

set_camera_zoom(factor, start=0, end=1, easing=smooth)¶

Animate the 3D camera zoom (scale multiplier) over [start, end].

Parameters:: factor (float) – Multiply the current scale by this factor.

Example: Zooming in on a 3D scene

# Zoom in 2x over 2 seconds
axes.set_camera_zoom(2.0, start=0, end=2)

Example: 3D Camera Zoom

"""Zooming in on a 3D scene with set_camera_zoom."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
faces = Cube(side_length=2, fill_color='#58C4DD')
for face in faces:
    axes.add_surface(face)
axes.set_camera_zoom(2.0, start=0, end=2)

v.add(axes)

v.show(end=2)

Projection

project_point(x, y, z, time=0)¶

Project a 3D point to screen coordinates using the current camera.

Returns:: (svg_x, svg_y, depth)

coords_to_point(x, y, z=0, time=0)¶

Convert 3D math coordinates to 2D SVG pixel coordinates.

Returns:: (svg_x, svg_y)

Lighting

set_light_direction(x, y, z)¶

Set the light direction vector for Lambertian shading on surfaces. The vector is normalized internally.

Parameters:

x (float) – Light direction x-component.
y (float) – Light direction y-component.
z (float) – Light direction z-component.

The default light direction is (0.5, -0.5, 0.7071).

Example: Setting light direction

# Light from directly above
axes.set_light_direction(0, 0, 1)

Example: Light Direction

"""Different light directions on a 3D surface."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.set_light_direction(0, 0, 1)  # Light from directly above
sphere = Sphere3D(radius=1.5, fill_color='#58C4DD')
axes.add_surface(sphere)

v.add(axes)

v.show(end=0)

Adding Surfaces

add_surface(surface)¶

Parameters:: surface (Surface) – The surface to add.

Example: Adding a sphere surface

sphere = Sphere3D(radius=1.5)
axes.add_surface(sphere)

Example: Sphere Surface

"""Adding a sphere surface via add_surface."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
sphere = Sphere3D(radius=1.5, checkerboard_colors=('#4488ff', '#2266cc'))
axes.add_surface(sphere)

v.add(axes)

v.show(end=0)

plot_surface(func, u_range=None, v_range=None, resolution=(20, 20), fill_color='#4488ff', checkerboard_colors=None, stroke_color='#333', stroke_width=0.5, fill_opacity=0.8)¶

Create and register a Surface. If u_range or v_range is None, the corresponding axis range is used. Returns the Surface.

Parameters:

func (callable) – z = func(x, y) or (x, y, z) = func(u, v).
resolution (tuple) – (u_steps, v_steps) grid resolution.
fill_color (str) – Base fill colour.
checkerboard_colors (tuple) – Optional (color_a, color_b) pair.

Example: Plotting a Gaussian surface

import math

def gaussian(x, y):
    return math.exp(-(x**2 + y**2) / 0.32)

axes.plot_surface(gaussian, resolution=(24, 24),
                  checkerboard_colors=('#FF862F', '#4488ff'))

Example: Gaussian Surface

"""Gaussian surface plot on ThreeDAxes."""
from vectormation.objects import *
import math

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-1, 2))
axes.plot_surface(lambda x, y: 1.5 * math.exp(-(x**2 + y**2) / 2),
                  resolution=(24, 24),
                  checkerboard_colors=('#FF862F', '#4488ff'))

v.add(axes)

v.show(end=0)

Adding Primitives

add_3d(obj)¶

Example: Adding 3D primitives

axes.add_3d(Dot3D((1, 0, 0), radius=6, fill='#FC6255'))
axes.add_3d(Line3D((0, 0, 0), (2, 1, 3), stroke='#FFFF00'))

3D Curves

get_graph_3d(func, x_range=None, plane='xz', num_points=100, stroke='#FFFF00', stroke_width=2)¶

Plot a 2D function as a 3D curve in the specified plane. Returns a ParametricCurve3D.

Parameters:

func (callable) – y = func(x) or z = func(x) depending on plane.
plane (str) – 'xz' (default), 'xy', or 'yz'.

Example: 3D function curve

import math

curve = axes.get_graph_3d(math.sin, plane='xz',
                          stroke='#83C167')

Example: 3D Function Curve

"""3D function curve using get_graph_3d."""
from vectormation.objects import *
import math

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
curve = axes.get_graph_3d(math.sin, plane='xz', stroke='#83C167', stroke_width=3)

v.add(axes)

v.show(end=0)

Wireframe Surfaces

plot_surface_wireframe(func, x_steps=20, y_steps=20, **styling)¶

Render a z = func(x, y) surface as a wireframe mesh.

Parameters:

x_steps (int) – Grid resolution along x.
y_steps (int) – Grid resolution along y.

plot_parametric_surface(func, u_range=(0, tau), v_range=(0, pi), u_steps=32, v_steps=16, **styling)¶: Plot a parametric surface (x, y, z) = func(u, v) as a wireframe.

Grid Planes

add_grid_plane(plane='xz', step=1, color='#444444', opacity=0.3, stroke_width=0.5)¶

Add a grid plane to the 3D axes.

Parameters:

plane (str) – 'xz', 'xy', or 'yz'.
step (float) – Grid line spacing in math units.

Example: 3D surface with camera rotation

Gaussian surface with ambient camera rotation.

"""3D surface with camera rotation."""
from vectormation.objects import *
import math

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-1, 2))
axes.plot_surface(lambda x, y: math.exp(-(x**2 + y**2) / 2),
                  resolution=(20, 20),
                  checkerboard_colors=('#FF862F', '#4488ff'))
axes.begin_ambient_camera_rotation(start=0, rate=0.3)

v.add(axes)

v.show(end=6)

Surface¶

class Surface(func, u_range=(-3, 3), v_range=(-3, 3), resolution=(20, 20), fill_color='#4488ff', checkerboard_colors=None, stroke_color='#333', stroke_width=0.5, fill_opacity=0.8)¶

Filled quad surface with Lambertian shading and depth sorting.

Surfaces auto-detect whether the given function is a height-map or parametric form:

Height-map – func(x, y) -> z:

Example: Height-map surface

def paraboloid(x, y):
    return x**2 + y**2

surface = Surface(paraboloid, u_range=(-2, 2), v_range=(-2, 2))
axes.add_surface(surface)

Parametric – func(u, v) -> (x, y, z):

Example: Parametric Mobius strip

import math

def mobius(u, v):
    x = (1 + v/2 * math.cos(u/2)) * math.cos(u)
    y = (1 + v/2 * math.cos(u/2)) * math.sin(u)
    z = v/2 * math.sin(u/2)
    return (x, y, z)

surface = Surface(mobius,
                   u_range=(0, math.tau),
                   v_range=(-0.5, 0.5),
                   resolution=(40, 8),
                   fill_color='#58C4DD')
axes.add_surface(surface)

Parameters:

func (callable) – Height-map or parametric function.
u_range (tuple) – (min, max) for the u parameter.
v_range (tuple) – (min, max) for the v parameter.
resolution (tuple) – (u_steps, v_steps) – number of quad subdivisions.
fill_color (str) – Base fill colour (hex).
checkerboard_colors (tuple) – Optional (color_a, color_b) pair for alternating face colours.
stroke_color (str) – Quad edge colour.
stroke_width (float) – Quad edge width (set to 0 for no edges).
fill_opacity (float) – Fill opacity (0–1).

set_checkerboard(color_a, color_b)¶

Update the checkerboard colours for this surface. Returns self.

Example: Setting checkerboard colours

surface.set_checkerboard('#FC6255', '#c44030')

Example: Height-map Surface

"""Height-map surface (z = f(x, y))."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))

def paraboloid(x, y):
    return (x**2 + y**2) / 4

surface = Surface(paraboloid, u_range=(-2, 2), v_range=(-2, 2),
                  resolution=(20, 20), fill_color='#4488ff')
axes.add_surface(surface)

v.add(axes)

v.show(end=0)

Example: Mobius Strip

"""Parametric Mobius strip surface."""
from vectormation.objects import *
import math

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))

def mobius(u, v):
    x = (1 + v / 2 * math.cos(u / 2)) * math.cos(u)
    y = (1 + v / 2 * math.cos(u / 2)) * math.sin(u)
    z = v / 2 * math.sin(u / 2)
    return (x, y, z)

surface = Surface(mobius, u_range=(0, math.tau), v_range=(-0.5, 0.5),
                  resolution=(40, 8), fill_color='#58C4DD')
axes.add_surface(surface)

v.add(axes)

v.show(end=0)

Example: Checkerboard Surface

"""Checkerboard surface colours."""
from vectormation.objects import *
import math

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
surface = Surface(lambda x, y: math.sin(x) * math.cos(y),
                  u_range=(-3, 3), v_range=(-3, 3),
                  resolution=(20, 20))
surface.set_checkerboard('#FC6255', '#c44030')
axes.add_surface(surface)

v.add(axes)

v.show(end=0)

Example: Wireframe Surface

"""Surface with wireframe mesh overlay using SurfaceMesh."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))

def saddle(x, y):
    return (x**2 - y**2) / 4

surface = Surface(saddle, resolution=(20, 20),
                  fill_color='#58C4DD', fill_opacity=0.8)
mesh = SurfaceMesh(surface, stroke_color='#ffffff', stroke_opacity=0.3)
axes.add_surface(surface)
axes.add_surface(mesh)

v.add(axes)

v.show(end=0)

SurfaceMesh¶

class SurfaceMesh(surface, resolution=None, stroke_color='#ffffff', stroke_width=1, stroke_opacity=0.4, creation=0, z=0)¶

Wireframe mesh overlay for a Surface, showing grid lines without fill. Inherits from Surface but renders only line segments along the U and V directions of the parameter grid.

Parameters:

surface (Surface) – The surface to overlay with a mesh.
resolution (tuple) – (u_steps, v_steps) grid resolution, or None to match the underlying surface’s resolution.
stroke_color (str) – Line colour (default '#ffffff').
stroke_width (float) – Line width (default 1).
stroke_opacity (float) – Line opacity (default 0.4).

Example: Surface with wireframe mesh overlay

import math

def saddle(x, y):
    return (x**2 - y**2) / 4

surface = Surface(saddle, resolution=(20, 20),
                   fill_color='#58C4DD', fill_opacity=0.8)
mesh = SurfaceMesh(surface, stroke_color='#ffffff',
                    stroke_opacity=0.3)
axes.add_surface(surface)
axes.add_surface(mesh)

3D Primitives¶

All primitives support show, z, copy(), shift(dx, dy, dz), move_to(x, y, z), and set_color(color).

Example: 3D primitives

Dot, line, and arrow in 3D space.

"""3D primitives: dot, line, arrow."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.add_3d(Dot3D((1, 0, 0), radius=8, fill='#FC6255'))
axes.add_3d(Dot3D((0, 2, 0), radius=8, fill='#83C167'))
axes.add_3d(Dot3D((0, 0, 1.5), radius=8, fill='#58C4DD'))
axes.add_3d(Line3D((0, 0, 0), (1, 0, 0), stroke='#FC6255', stroke_width=3))
axes.add_3d(Line3D((0, 0, 0), (0, 2, 0), stroke='#83C167', stroke_width=3))
axes.add_3d(Arrow3D((0, 0, 0), (0, 0, 1.5), stroke='#58C4DD', stroke_width=3))

v.add(axes)

v.show(end=2)

Example: 3D Primitives

"""Multiple 3D primitives: Line3D, Dot3D, Arrow3D together."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.add_3d(Dot3D((1, 0, 0), radius=8, fill='#FC6255'))
axes.add_3d(Dot3D((0, 2, 0), radius=8, fill='#83C167'))
axes.add_3d(Dot3D((0, 0, 1.5), radius=8, fill='#58C4DD'))
axes.add_3d(Line3D((1, 0, 0), (0, 2, 0), stroke='#FFFF00', stroke_width=3))
axes.add_3d(Arrow3D((0, 0, 0), (0, 0, 1.5), stroke='#58C4DD', stroke_width=3))
axes.add_3d(Arrow3D((0, 0, 0), (1, 0, 0), stroke='#FC6255', stroke_width=3))

v.add(axes)

v.show(end=0)

Line3D¶

class Line3D(start, end, stroke='#fff', stroke_width=2)¶

Line segment in 3D space.

Parameters:

start (tuple) – (x, y, z) start point.
end (tuple) – (x, y, z) end point.
stroke (str) – Stroke colour.
stroke_width (float) – Stroke width.

get_midpoint()¶: Return the 3D midpoint as (x, y, z).

get_length()¶: Return the Euclidean length.

Example: Line segment in 3D

line = Line3D((0, 0, 0), (2, 1, 3), stroke='#FFFF00')
axes.add_3d(line)

Example: Line3D

"""Line3D segment in 3D space."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.add_3d(Line3D((0, 0, 0), (2, 1, 1.5), stroke='#FFFF00', stroke_width=3))
axes.add_3d(Line3D((-2, -1, 0), (1, 2, -1), stroke='#FC6255', stroke_width=3))

v.add(axes)

v.show(end=0)

Arrow3D¶

class Arrow3D(start, end, stroke='#fff', stroke_width=2, tip_length=12, tip_radius=4)¶

Arrow in 3D space with a triangular tip.

Parameters:

start (tuple) – (x, y, z) tail point.
end (tuple) – (x, y, z) tip point.
stroke (str) – Shaft and tip colour.
tip_length (float) – Length of the arrowhead in pixels.
tip_radius (float) – Half-width of the arrowhead in pixels.

get_midpoint()¶: Return the 3D midpoint as (x, y, z).

get_length()¶: Return the Euclidean length of the shaft.

Example: Arrow in 3D space

arrow = Arrow3D((0, 0, 0), (1, 1, 2), stroke='#FC6255',
                 tip_length=14, tip_radius=5)
axes.add_3d(arrow)

Example: Arrow3D

"""Arrow3D in 3D space."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.add_3d(Arrow3D((0, 0, 0), (2, 0, 0), stroke='#FC6255', stroke_width=3))
axes.add_3d(Arrow3D((0, 0, 0), (0, 2, 0), stroke='#83C167', stroke_width=3))
axes.add_3d(Arrow3D((0, 0, 0), (0, 0, 1.5), stroke='#58C4DD', stroke_width=3))

v.add(axes)

v.show(end=0)

Dot3D¶

class Dot3D(point=(0, 0, 0), radius=5, fill='#fff')¶

Filled circle in 3D space.

Parameters:

point (tuple) – (x, y, z) position.
radius (float) – Circle radius in pixels.
fill (str) – Fill colour.

get_position()¶: Return the 3D position as (x, y, z).

set_radius(radius)¶: Set the dot radius. Returns self.

Example: Dot in 3D space

dot = Dot3D((1, 0, 0), radius=6, fill='#83C167')
axes.add_3d(dot)

Example: Dot3D

"""Dot3D in 3D space."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.add_3d(Dot3D((1, 0, 0), radius=8, fill='#FC6255'))
axes.add_3d(Dot3D((0, 2, 0), radius=8, fill='#83C167'))
axes.add_3d(Dot3D((0, 0, 1.5), radius=8, fill='#58C4DD'))
axes.add_3d(Dot3D((-1, -1, 1), radius=6, fill='#FFFF00'))

v.add(axes)

v.show(end=0)

ParametricCurve3D¶

class ParametricCurve3D(func, t_range=(0, 1), num_points=100, stroke='#fff', stroke_width=2)¶

Parametric curve func(t) -> (x, y, z) sampled at num_points points.

Parameters:

func (callable) – Function mapping t to (x, y, z).
t_range (tuple) – (t_min, t_max) parameter range.
num_points (int) – Number of sample points.
stroke (str) – Stroke colour.
stroke_width (float) – Stroke width.

Example: Parametric helix curve

import math

def helix(t):
    return (math.cos(t), math.sin(t), t / (2 * math.pi))

curve = ParametricCurve3D(helix,
                           t_range=(0, 4 * math.pi),
                           num_points=200,
                           stroke='#FFFF00',
                           stroke_width=3)
axes.add_3d(curve)

Example: Helix Curve

"""ParametricCurve3D helix."""
from vectormation.objects import *
import math

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))

def helix(t):
    return (math.cos(t), math.sin(t), t / (2 * math.pi))

curve = ParametricCurve3D(helix, t_range=(0, 4 * math.pi),
                          num_points=200, stroke='#FFFF00', stroke_width=3)
axes.add_3d(curve)

v.add(axes)

v.show(end=0)

Text3D¶

class Text3D(text, point=(0, 0, 0), font_size=20, fill='#fff')¶

Text label placed at a 3D position. The label always faces the camera (billboard style).

Parameters:

text (str) – Displayed text string.
point (tuple) – (x, y, z) position.
font_size (float) – Font size in pixels.
fill (str) – Text fill colour.

get_position()¶: Return the 3D position as (x, y, z).

set_text(text)¶: Update the displayed text. Returns self.

Example: Text label in 3D

label = Text3D('Origin', point=(0, 0, 0), font_size=18)
axes.add_3d(label)

Example: Text3D

"""Text3D label in 3D space."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
axes.add_3d(Dot3D((1, 1, 1), radius=6, fill='#FC6255'))
axes.add_3d(Text3D('P(1,1,1)', point=(1.3, 1.3, 1.2), font_size=18, fill='#FC6255'))
axes.add_3d(Text3D('Origin', point=(0.2, 0.2, 0.2), font_size=16, fill='#aaaaaa'))

v.add(axes)

v.show(end=0)

3D Factory Functions¶

Factory functions create pre-built Surface objects (or lists of them) for common shapes. They all accept fill_color, stroke_color, stroke_width, fill_opacity, checkerboard_colors, creation, and z keyword arguments.

Sphere3D¶

Sphere3D(radius=1.5, center=(0, 0, 0), resolution=(16, 32), **kwargs)¶

Create a sphere Surface.

Parameters:

radius (float) – Sphere radius in math units.
center (tuple) – (x, y, z) centre.
resolution (tuple) – (lat_steps, lon_steps) grid resolution.

Returns:

Surface

Default fill: #FC6255.

Example: Creating a sphere

sphere = Sphere3D(radius=1.5,
                   checkerboard_colors=('#FC6255', '#c44030'))
axes.add_surface(sphere)

Example: Sphere3D

"""Sphere3D on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
sphere = Sphere3D(radius=1.5, checkerboard_colors=('#FC6255', '#c44030'))
axes.add_surface(sphere)

v.add(axes)

v.show(end=0)

Cube¶

Cube(side_length=2, center=(0, 0, 0), **kwargs)¶

Create a cube as a list of 6 flat Surface objects (one per face).

Parameters:

side_length (float) – Edge length in math units.
center (tuple) – (x, y, z) centre.

Returns:

list[Surface]

Default fill: #58C4DD.

Example: Creating a cube

faces = Cube(side_length=2)
for face in faces:
    axes.add_surface(face)

Example: Cube

"""Cube on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
faces = Cube(side_length=2, fill_color='#58C4DD')
for face in faces:
    axes.add_surface(face)

v.add(axes)

v.show(end=0)

Cylinder3D¶

Cylinder3D(radius=1, height=2, center=(0, 0, 0), resolution=(16, 16), **kwargs)¶

Create an open-ended cylinder (side surface only) as a Surface.

Parameters:

radius (float) – Cylinder radius.
height (float) – Cylinder height.
center (tuple) – (x, y, z) centre.
resolution (tuple) – (angular_steps, height_steps) grid resolution.

Returns:

Surface

Default fill: #58C4DD.

Example: Cylinder3D

"""Cylinder3D on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
cylinder = Cylinder3D(radius=1, height=2,
                      fill_color='#58C4DD', fill_opacity=0.8)
axes.add_surface(cylinder)

v.add(axes)

v.show(end=0)

Cone3D¶

Cone3D(radius=1, height=2, center=(0, 0, 0), resolution=(16, 16), **kwargs)¶

Create an open-ended cone (side surface only) as a Surface.

Parameters:

radius (float) – Base radius.
height (float) – Cone height.
center (tuple) – (x, y, z) centre.
resolution (tuple) – (angular_steps, height_steps) grid resolution.

Returns:

Surface

Default fill: #58C4DD.

Example: Cone3D

"""Cone3D on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
cone = Cone3D(radius=1.2, height=2, fill_color='#FF862F', fill_opacity=0.8)
axes.add_surface(cone)

v.add(axes)

v.show(end=0)

Torus3D¶

Torus3D(major_radius=2, minor_radius=0.5, center=(0, 0, 0), resolution=(24, 12), **kwargs)¶

Create a torus Surface.

Parameters:

major_radius (float) – Distance from torus centre to tube centre.
minor_radius (float) – Tube radius.
center (tuple) – (x, y, z) centre.
resolution (tuple) – (major_steps, minor_steps) grid resolution.

Returns:

Surface

Default fill: #58C4DD.

Example: Torus3D

"""Torus3D on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-4, 4), y_range=(-4, 4), z_range=(-2, 2))
torus = Torus3D(major_radius=2, minor_radius=0.5,
                checkerboard_colors=('#9B59B6', '#7D3C98'))
axes.add_surface(torus)

v.add(axes)

v.show(end=0)

Prism3D¶

Prism3D(n_sides=6, radius=1, height=2, center=(0, 0, 0), **kwargs)¶

Create a prism with an n-sided polygon cross-section. Returns a list of Surface objects (side faces + top and bottom caps).

Parameters:

n_sides (int) – Number of sides of the polygon base.
radius (float) – Circumscribed radius of the polygon.
height (float) – Prism height.
center (tuple) – (x, y, z) centre.

Returns:

list[Surface]

Default fill: #58C4DD.

Example: Prism3D

"""Prism3D (hexagonal) on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
faces = Prism3D(n_sides=6, radius=1.2, height=2, fill_color='#9B59B6')
for face in faces:
    axes.add_surface(face)

v.add(axes)

v.show(end=0)

Platonic Solids¶

The Platonic solid factories create lists of flat Surface objects (one per face). They all accept fill_color, stroke_color, stroke_width, fill_opacity, creation, and z keyword arguments.

Tetrahedron¶

Tetrahedron(cx=0, cy=0, cz=0, size=1.0, **kwargs)¶

Regular tetrahedron (4 triangular faces).

Parameters:

cx (float) – Centre x.
cy (float) – Centre y.
cz (float) – Centre z.
size (float) – Scale factor applied to vertex coordinates.

Returns:

list[Surface]

Default fill: #58C4DD, default stroke: #FFFFFF.

Example: Creating a tetrahedron

faces = Tetrahedron(size=1.2, fill_color='#FC6255')
for face in faces:
    axes.add_surface(face)

Example: Tetrahedron

"""Tetrahedron on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
faces = Tetrahedron(size=1.5, fill_color='#FC6255')
for face in faces:
    axes.add_surface(face)

v.add(axes)

v.show(end=0)

Octahedron¶

Octahedron(cx=0, cy=0, cz=0, size=1.0, **kwargs)¶

Regular octahedron (8 triangular faces).

Parameters:

cx (float) – Centre x.
cy (float) – Centre y.
cz (float) – Centre z.
size (float) – Scale factor applied to vertex coordinates.

Returns:

list[Surface]

Example: Octahedron

"""Octahedron on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
faces = Octahedron(size=1.5, fill_color='#83C167')
for face in faces:
    axes.add_surface(face)

v.add(axes)

v.show(end=0)

Icosahedron¶

Icosahedron(cx=0, cy=0, cz=0, size=1.0, **kwargs)¶

Regular icosahedron (20 triangular faces).

Parameters:

cx (float) – Centre x.
cy (float) – Centre y.
cz (float) – Centre z.
size (float) – Scale factor applied to vertex coordinates.

Returns:

list[Surface]

Example: Icosahedron

"""Icosahedron on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
faces = Icosahedron(size=1.5, fill_color='#58C4DD')
for face in faces:
    axes.add_surface(face)

v.add(axes)

v.show(end=0)

Dodecahedron¶

Dodecahedron(cx=0, cy=0, cz=0, size=1.0, **kwargs)¶

Regular dodecahedron (12 pentagonal faces).

Parameters:

cx (float) – Centre x.
cy (float) – Centre y.
cz (float) – Centre z.
size (float) – Scale factor applied to vertex coordinates.

Returns:

list[Surface]

Example: Dodecahedron

"""Dodecahedron on ThreeDAxes."""
from vectormation.objects import *

v = VectorMathAnim()
v.set_background()

axes = ThreeDAxes(x_range=(-3, 3), y_range=(-3, 3), z_range=(-2, 2))
faces = Dodecahedron(size=1.2, fill_color='#FFFF00')
for face in faces:
    axes.add_surface(face)

v.add(axes)

v.show(end=0)