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Physics with Verlet Integration

This is a Python physics library to calculate verlet integration. It is easy and simple to use, and there are many options. You will need pygame to run the sandbox.

The rest of this documentation will assume that you have already imported the verlet library:

import verlet

Creating a World

Initialize a new world with verlet.World.

Parameters:

Parameter Type Description
gravity tuple A tuple containing the (horizontal, vertical) gravity, measured in units/second squared
airFriction float The air friction/drag coefficient, e.g. 0.99 for slight resistance
boundaryFunction function A function that takes a Node object as input and modifies its position according to your boundaries
timeStep float The delta time of your simulation, e.g. 1 / FPS

Here is an example of a boundary function. In this case, boundary would be the appropriate argument.

def boundary(point):
     x, y = node.x, node.y

     if x < node.radius:
         node.x = node.radius
     if y < node.radius:
         node.y = node.radius
     if x > node.world.width - node.radius:
         node.x = node.world.width - node.radius
     if y > node.world.height - node.radius:
         node.y = node.world.height - node.radius

world = verlet.World((0, -32), 0.99, boundary, 1 / 60)

World functions

world.newNode

See "Adding Things to Your World"

world.newConstraint

See "Adding Things to Your World"

world.countNodes -> int

Returns how many nodes currently exist in the simulation

Warning Do not use len(world.nodes), as this list contains deleted nodes as well

world.countConstraints -> int

Returns how many constraints currently exist in the simulation

Warning Do not use len(world.constraints), as this list contains deleted constraints as well

world.getNodeObject -> None | Node

Returns the node object given its ID, allowing to manually change its properties

If the node was deleted, return None

Parameters:

Parameter Type Description
ID integer An ID returned by world.newNode

world.getConstraintObject -> None | Constraint

Returns the constraint object given its ID, allowing to manually change its properties

If the constraint was deleted, return None

Parameters:

Parameter Type Description
ID integer An ID returned by world.newConstraint

world.getNodes -> filter

Returns all currently existing nodes in the simulation as Node objects (to be iterated through)

Warning Do not use world.nodes, as this list contains deleted nodes as well

world.getConstraints -> filter

Returns all currently existing constraints in the simulation as Constraint objects (to be iterated through)

Warning Do not use world.constraints, as this list contains deleted nodes as well

world.deleteNode

Delete a node given its ID

This will also delete any attached constraints

Parameters:

Parameter Type Description
ID integer An ID returned by world.newNode

world.deleteConstraint

Delete a constraint given its ID

Parameters:

Parameter Type Default Description
ID integer An ID returned by world.newNode
deleteConnectedNodes boolean False Whether or not to delete all nodes the constraint was a part of

world.setNodeVelocity

Sets the velocity, in units/second, of a node

Parameters:

Parameter Type Description
ID integer An ID returned by world.newNode
xVel integer or float The horizontal velocity, in units/second
yVel integer or float The vertical velocity, in units/second

world.addNodeVelocity

Changes the velocity, in units/second, of a node

Parameters:

Parameter Type Description
ID integer An ID returned by world.newNode
xVel integer or float The horizontal velocity, in units/second, to be added
yVel integer or float The vertical velocity, in units/second, to be added

world.configureNode

Directly changes any parameter of a node

Parameters:

Parameter Type Default Description
ID integer An ID returned by world.newNode

See "Adding Things to Your World"

world.configureConstraint

Directly changes any parameter of a constraint

Parameters:

Parameter Type Default Description
ID integer An ID returned by world.newConstraint

See "Adding Things to Your World"

world.update

Updates all nodes and constraints in the simulation

Parameters:

Parameter Type Default Description
exclusions 2D tuple ((), ()) A 2-dimensional tuple containing Node and Constraint objects which should not be updated. The first tuple contains excluded Node objects, and the second tuple contains excluded Constraint objects.
updateRandomly tuple (False, False) Whether or not to randomly update the (nodes, constraints)
constraintIterations integer 1 How many times to update the constraints, e.g. if you want them to be stiffer

Adding Things to Your World

You can add nodes and constraints to your simulation by using world.newNode and world.newConstraint respectively.

world.newNode -> int

Creates a new node in the simulation, and returns its ID

Parameters:

Parameter Type Default Description
x integer or float The X position of the node
y integer or float The Y position of the node
xVel integer or float 0 The horizontal velocity of the node, measured in units/second
yVel integer or float 0 The vertical velocity of the node, measured in units/second
pinned boolean False Whether or not the node is restricted from moving
radius integer or float 5 The radius of the node

Example:

>>> node1 = world.newNode(100, 100, pinned=True)
>>> node2 = world.newNode(100, 200, yVel=10, radius=15)

world.newConstraint -> int

Creates a new constraint in the simulation, and returns its ID

Parameters:

Parameter Type Default Description
startPoint integer A node ID returned by world.newNode
endPoint integer A node ID returned by world.newNode
length None or integer or float None The target length of the constraint in units. If None, automatically calculate it
stiffness float 0.5 The stiffness scalar of the constraint, higher = stiffer. Must be between 0 and 1

Example:

>>> constraint = world.newConstraint(node1, node2, stiffness=0.1) # Stretchy loose constraint