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deferred class
	EG_PARTICLE_SIMULATION_BH [G -> NUMERIC]

General
	cluster: physics
	description: 
		"This is the Barnes and Hut implementation for the n_body_force_solver of
		a particle system. The runtime is O (n log n) where n is the number of particles.
		The method was first proposed in:
		%"A Hierarchical O(n log n) force calculation algorithm%", J. Barnes and P. Hut, Nature, v. 324 (1986)
		
		To calculate the force on a_particle an EG_QUAD_TREE (node) is traversed where force is either
		
		traverse (node):
		1. if node is a leaf
		force := n_body_force (a_particle, node.particle)
		2. size of node region / distance between a_particle and center of mass of node < theta
		force := n_body_force (a_particle, node.center_of_mass_particle)
		3. none of the above
		for all children c of node
		force := force + traverse (c)
		
		The larger theta the better the runtime but also the higher the error since center_of_mass_particle
		is only an approximation of all the particle in the children of node.
		"

Ancestors
	EG_PARTICLE_SIMULATION* [G -> NUMERIC]
	EV_MODEL_DOUBLE_MATH

Queries
	arc_cosine (v: REAL_64): REAL_64
	arc_sine (v: REAL_64): REAL_64
	arc_tangent (v: REAL_64): REAL_64
	between (n, a, b: REAL_64): BOOLEAN
	ceiling (v: REAL_64): REAL_64
	cosine (v: REAL_64): REAL_64
	dabs (v: REAL_64): REAL_64
	delta_x (angle, length: REAL_64): REAL_64
	delta_y (angle, length: REAL_64): REAL_64
	distance (x1, y1, x2, y2: REAL_64): REAL_64
	distance_from_line (x, y, x1, y1, x2, y2: REAL_64): REAL_64
	Euler: REAL_64
	exp (x: REAL_64): REAL_64
	floor (v: REAL_64): REAL_64
	force (a_particle: [like particle_type] EG_PARTICLE): G
	last_theta_average: REAL_64
	line_angle (x1, y1, x2, y2: REAL_64): REAL_64
	log (v: REAL_64): REAL_64
	log10 (v: REAL_64): REAL_64
	log_2 (v: REAL_64): REAL_64
	modulo (a, b: REAL_64): REAL_64
	particles: LIST [[like particle_type] EG_PARTICLE]
	Pi: REAL_64
	Pi_2: REAL_64
	Pi_4: REAL_64
	point_on_ellipse (x, y, xc, yc, r1, r2: REAL_64): BOOLEAN
	point_on_ellipse_boundary (x, y, xc, yc, r1, r2, width: REAL_64): BOOLEAN
	point_on_line (x, y, x1, y1, x2, y2, width: REAL_64): BOOLEAN
	point_on_polygon (x, y: REAL_64; points: SPECIAL [EV_COORDINATE]): BOOLEAN
	point_on_rectangle (x, y, x1, y1, x2, y2: REAL_64): BOOLEAN
	point_on_rotated_ellipse (x, y, xc, yc, r1, r2, angle: REAL_64): BOOLEAN
	point_on_rotated_ellipse_boundary (x, y, xc, yc, r1, r2, angle, width: REAL_64): BOOLEAN
	point_on_segment (x, y, x1, y1, x2, y2, width: REAL_64): BOOLEAN
	quad_tree: detachable EG_QUAD_TREE
	sine (v: REAL_64): REAL_64
	sqrt (v: REAL_64): REAL_64
	Sqrt2: REAL_64
	tangent (v: REAL_64): REAL_64
	theta: REAL_64

Commands
	set_particles (a_particles: [like particles] LIST [[like particle_type] EG_PARTICLE])
	set_theta (a_theta: [like theta] REAL_64)

Constraints
	quad tree exists



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