fixed dependencies

vendor/gonum.org/v1/gonum/spatial/r3/rotation.go

@@ -0,0 +1,58 @@
+// Copyright ©2021 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 r3
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/num/quat"
+)
+
+// TODO: possibly useful additions to the current rotation API:
+//  - create rotations from Euler angles (NewRotationFromEuler?)
+//  - create rotations from rotation matrices (NewRotationFromMatrix?)
+//  - return the equivalent Euler angles from a Rotation
+//
+// Euler angles have issues (see [1] for a discussion).
+// We should think carefully before adding them in.
+// [1]: http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/
+
+// Rotation describes a rotation in space.
+type Rotation quat.Number
+
+// NewRotation creates a rotation by alpha, around axis.
+func NewRotation(alpha float64, axis Vec) Rotation {
+	if alpha == 0 {
+		return Rotation{Real: 1}
+	}
+	q := raise(axis)
+	sin, cos := math.Sincos(0.5 * alpha)
+	q = quat.Scale(sin/quat.Abs(q), q)
+	q.Real += cos
+	if len := quat.Abs(q); len != 1 {
+		q = quat.Scale(1/len, q)
+	}
+
+	return Rotation(q)
+}
+
+// Rotate returns p rotated according to the parameters used to construct
+// the receiver.
+func (r Rotation) Rotate(p Vec) Vec {
+	if r.isIdentity() {
+		return p
+	}
+	qq := quat.Number(r)
+	pp := quat.Mul(quat.Mul(qq, raise(p)), quat.Conj(qq))
+	return Vec{X: pp.Imag, Y: pp.Jmag, Z: pp.Kmag}
+}
+
+func (r Rotation) isIdentity() bool {
+	return r == Rotation{Real: 1}
+}
+
+func raise(p Vec) quat.Number {
+	return quat.Number{Imag: p.X, Jmag: p.Y, Kmag: p.Z}
+}