Forces

Force functions for particles.

This module contains functions for applying forces to particles. It includes functions for moving, attracting, repelling and gravitating particles. It also includes variations of these functions for specific species of particles.

attract(particles, pos, mass, radius)

Attract the particles to a position.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
pos	vec2	Attraction position.	required
mass	f32	Attraction mass.	required
radius	f32	Attraction radius.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def attract(particles: ti.template(), pos: ti.math.vec2, mass: ti.f32, radius: ti.f32):
    """Attract the particles to a position.

    Args:
        particles (ti.template): Particles.
        pos (ti.math.vec2): Attraction position.
        mass (ti.f32): Attraction mass.
        radius (ti.f32): Attraction radius.
    """
    for i in range(particles.field.shape[0]):
        p = particles.field[i]
        if p.active == 0:
            continue
        particles.field[i].vel += attract_particle(p, pos, mass, radius)

attract_particle(p, pos, mass, radius)

Attract a particle to a position.

Parameters:

Name	Type	Description	Default
particles	Particle	Individual particle.	required
pos	vec2	Attraction position.	required
mass	f32	Attraction mass.	required
radius	f32	Attraction radius.	required

Returns:

Type	Description
vec2	ti.math.vec2: Attraction velocity.

Source code in src/tolvera/vera/forces.py

@ti.func
def attract_particle(
    p: Particle, pos: ti.math.vec2, mass: ti.f32, radius: ti.f32
) -> ti.math.vec2:
    """Attract a particle to a position.

    Args:
        particles (Particle): Individual particle.
        pos (ti.math.vec2): Attraction position.
        mass (ti.f32): Attraction mass.
        radius (ti.f32): Attraction radius.

    Returns:
        ti.math.vec2: Attraction velocity.
    """
    target_distance = (pos - p.pos).norm()
    vel = ti.Vector([0.0, 0.0])
    if target_distance < radius:
        factor = (radius - target_distance) / radius
        vel = (pos - p.pos).normalized() * mass * factor
    return vel

attract_species(particles, pos, mass, radius, species)

Attract the particles of a given species to a position.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
pos	vec2	Attraction position.	required
mass	f32	Attraction mass.	required
radius	f32	Attraction radius.	required
species	i32	Species index.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def attract_species(
    particles: ti.template(),
    pos: ti.math.vec2,
    mass: ti.f32,
    radius: ti.f32,
    species: ti.i32,
):
    """Attract the particles of a given species to a position.

    Args:
        particles (ti.template): Particles.
        pos (ti.math.vec2): Attraction position.
        mass (ti.f32): Attraction mass.
        radius (ti.f32): Attraction radius.
        species (ti.i32): Species index.
    """
    for i in range(particles.field.shape[0]):
        p = particles.field[i]
        if p.active == 0:
            continue
        if p.species != species:
            continue
        particles.field[i].vel += attract_particle(p, pos, mass, radius)

centripetal(particles, centre, direction, weight)

Apply a centripetal force to the particles.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
centre	vec2	Centripetal centre.	required
direction	i32	Centripetal direction.	required
weight	f32	Centripetal weight.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def centripetal(particles: ti.template(), centre: ti.math.vec2, direction: ti.i32, weight: ti.f32):
    """Apply a centripetal force to the particles.

    Args:
        particles (ti.template): Particles.
        centre (ti.math.vec2): Centripetal centre.
        direction (ti.i32): Centripetal direction.
        weight (ti.f32): Centripetal weight.
    """
    for i in range(particles.field.shape[0]):
        p = particles.field[i]
        if p.active == 0:
            continue
        particles.field[i].vel += centripetal_particle(p, centre, direction, weight)

centripetal_particle(p, centre, direction, weight)

Apply a centripetal force to a particle.

Parameters:

Name	Type	Description	Default
p	Particle	Individual particle.	required
centre	vec2	Centripetal centre.	required
direction	i32	Centripetal direction.	required
weight	f32	Centripetal weight.	required

Returns:

Type	Description
vec2	ti.math.vec2: Centripetal velocity.

Source code in src/tolvera/vera/forces.py

@ti.func
def centripetal_particle(p: ti.template(), centre: ti.math.vec2, direction: ti.i32, weight: ti.f32) -> ti.math.vec2:
    """Apply a centripetal force to a particle.

    Args:
        p (Particle): Individual particle.
        centre (ti.math.vec2): Centripetal centre.
        direction (ti.i32): Centripetal direction.
        weight (ti.f32): Centripetal weight.

    Returns:
        ti.math.vec2: Centripetal velocity.
    """
    r = p.pos - centre
    if direction == 0:
        r = -r
    v_perp = ti.Vector([-r[1], r[0]])
    norm = v_perp.norm() + 1e-5
    v_perp_normalized = v_perp / norm
    speed = p.vel.norm()
    new_vel = v_perp_normalized * speed * weight
    return new_vel

gravitate(particles, G, radius)

Gravitate the particles.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
G	f32	Gravitational constant.	required
radius	f32	Gravitational radius.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def gravitate(particles: ti.template(), G: ti.f32, radius: ti.f32):
    """Gravitate the particles.

    Args:
        particles (ti.template): Particles.
        G (ti.f32): Gravitational constant.
        radius (ti.f32): Gravitational radius.
    """
    for i, j in ti.ndrange(particles.field.shape[0], particles.field.shape[0]):
        if i == j:
            continue
        p1 = particles.field[i]
        p2 = particles.field[j]
        if (p2.pos - p1.pos).norm() > radius:
            continue
        particles.field[i].vel += gravitation(p1, p2, G)

gravitate_species(particles, G, radius, species)

Gravitate the particles of a given species.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
G	f32	Gravitational constant.	required
radius	f32	Gravitational radius.	required
species	i32	Species index.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def gravitate_species(
    particles: ti.template(), G: ti.f32, radius: ti.f32, species: ti.i32
):
    """Gravitate the particles of a given species.

    Args:
        particles (ti.template): Particles.
        G (ti.f32): Gravitational constant.
        radius (ti.f32): Gravitational radius.
        species (ti.i32): Species index.
    """
    for i, j in ti.ndrange(particles.field.shape[0], particles.field.shape[0]):
        if i == j:
            continue
        p1 = particles.field[i]
        p2 = particles.field[j]
        if p1.species != species or p2.species != species:
            continue
        if (p2.pos - p1.pos).norm() > radius:
            continue
        particles.field[i].vel += gravitation(p1, p2, G)

gravitation(p1, p2, G)

Calculate the gravitational force between two particles.

Parameters:

Name	Type	Description	Default
p1	Particle	Particle 1.	required
p2	Particle	Particle 2.	required
G	f32	Gravitational constant.	required

Returns:

Type	Description
vec2	ti.math.vec2: Gravitational force.

Source code in src/tolvera/vera/forces.py

@ti.func
def gravitation(p1: Particle, p2: Particle, G: ti.f32) -> ti.math.vec2:
    """Calculate the gravitational force between two particles.

    Args:
        p1 (Particle): Particle 1.
        p2 (Particle): Particle 2.
        G (ti.f32): Gravitational constant.

    Returns:
        ti.math.vec2: Gravitational force.
    """
    r = p2.pos - p1.pos
    distance = r.norm() + 1e-5
    force_direction = r.normalized()
    force_magnitude = G * p1.mass * p2.mass / (distance**2)
    force = force_direction * force_magnitude
    return force / p1.mass

move(particles)

Move the particles.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def move(particles: ti.template()):
    """Move the particles.

    Args:
        particles (ti.template): Particles.
    """
    for i in range(particles.field.shape[0]):
        if particles.field[i].active == 0:
            continue
        p1 = particles.field[i]
        particles.field[i].pos += p1.vel * p1.speed * p1.active

noise(particles, weight)

Add noise to the particles.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
weight	f32	Noise weight.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def noise(particles: ti.template(), weight: ti.f32):
    """Add noise to the particles.

    Args:
        particles (ti.template): Particles.
        weight (ti.f32): Noise weight.
    """
    for i in range(particles.field.shape[0]):
        p = particles.field[i]
        if p.active == 0:
            continue
        particles.field[i].vel += (ti.Vector([ti.random() - 0.5, ti.random() - 0.5]) * weight)
        particles.field[i].pos += p.vel * p.speed * p.active

repel(particles, pos, mass, radius)

Repel the particles from a position.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
pos	vec2	Repulsion position.	required
mass	f32	Repulsion mass.	required
radius	f32	Repulsion radius.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def repel(particles: ti.template(), pos: ti.math.vec2, mass: ti.f32, radius: ti.f32):
    """Repel the particles from a position.

    Args:
        particles (ti.template): Particles.
        pos (ti.math.vec2): Repulsion position.
        mass (ti.f32): Repulsion mass.
        radius (ti.f32): Repulsion radius.
    """
    for i in range(particles.field.shape[0]):
        p = particles.field[i]
        if p.active == 0:
            continue
        particles.field[i].vel += repel_particle(p, pos, mass, radius)

repel_particle(p, pos, mass, radius)

Repel a particle from a position.

Parameters:

Name	Type	Description	Default
p	Particle	Individual particle.	required
pos	vec2	Repulsion position.	required
mass	f32	Repulsion mass.	required
radius	f32	Repulsion radius.	required

Returns:

Type	Description
vec2	ti.math.vec2: Repulsion velocity.

Source code in src/tolvera/vera/forces.py

@ti.func
def repel_particle(
    p: Particle, pos: ti.math.vec2, mass: ti.f32, radius: ti.f32
) -> ti.math.vec2:
    """Repel a particle from a position.

    Args:
        p (Particle): Individual particle.
        pos (ti.math.vec2): Repulsion position.
        mass (ti.f32): Repulsion mass.
        radius (ti.f32): Repulsion radius.

    Returns:
        ti.math.vec2: Repulsion velocity.
    """
    target_distance = (pos - p.pos).norm()
    vel = ti.Vector([0.0, 0.0])
    if target_distance < radius:
        factor = (target_distance - radius) / radius
        vel = (pos - p.pos).normalized() * mass * factor
    return vel

repel_species(particles, pos, mass, radius, species)

Repel the particles of a given species from a position.

Parameters:

Name	Type	Description	Default
particles	template	Particles.	required
pos	vec2	Repulsion position.	required
mass	f32	Repulsion mass.	required
radius	f32	Repulsion radius.	required
species	i32	Species index.	required

Source code in src/tolvera/vera/forces.py

@ti.kernel
def repel_species(
    particles: ti.template(),
    pos: ti.math.vec2,
    mass: ti.f32,
    radius: ti.f32,
    species: ti.i32,
):
    """Repel the particles of a given species from a position.

    Args:
        particles (ti.template): Particles.
        pos (ti.math.vec2): Repulsion position.
        mass (ti.f32): Repulsion mass.
        radius (ti.f32): Repulsion radius.
        species (ti.i32): Species index.
    """
    for i in range(particles.field.shape[0]):
        p = particles.field[i]
        if p.active == 0:
            continue
        if p.species != species:
            continue
        particles.field[i].vel += repel_particle(p, pos, mass, radius)