+/*
+ * Copyright © 2014 Keith Packard <keithp@keithp.com>
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; version 2 of the License.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License along
+ * with this program; if not, write to the Free Software Foundation, Inc.,
+ * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA.
+ */
+
+package org.altusmetrum.altoslib_5;
+
+public class AltosQuaternion {
+ double r; /* real bit */
+ double x, y, z; /* imaginary bits */
+
+ public AltosQuaternion multiply(AltosQuaternion b) {
+ return new AltosQuaternion(
+ this.r * b.r - this.x * b.x - this.y * b.y - this.z * b.z,
+ this.r * b.x + this.x * b.r + this.y * b.z - this.z * b.y,
+ this.r * b.y - this.x * b.z + this.y * b.r + this.z * b.x,
+ this.r * b.z + this.x * b.y - this.y * b.x + this.z * b.r);
+ }
+
+ public AltosQuaternion conjugate() {
+ return new AltosQuaternion(
+ this.r,
+ -this.x,
+ -this.y,
+ -this.z);
+ }
+
+ public double normal() {
+ return (this.r * this.r +
+ this.x * this.x +
+ this.y * this.y +
+ this.z * this.z);
+ }
+
+ public AltosQuaternion scale(double b) {
+ return new AltosQuaternion(
+ this.r * b,
+ this.x * b,
+ this.y * b,
+ this.z * b);
+ }
+
+ public AltosQuaternion normalize() {
+ double n = normal();
+ if (n <= 0)
+ return this;
+ return scale(1/Math.sqrt(n));
+ }
+
+ public double dot(AltosQuaternion b) {
+ return (this.r * b.r +
+ this.x * b.x +
+ this.y * b.y +
+ this.z * b.z);
+ }
+
+ public AltosQuaternion rotate(AltosQuaternion b) {
+ return (b.multiply(this)).multiply(b.conjugate());
+ }
+
+ public AltosQuaternion vectors_to_rotation(AltosQuaternion b) {
+ /*
+ * The cross product will point orthogonally to the two
+ * vectors, forming our rotation axis. The length will be
+ * sin(θ), so these values are already multiplied by that.
+ */
+
+ double x = this.y * b.z - this.z * b.y;
+ double y = this.z * b.x - this.x * b.z;
+ double z = this.x * b.y - this.y * b.x;
+
+ double s_2 = x*x + y*y + z*z;
+ double s = Math.sqrt(s_2);
+
+ /* cos(θ) = a · b / (|a| |b|).
+ *
+ * a and b are both unit vectors, so the divisor is one
+ */
+ double c = this.x*b.x + this.y*b.y + this.z*b.z;
+
+ double c_half = Math.sqrt ((1 + c) / 2);
+ double s_half = Math.sqrt ((1 - c) / 2);
+
+ /*
+ * Divide out the sine factor from the
+ * cross product, then multiply in the
+ * half sine factor needed for the quaternion
+ */
+ double s_scale = s_half / s;
+
+ AltosQuaternion r = new AltosQuaternion(c_half,
+ x * s_scale,
+ y * s_scale,
+ z * s_scale);
+ return r.normalize();
+ }
+
+ public AltosQuaternion(double r, double x, double y, double z) {
+ this.r = r;
+ this.x = x;
+ this.y = y;
+ this.z = z;
+ }
+
+ public AltosQuaternion(AltosQuaternion q) {
+ this.r = q.r;
+ this.x = q.x;
+ this.y = q.y;
+ this.z = q.z;
+ }
+
+ static public AltosQuaternion vector(double x, double y, double z) {
+ return new AltosQuaternion(0, x, y, z);
+ }
+
+ static public AltosQuaternion rotation(double x, double y, double z,
+ double s, double c) {
+ return new AltosQuaternion(c,
+ s*x,
+ s*y,
+ s*z);
+ }
+
+ static public AltosQuaternion zero_rotation() {
+ return new AltosQuaternion(1, 0, 0, 0);
+ }
+
+ static public AltosQuaternion half_euler(double x, double y, double z) {
+ double s_x = Math.sin(x), c_x = Math.cos(x);
+ double s_y = Math.sin(y), c_y = Math.cos(y);
+ double s_z = Math.sin(z), c_z = Math.cos(z);;
+
+ return new AltosQuaternion(c_x * c_y * c_z + s_x * s_y * s_z,
+ s_x * c_y * c_z - c_x * s_y * s_z,
+ c_x * s_y * c_z + s_x * c_y * s_z,
+ c_x * c_y * s_z - s_x * s_y * c_z);
+ }
+}