spatial/barneshut: add Barnes-Hut force approximation package and R2/R3 helpers

spatial/barneshut/galaxy_example_test.go

@@ -0,0 +1,78 @@
+// Copyright ©2019 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package barneshut_test
+
+import (
+	"golang.org/x/exp/rand"
+
+	"gonum.org/v1/gonum/spatial/barneshut"
+	"gonum.org/v1/gonum/spatial/r2"
+)
+
+type mass struct {
+	d r2.Vec
+	v r2.Vec
+	m float64
+}
+
+func (m *mass) Coord2() r2.Vec { return m.d }
+func (m *mass) Mass() float64  { return m.m }
+func (m *mass) move(f r2.Vec) {
+	m.v = m.v.Add(f.Scale(1 / m.m))
+	m.d = m.d.Add(m.v)
+}
+
+func Example_galaxy() {
+	rnd := rand.New(rand.NewSource(1))
+
+	// Make 1000 stars in random locations.
+	stars := make([]*mass, 1000)
+	p := make([]barneshut.Particle2, len(stars))
+	for i := range stars {
+		s := &mass{
+			d: r2.Vec{
+				X: 100 * rnd.Float64(),
+				Y: 100 * rnd.Float64(),
+			},
+			v: r2.Vec{
+				X: rnd.NormFloat64(),
+				Y: rnd.NormFloat64(),
+			},
+			m: 10 * rnd.Float64(),
+		}
+		stars[i] = s
+		p[i] = s
+	}
+	vectors := make([]r2.Vec, len(stars))
+
+	// Make a plane to calculate approximate forces
+	plane := barneshut.Plane{Particles: p}
+
+	// Run a simulation for 100 updates.
+	for i := 0; i < 1000; i++ {
+		// Build the data structure. For small systems
+		// this step may be omitted and ForceOn will
+		// perform the naive quadratic calculation
+		// without building the data structure.
+		plane.Reset()
+
+		// Calculate the force vectors using the theta
+		// parameter...
+		const theta = 0.5
+		// and an imaginary gravitational constant.
+		const G = 10
+		for j, s := range stars {
+			vectors[j] = plane.ForceOn(s, theta, barneshut.Gravity2).Scale(G)
+		}
+
+		// Update positions.
+		for j, s := range stars {
+			s.move(vectors[j])
+		}
+
+		// Rendering stars is left as an exercise for
+		// the reader.
+	}
+}