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Flock

Flock behaviour based on the Boids algorithm.

Flock

Flock behaviour.

The flock operates via a species rule matrix, which is a 2D matrix of species rules, such that every species has a separate relationship with every other species including itself. As in the Boids algorithm, the rules are: - separate: how much a particle should separate from its neighbours. - align: how much a particle should align (match velocity) with its neighbours. - cohere: how much a particle should cohere (move towards) its neighbours.

Taichi Boids implementation inspired by: https://forum.taichi-lang.cn/t/homework0-boids/563

Source code in src/tolvera/vera/flock.py 
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@ti.data_oriented
class Flock:
    """Flock behaviour.

    The flock operates via a species rule matrix, which is a 2D matrix of species 
    rules, such that every species has a separate relationship with every other 
    species including itself. As in the Boids algorithm, the rules are:
    - `separate`: how much a particle should separate from its neighbours.
    - `align`: how much a particle should align (match velocity) with its neighbours.
    - `cohere`: how much a particle should cohere (move towards) its neighbours.

    Taichi Boids implementation inspired by:
    https://forum.taichi-lang.cn/t/homework0-boids/563
    """
    def __init__(self, tolvera, **kwargs):
        """Initialise the Flock behaviour.

        `flock_s` stores the species rule matrix. 
        `flock_p` stores the rule values per particle, and the number of neighbours.
        `flock_dist` stores the distance between particles.

        Args:
            tolvera (Tolvera): A Tolvera instance.
            **kwargs: Keyword arguments (currently none).
        """
        self.tv = tolvera
        self.kwargs = kwargs
        self.CONSTS = CONSTS({"MAX_RADIUS": (ti.f32, 300.0)})
        self.tv.s.flock_s = {
            "state": {
                "separate": (ti.f32, 0.01, 1.0),
                "align": (ti.f32, 0.01, 1.0),
                "cohere": (ti.f32, 0.01, 1.0),
                "radius": (ti.f32, 0.01, 1.0),
            },
            "shape": (self.tv.sn, self.tv.sn),
            "osc": ("set"),
            "randomise": True,
        }
        self.tv.s.flock_p = {
            "state": {
                "separate": (ti.math.vec2, 0.0, 1.0),
                "align": (ti.math.vec2, 0.0, 1.0),
                "cohere": (ti.math.vec2, 0.0, 1.0),
                "nearby": (ti.i32, 0.0, self.tv.p.n - 1),
            },
            "shape": self.tv.pn,
            "osc": ("get"),
            "randomise": False,
        }
        self.tv.s.flock_dist = {
            "state": {
                "dist": (ti.f32, 0.0, self.tv.x * 2),
                "dist_wrap": (ti.f32, 0.0, self.tv.x * 2),
            },
            "shape": (self.tv.pn, self.tv.pn),
            "osc": ("get"),
            "randomise": False,
        }

    def randomise(self):
        """Randomise the Flock behaviour."""
        self.tv.s.flock_s.randomise()

    @ti.kernel
    def step(self, particles: ti.template(), weight: ti.f32):
        """Step the Flock behaviour.

        Pairwise comparison is made and inactive particles are ignored. 
        When the distance between two particles is less than the radius 
        of the species, the particles are considered neighbours. 

        The separation, alignment and cohesion are calculated for
        each particle and the velocity is updated accordingly.

        State is updated in `flock_p` and `flock_dist`.

        Args:
            particles (ti.template()): A template for the particles.
            weight (ti.f32): The weight of the Flock behaviour.
        """
        n = particles.shape[0]
        for i in range(n):
            if particles[i].active == 0:
                continue
            p1 = particles[i]
            separate = ti.Vector([0.0, 0.0])
            align = ti.Vector([0.0, 0.0])
            cohere = ti.Vector([0.0, 0.0])
            nearby = 0
            species = self.tv.s.flock_s.struct()
            for j in range(n):
                if i == j and particles[j].active == 0:
                    continue
                p2 = particles[j]
                species = self.tv.s.flock_s[p1.species, p2.species]
                dis_wrap = p1.dist_wrap(p2, self.tv.x, self.tv.y)
                dis_wrap_norm = dis_wrap.norm()
                if dis_wrap_norm < species.radius * self.CONSTS.MAX_RADIUS:
                    separate += dis_wrap
                    align += p2.vel
                    cohere += p2.pos
                    nearby += 1
                self.tv.s.flock_dist[i, j].dist = p1.dist(p2).norm()
                self.tv.s.flock_dist[i, j].dist_wrap = dis_wrap_norm
            if nearby > 0:
                separate = (
                    separate / nearby * p1.active * ti.math.max(species.separate, 0.2)
                )
                align = align / nearby * p1.active * species.align
                cohere = (cohere / nearby - p1.pos) * p1.active * species.cohere
                vel = (separate + align + cohere).normalized()
                particles[i].vel += vel * weight * p1.speed * p1.active 
                particles[i].pos += particles[i].vel
            self.tv.s.flock_p[i] = self.tv.s.flock_p.struct(
                separate, align, cohere, nearby
            )

    def __call__(self, particles, weight: ti.f32 = 1.0):
        """Call the Flock behaviour.

        Args:
            particles (Particles): Particles to step.
            weight (ti.f32, optional): The weight of the Flock behaviour. Defaults to 1.0.
        """
        self.step(particles.field, weight)

__call__(particles, weight=1.0)

Call the Flock behaviour.

Parameters:

Name Type Description Default
particles Particles

Particles to step.

 required
weight f32

The weight of the Flock behaviour. Defaults to 1.0.

 1.0
Source code in src/tolvera/vera/flock.py 
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def __call__(self, particles, weight: ti.f32 = 1.0):
    """Call the Flock behaviour.

    Args:
        particles (Particles): Particles to step.
        weight (ti.f32, optional): The weight of the Flock behaviour. Defaults to 1.0.
    """
    self.step(particles.field, weight)

__init__(tolvera, **kwargs)

Initialise the Flock behaviour.

flock_s stores the species rule matrix. flock_p stores the rule values per particle, and the number of neighbours. flock_dist stores the distance between particles.

Parameters:

Name Type Description Default
tolvera Tolvera

A Tolvera instance.

 required
**kwargs

Keyword arguments (currently none).

 {}
Source code in src/tolvera/vera/flock.py 
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def __init__(self, tolvera, **kwargs):
    """Initialise the Flock behaviour.

    `flock_s` stores the species rule matrix. 
    `flock_p` stores the rule values per particle, and the number of neighbours.
    `flock_dist` stores the distance between particles.

    Args:
        tolvera (Tolvera): A Tolvera instance.
        **kwargs: Keyword arguments (currently none).
    """
    self.tv = tolvera
    self.kwargs = kwargs
    self.CONSTS = CONSTS({"MAX_RADIUS": (ti.f32, 300.0)})
    self.tv.s.flock_s = {
        "state": {
            "separate": (ti.f32, 0.01, 1.0),
            "align": (ti.f32, 0.01, 1.0),
            "cohere": (ti.f32, 0.01, 1.0),
            "radius": (ti.f32, 0.01, 1.0),
        },
        "shape": (self.tv.sn, self.tv.sn),
        "osc": ("set"),
        "randomise": True,
    }
    self.tv.s.flock_p = {
        "state": {
            "separate": (ti.math.vec2, 0.0, 1.0),
            "align": (ti.math.vec2, 0.0, 1.0),
            "cohere": (ti.math.vec2, 0.0, 1.0),
            "nearby": (ti.i32, 0.0, self.tv.p.n - 1),
        },
        "shape": self.tv.pn,
        "osc": ("get"),
        "randomise": False,
    }
    self.tv.s.flock_dist = {
        "state": {
            "dist": (ti.f32, 0.0, self.tv.x * 2),
            "dist_wrap": (ti.f32, 0.0, self.tv.x * 2),
        },
        "shape": (self.tv.pn, self.tv.pn),
        "osc": ("get"),
        "randomise": False,
    }

randomise()

Randomise the Flock behaviour.

Source code in src/tolvera/vera/flock.py 
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def randomise(self):
    """Randomise the Flock behaviour."""
    self.tv.s.flock_s.randomise()

step(particles, weight)

Step the Flock behaviour.

Pairwise comparison is made and inactive particles are ignored. When the distance between two particles is less than the radius of the species, the particles are considered neighbours.

The separation, alignment and cohesion are calculated for each particle and the velocity is updated accordingly.

State is updated in flock_p and flock_dist.

Parameters:

Name Type Description Default
particles template

A template for the particles.

 required
weight f32

The weight of the Flock behaviour.

 required
Source code in src/tolvera/vera/flock.py 
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@ti.kernel
def step(self, particles: ti.template(), weight: ti.f32):
    """Step the Flock behaviour.

    Pairwise comparison is made and inactive particles are ignored. 
    When the distance between two particles is less than the radius 
    of the species, the particles are considered neighbours. 

    The separation, alignment and cohesion are calculated for
    each particle and the velocity is updated accordingly.

    State is updated in `flock_p` and `flock_dist`.

    Args:
        particles (ti.template()): A template for the particles.
        weight (ti.f32): The weight of the Flock behaviour.
    """
    n = particles.shape[0]
    for i in range(n):
        if particles[i].active == 0:
            continue
        p1 = particles[i]
        separate = ti.Vector([0.0, 0.0])
        align = ti.Vector([0.0, 0.0])
        cohere = ti.Vector([0.0, 0.0])
        nearby = 0
        species = self.tv.s.flock_s.struct()
        for j in range(n):
            if i == j and particles[j].active == 0:
                continue
            p2 = particles[j]
            species = self.tv.s.flock_s[p1.species, p2.species]
            dis_wrap = p1.dist_wrap(p2, self.tv.x, self.tv.y)
            dis_wrap_norm = dis_wrap.norm()
            if dis_wrap_norm < species.radius * self.CONSTS.MAX_RADIUS:
                separate += dis_wrap
                align += p2.vel
                cohere += p2.pos
                nearby += 1
            self.tv.s.flock_dist[i, j].dist = p1.dist(p2).norm()
            self.tv.s.flock_dist[i, j].dist_wrap = dis_wrap_norm
        if nearby > 0:
            separate = (
                separate / nearby * p1.active * ti.math.max(species.separate, 0.2)
            )
            align = align / nearby * p1.active * species.align
            cohere = (cohere / nearby - p1.pos) * p1.active * species.cohere
            vel = (separate + align + cohere).normalized()
            particles[i].vel += vel * weight * p1.speed * p1.active 
            particles[i].pos += particles[i].vel
        self.tv.s.flock_p[i] = self.tv.s.flock_p.struct(
            separate, align, cohere, nearby
        )