Initial Commit - Copy from Altus Metrum AltOS

altoslib/AltosQuaternion.java

@@ -0,0 +1,170 @@
+/*
+ * 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; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * 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_14;
+
+public class AltosQuaternion {
+	double	r;		/* real bit */
+	double	x, y, z;	/* imaginary bits */
+
+	/* Multiply by b */
+	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 Math.sqrt(this.r * this.r +
+				 this.x * this.x +
+				 this.y * this.y +
+				 this.z * this.z);
+	}
+
+	/* Scale by a real value */
+	public AltosQuaternion scale(double b) {
+		return new AltosQuaternion(this.r * b,
+					   this.x * b,
+					   this.y * b,
+					   this.z * b);
+	}
+
+	/* Divide by the length to end up with a quaternion of length 1 */
+	public AltosQuaternion normalize() {
+		double	n = normal();
+		if (n <= 0)
+			return this;
+		return scale(1/n);
+	}
+
+	/* dot product */
+	public double dot(AltosQuaternion b) {
+		return (this.r * b.r +
+			this.x * b.x +
+			this.y * b.y +
+			this.z * b.z);
+	}
+
+	/* Rotate 'this' by 'b' */
+	public AltosQuaternion rotate(AltosQuaternion b) {
+		return (b.multiply(this)).multiply(b.conjugate());
+	}
+
+	/* Given two vectors (this and b), compute a quaternion
+	 * representing the rotation between them
+	 */
+	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) {
+		r = q.r;
+		x = q.x;
+		y = q.y;
+		z = q.z;
+	}
+
+	public AltosQuaternion() {
+		r = 1;
+		x = 0;
+		y = 0;
+		z = 0;
+	}
+
+	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 euler(double x, double y, double z) {
+
+		/* Halve the euler angles */
+		x = x / 2.0;
+		y = y / 2.0;
+		z = z / 2.0;
+
+		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);
+	}
+}