1324 lines
No EOL
46 KiB
C#
1324 lines
No EOL
46 KiB
C#
#region --- License ---
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/*
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Copyright (c) 2006 - 2008 The Open Toolkit library.
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Permission is hereby granted, free of charge, to any person obtaining a copy of
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this software and associated documentation files (the "Software"), to deal in
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the Software without restriction, including without limitation the rights to
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use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
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of the Software, and to permit persons to whom the Software is furnished to do
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so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#endregion
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using System;
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using System.Runtime.InteropServices;
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using System.ComponentModel;
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using System.Xml.Serialization;
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namespace OpenTK
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{
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/// <summary>
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/// Represents a double-precision Quaternion.
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/// </summary>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Quaterniond : IEquatable<Quaterniond>
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{
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#region Fields
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Vector3d xyz;
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double w;
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#endregion
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#region Constructors
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/// <summary>
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/// Construct a new Quaterniond from vector and w components
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/// </summary>
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/// <param name="v">The vector part</param>
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/// <param name="w">The w part</param>
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public Quaterniond(Vector3d v, double w)
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{
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this.xyz = v;
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this.w = w;
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}
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/// <summary>
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/// Construct a new Quaterniond
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/// </summary>
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/// <param name="x">The x component</param>
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/// <param name="y">The y component</param>
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/// <param name="z">The z component</param>
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/// <param name="w">The w component</param>
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public Quaterniond(double x, double y, double z, double w)
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: this(new Vector3d(x, y, z), w)
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{ }
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#endregion
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#region Public Members
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#region Properties
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/// <summary>
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/// Gets or sets an OpenTK.Vector3d with the X, Y and Z components of this instance.
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/// </summary>
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[Obsolete("Use Xyz property instead.")]
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[CLSCompliant(false)]
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[EditorBrowsable(EditorBrowsableState.Never)]
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[XmlIgnore]
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public Vector3d XYZ { get { return Xyz; } set { Xyz = value; } }
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/// <summary>
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/// Gets or sets an OpenTK.Vector3d with the X, Y and Z components of this instance.
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/// </summary>
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public Vector3d Xyz { get { return xyz; } set { xyz = value; } }
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/// <summary>
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/// Gets or sets the X component of this instance.
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/// </summary>
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[XmlIgnore]
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public double X { get { return xyz.X; } set { xyz.X = value; } }
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/// <summary>
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/// Gets or sets the Y component of this instance.
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/// </summary>
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[XmlIgnore]
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public double Y { get { return xyz.Y; } set { xyz.Y = value; } }
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/// <summary>
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/// Gets or sets the Z component of this instance.
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/// </summary>
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[XmlIgnore]
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public double Z { get { return xyz.Z; } set { xyz.Z = value; } }
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/// <summary>
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/// Gets or sets the W component of this instance.
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/// </summary>
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public double W { get { return w; } set { w = value; } }
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#endregion
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#region Instance
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#region ToAxisAngle
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/// <summary>
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/// Convert the current quaternion to axis angle representation
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/// </summary>
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/// <param name="axis">The resultant axis</param>
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/// <param name="angle">The resultant angle</param>
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public void ToAxisAngle(out Vector3d axis, out double angle)
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{
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Vector4d result = ToAxisAngle();
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axis = result.Xyz;
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angle = result.W;
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}
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/// <summary>
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/// Convert this instance to an axis-angle representation.
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/// </summary>
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/// <returns>A Vector4 that is the axis-angle representation of this quaternion.</returns>
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public Vector4d ToAxisAngle()
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{
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Quaterniond q = this;
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if (q.W > 1.0f)
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q.Normalize();
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Vector4d result = new Vector4d();
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result.W = 2.0f * (float)System.Math.Acos(q.W); // angle
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float den = (float)System.Math.Sqrt(1.0 - q.W * q.W);
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if (den > 0.0001f)
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{
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result.Xyz = q.Xyz / den;
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}
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else
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{
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// This occurs when the angle is zero.
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// Not a problem: just set an arbitrary normalized axis.
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result.Xyz = Vector3d.UnitX;
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}
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return result;
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}
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#endregion
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#region public double Length
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/// <summary>
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/// Gets the length (magnitude) of the Quaterniond.
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/// </summary>
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/// <seealso cref="LengthSquared"/>
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public double Length
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{
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get
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{
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return (double)System.Math.Sqrt(W * W + Xyz.LengthSquared);
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}
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}
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#endregion
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#region public double LengthSquared
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/// <summary>
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/// Gets the square of the Quaterniond length (magnitude).
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/// </summary>
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public double LengthSquared
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{
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get
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{
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return W * W + Xyz.LengthSquared;
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}
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}
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#endregion
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#region public void Normalize()
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/// <summary>
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/// Scales the Quaterniond to unit length.
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/// </summary>
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public void Normalize()
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{
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double scale = 1.0f / this.Length;
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Xyz *= scale;
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W *= scale;
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}
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#endregion
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#region public void Conjugate()
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/// <summary>
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/// Convert this Quaterniond to its conjugate
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/// </summary>
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public void Conjugate()
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{
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Xyz = -Xyz;
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}
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#endregion
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#endregion
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#region Static
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#region Fields
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/// <summary>
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/// Defines the identity quaternion.
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/// </summary>
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public readonly static Quaterniond Identity = new Quaterniond(0, 0, 0, 1);
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#endregion
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#region Add
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/// <summary>
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/// Add two quaternions
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/// </summary>
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/// <param name="left">The first operand</param>
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/// <param name="right">The second operand</param>
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/// <returns>The result of the addition</returns>
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public static Quaterniond Add(Quaterniond left, Quaterniond right)
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{
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return new Quaterniond(
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left.Xyz + right.Xyz,
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left.W + right.W);
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}
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/// <summary>
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/// Add two quaternions
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/// </summary>
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/// <param name="left">The first operand</param>
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/// <param name="right">The second operand</param>
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/// <param name="result">The result of the addition</param>
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public static void Add(ref Quaterniond left, ref Quaterniond right, out Quaterniond result)
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{
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result = new Quaterniond(
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left.Xyz + right.Xyz,
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left.W + right.W);
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}
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#endregion
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#region Sub
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/// <summary>
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/// Subtracts two instances.
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/// </summary>
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/// <param name="left">The left instance.</param>
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/// <param name="right">The right instance.</param>
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/// <returns>The result of the operation.</returns>
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public static Quaterniond Sub(Quaterniond left, Quaterniond right)
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{
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return new Quaterniond(
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left.Xyz - right.Xyz,
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left.W - right.W);
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}
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/// <summary>
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/// Subtracts two instances.
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/// </summary>
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/// <param name="left">The left instance.</param>
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/// <param name="right">The right instance.</param>
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/// <param name="result">The result of the operation.</param>
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public static void Sub(ref Quaterniond left, ref Quaterniond right, out Quaterniond result)
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{
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result = new Quaterniond(
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left.Xyz - right.Xyz,
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left.W - right.W);
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}
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#endregion
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#region Mult
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/// <summary>
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/// Multiplies two instances.
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/// </summary>
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/// <param name="left">The first instance.</param>
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/// <param name="right">The second instance.</param>
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/// <returns>A new instance containing the result of the calculation.</returns>
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[Obsolete("Use Multiply instead.")]
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public static Quaterniond Mult(Quaterniond left, Quaterniond right)
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{
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return new Quaterniond(
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right.W * left.Xyz + left.W * right.Xyz + Vector3d.Cross(left.Xyz, right.Xyz),
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left.W * right.W - Vector3d.Dot(left.Xyz, right.Xyz));
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}
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/// <summary>
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/// Multiplies two instances.
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/// </summary>
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/// <param name="left">The first instance.</param>
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/// <param name="right">The second instance.</param>
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/// <param name="result">A new instance containing the result of the calculation.</param>
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[Obsolete("Use Multiply instead.")]
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public static void Mult(ref Quaterniond left, ref Quaterniond right, out Quaterniond result)
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{
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result = new Quaterniond(
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right.W * left.Xyz + left.W * right.Xyz + Vector3d.Cross(left.Xyz, right.Xyz),
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left.W * right.W - Vector3d.Dot(left.Xyz, right.Xyz));
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}
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/// <summary>
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/// Multiplies two instances.
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/// </summary>
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/// <param name="left">The first instance.</param>
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/// <param name="right">The second instance.</param>
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/// <returns>A new instance containing the result of the calculation.</returns>
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public static Quaterniond Multiply(Quaterniond left, Quaterniond right)
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{
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Quaterniond result;
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Multiply(ref left, ref right, out result);
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return result;
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}
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/// <summary>
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/// Multiplies two instances.
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/// </summary>
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/// <param name="left">The first instance.</param>
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/// <param name="right">The second instance.</param>
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/// <param name="result">A new instance containing the result of the calculation.</param>
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public static void Multiply(ref Quaterniond left, ref Quaterniond right, out Quaterniond result)
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{
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result = new Quaterniond(
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right.W * left.Xyz + left.W * right.Xyz + Vector3d.Cross(left.Xyz, right.Xyz),
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left.W * right.W - Vector3d.Dot(left.Xyz, right.Xyz));
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}
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/// <summary>
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/// Multiplies an instance by a scalar.
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/// </summary>
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/// <param name="quaternion">The instance.</param>
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/// <param name="scale">The scalar.</param>
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/// <param name="result">A new instance containing the result of the calculation.</param>
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public static void Multiply(ref Quaterniond quaternion, double scale, out Quaterniond result)
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{
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result = new Quaterniond(quaternion.X * scale, quaternion.Y * scale, quaternion.Z * scale, quaternion.W * scale);
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}
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/// <summary>
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/// Multiplies an instance by a scalar.
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/// </summary>
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/// <param name="quaternion">The instance.</param>
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/// <param name="scale">The scalar.</param>
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/// <returns>A new instance containing the result of the calculation.</returns>
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public static Quaterniond Multiply(Quaterniond quaternion, double scale)
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{
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return new Quaterniond(quaternion.X * scale, quaternion.Y * scale, quaternion.Z * scale, quaternion.W * scale);
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}
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#endregion
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#region Conjugate
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/// <summary>
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/// Get the conjugate of the given Quaterniond
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/// </summary>
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/// <param name="q">The Quaterniond</param>
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/// <returns>The conjugate of the given Quaterniond</returns>
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public static Quaterniond Conjugate(Quaterniond q)
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{
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return new Quaterniond(-q.Xyz, q.W);
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}
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/// <summary>
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/// Get the conjugate of the given Quaterniond
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/// </summary>
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/// <param name="q">The Quaterniond</param>
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/// <param name="result">The conjugate of the given Quaterniond</param>
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public static void Conjugate(ref Quaterniond q, out Quaterniond result)
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{
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result = new Quaterniond(-q.Xyz, q.W);
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}
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#endregion
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#region Invert
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/// <summary>
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/// Get the inverse of the given Quaterniond
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/// </summary>
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/// <param name="q">The Quaterniond to invert</param>
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/// <returns>The inverse of the given Quaterniond</returns>
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public static Quaterniond Invert(Quaterniond q)
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{
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Quaterniond result;
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Invert(ref q, out result);
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return result;
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}
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/// <summary>
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/// Get the inverse of the given Quaterniond
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/// </summary>
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/// <param name="q">The Quaterniond to invert</param>
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/// <param name="result">The inverse of the given Quaterniond</param>
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public static void Invert(ref Quaterniond q, out Quaterniond result)
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{
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double lengthSq = q.LengthSquared;
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if (lengthSq != 0.0)
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{
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double i = 1.0f / lengthSq;
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result = new Quaterniond(q.Xyz * -i, q.W * i);
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}
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else
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{
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result = q;
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}
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}
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#endregion
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#region Normalize
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/// <summary>
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/// Scale the given Quaterniond to unit length
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/// </summary>
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/// <param name="q">The Quaterniond to normalize</param>
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/// <returns>The normalized Quaterniond</returns>
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public static Quaterniond Normalize(Quaterniond q)
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{
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Quaterniond result;
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Normalize(ref q, out result);
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return result;
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}
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/// <summary>
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/// Scale the given Quaterniond to unit length
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/// </summary>
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/// <param name="q">The Quaterniond to normalize</param>
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/// <param name="result">The normalized Quaterniond</param>
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public static void Normalize(ref Quaterniond q, out Quaterniond result)
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{
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double scale = 1.0f / q.Length;
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result = new Quaterniond(q.Xyz * scale, q.W * scale);
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}
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#endregion
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#region FromAxisAngle
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/// <summary>
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/// Build a Quaterniond from the given axis and angle
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/// </summary>
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/// <param name="axis">The axis to rotate about</param>
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/// <param name="angle">The rotation angle in radians</param>
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/// <returns></returns>
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public static Quaterniond FromAxisAngle(Vector3d axis, double angle)
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{
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if (axis.LengthSquared == 0.0f)
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return Identity;
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Quaterniond result = Identity;
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angle *= 0.5f;
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axis.Normalize();
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result.Xyz = axis * (double)System.Math.Sin(angle);
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result.W = (double)System.Math.Cos(angle);
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return Normalize(result);
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}
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#endregion
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#region Slerp
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/// <summary>
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/// Do Spherical linear interpolation between two quaternions
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/// </summary>
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/// <param name="q1">The first Quaterniond</param>
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/// <param name="q2">The second Quaterniond</param>
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/// <param name="blend">The blend factor</param>
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/// <returns>A smooth blend between the given quaternions</returns>
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public static Quaterniond Slerp(Quaterniond q1, Quaterniond q2, double blend)
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{
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// if either input is zero, return the other.
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if (q1.LengthSquared == 0.0f)
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{
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if (q2.LengthSquared == 0.0f)
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{
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return Identity;
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}
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return q2;
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}
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else if (q2.LengthSquared == 0.0f)
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{
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return q1;
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}
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double cosHalfAngle = q1.W * q2.W + Vector3d.Dot(q1.Xyz, q2.Xyz);
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if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f)
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{
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// angle = 0.0f, so just return one input.
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return q1;
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}
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else if (cosHalfAngle < 0.0f)
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{
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q2.Xyz = -q2.Xyz;
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q2.W = -q2.W;
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cosHalfAngle = -cosHalfAngle;
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}
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double blendA;
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double blendB;
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if (cosHalfAngle < 0.99f)
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{
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// do proper slerp for big angles
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double halfAngle = (double)System.Math.Acos(cosHalfAngle);
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double sinHalfAngle = (double)System.Math.Sin(halfAngle);
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double oneOverSinHalfAngle = 1.0f / sinHalfAngle;
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blendA = (double)System.Math.Sin(halfAngle * (1.0f - blend)) * oneOverSinHalfAngle;
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blendB = (double)System.Math.Sin(halfAngle * blend) * oneOverSinHalfAngle;
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}
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else
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{
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// do lerp if angle is really small.
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blendA = 1.0f - blend;
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blendB = blend;
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}
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Quaterniond result = new Quaterniond(blendA * q1.Xyz + blendB * q2.Xyz, blendA * q1.W + blendB * q2.W);
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if (result.LengthSquared > 0.0f)
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return Normalize(result);
|
|
else
|
|
return Identity;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region Operators
|
|
|
|
/// <summary>
|
|
/// Adds two instances.
|
|
/// </summary>
|
|
/// <param name="left">The first instance.</param>
|
|
/// <param name="right">The second instance.</param>
|
|
/// <returns>The result of the calculation.</returns>
|
|
public static Quaterniond operator +(Quaterniond left, Quaterniond right)
|
|
{
|
|
left.Xyz += right.Xyz;
|
|
left.W += right.W;
|
|
return left;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Subtracts two instances.
|
|
/// </summary>
|
|
/// <param name="left">The first instance.</param>
|
|
/// <param name="right">The second instance.</param>
|
|
/// <returns>The result of the calculation.</returns>
|
|
public static Quaterniond operator -(Quaterniond left, Quaterniond right)
|
|
{
|
|
left.Xyz -= right.Xyz;
|
|
left.W -= right.W;
|
|
return left;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Multiplies two instances.
|
|
/// </summary>
|
|
/// <param name="left">The first instance.</param>
|
|
/// <param name="right">The second instance.</param>
|
|
/// <returns>The result of the calculation.</returns>
|
|
public static Quaterniond operator *(Quaterniond left, Quaterniond right)
|
|
{
|
|
Multiply(ref left, ref right, out left);
|
|
return left;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Multiplies an instance by a scalar.
|
|
/// </summary>
|
|
/// <param name="quaternion">The instance.</param>
|
|
/// <param name="scale">The scalar.</param>
|
|
/// <returns>A new instance containing the result of the calculation.</returns>
|
|
public static Quaterniond operator *(Quaterniond quaternion, double scale)
|
|
{
|
|
Multiply(ref quaternion, scale, out quaternion);
|
|
return quaternion;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Multiplies an instance by a scalar.
|
|
/// </summary>
|
|
/// <param name="quaternion">The instance.</param>
|
|
/// <param name="scale">The scalar.</param>
|
|
/// <returns>A new instance containing the result of the calculation.</returns>
|
|
public static Quaterniond operator *(double scale, Quaterniond quaternion)
|
|
{
|
|
return new Quaterniond(quaternion.X * scale, quaternion.Y * scale, quaternion.Z * scale, quaternion.W * scale);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Compares two instances for equality.
|
|
/// </summary>
|
|
/// <param name="left">The first instance.</param>
|
|
/// <param name="right">The second instance.</param>
|
|
/// <returns>True, if left equals right; false otherwise.</returns>
|
|
public static bool operator ==(Quaterniond left, Quaterniond right)
|
|
{
|
|
return left.Equals(right);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Compares two instances for inequality.
|
|
/// </summary>
|
|
/// <param name="left">The first instance.</param>
|
|
/// <param name="right">The second instance.</param>
|
|
/// <returns>True, if left does not equal right; false otherwise.</returns>
|
|
public static bool operator !=(Quaterniond left, Quaterniond right)
|
|
{
|
|
return !left.Equals(right);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Overrides
|
|
|
|
#region public override string ToString()
|
|
|
|
/// <summary>
|
|
/// Returns a System.String that represents the current Quaterniond.
|
|
/// </summary>
|
|
/// <returns></returns>
|
|
public override string ToString()
|
|
{
|
|
return String.Format("V: {0}, W: {1}", Xyz, W);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public override bool Equals (object o)
|
|
|
|
/// <summary>
|
|
/// Compares this object instance to another object for equality.
|
|
/// </summary>
|
|
/// <param name="other">The other object to be used in the comparison.</param>
|
|
/// <returns>True if both objects are Quaternions of equal value. Otherwise it returns false.</returns>
|
|
public override bool Equals(object other)
|
|
{
|
|
if (other is Quaterniond == false) return false;
|
|
return this == (Quaterniond)other;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public override int GetHashCode ()
|
|
|
|
/// <summary>
|
|
/// Provides the hash code for this object.
|
|
/// </summary>
|
|
/// <returns>A hash code formed from the bitwise XOR of this objects members.</returns>
|
|
public override int GetHashCode()
|
|
{
|
|
return Xyz.GetHashCode() ^ W.GetHashCode();
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#if false
|
|
|
|
#region Fields
|
|
|
|
/// <summary>The W component of the Quaterniond.</summary>
|
|
public double W;
|
|
|
|
/// <summary>The X component of the Quaterniond.</summary>
|
|
public double X;
|
|
|
|
/// <summary>The Y component of the Quaterniond.</summary>
|
|
public double Y;
|
|
|
|
/// <summary>The Z component of the Quaterniond.</summary>
|
|
public double Z;
|
|
|
|
#endregion
|
|
|
|
#region Constructors
|
|
|
|
/// <summary>Constructs left Quaterniond that is left copy of the given Quaterniond.</summary>
|
|
/// <param name="quaterniond">The Quaterniond to copy.</param>
|
|
public Quaterniond(ref Quaterniond Quaterniond) : this(Quaterniond.W, Quaterniond.X, Quaterniond.Y, Quaterniond.Z) { }
|
|
|
|
/// <summary>Constructs left Quaterniond from the given components.</summary>
|
|
/// <param name="w">The W component for the Quaterniond.</param>
|
|
/// <param name="vector3d">A Vector representing the X, Y, and Z componets for the quaterion.</param>
|
|
public Quaterniond(double w, ref Vector3d vector3d) : this(w, vector3d.X, vector3d.Y, vector3d.Z) { }
|
|
|
|
/// <summary>Constructs left Quaterniond from the given axis and angle.</summary>
|
|
/// <param name="axis">The axis for the Quaterniond.</param>
|
|
/// <param name="angle">The angle for the quaternione.</param>
|
|
public Quaterniond(ref Vector3d axis, double angle)
|
|
{
|
|
double halfAngle = Functions.DTOR * angle / 2;
|
|
|
|
this.W = System.Math.Cos(halfAngle);
|
|
|
|
double sin = System.Math.Sin(halfAngle);
|
|
Vector3d axisNormalized;
|
|
Vector3d.Normalize(ref axis, out axisNormalized);
|
|
this.X = axisNormalized.X * sin;
|
|
this.Y = axisNormalized.Y * sin;
|
|
this.Z = axisNormalized.Z * sin;
|
|
}
|
|
|
|
/// <summary>Constructs left Quaterniond from the given components.</summary>
|
|
/// <param name="w">The W component for the Quaterniond.</param>
|
|
/// <param name="x">The X component for the Quaterniond.</param>
|
|
/// <param name="y">The Y component for the Quaterniond.</param>
|
|
/// <param name="z">The Z component for the Quaterniond.</param>
|
|
public Quaterniond(double w, double x, double y, double z)
|
|
{
|
|
this.W = w;
|
|
this.X = x;
|
|
this.Y = y;
|
|
this.Z = z;
|
|
}
|
|
|
|
/// <summary>Constructs left Quaterniond from the given array of double-precision floating-point numbers.</summary>
|
|
/// <param name="doubleArray">The array of doubles for the components of the Quaterniond.</param>
|
|
public Quaterniond(double[] doubleArray)
|
|
{
|
|
if (doubleArray == null || doubleArray.GetLength(0) < 4) throw new MissingFieldException();
|
|
|
|
this.W = doubleArray[0];
|
|
this.X = doubleArray[1];
|
|
this.Y = doubleArray[2];
|
|
this.Z = doubleArray[3];
|
|
}
|
|
|
|
/// <summary>Constructs left Quaterniond from the given matrix. Only contains rotation information.</summary>
|
|
/// <param name="matrix">The matrix for the components of the Quaterniond.</param>
|
|
public Quaterniond(ref Matrix4d matrix)
|
|
{
|
|
double scale = System.Math.Pow(matrix.Determinant, 1.0d/3.0d);
|
|
|
|
W = System.Math.Sqrt(System.Math.Max(0, scale + matrix[0, 0] + matrix[1, 1] + matrix[2, 2])) / 2;
|
|
X = System.Math.Sqrt(System.Math.Max(0, scale + matrix[0, 0] - matrix[1, 1] - matrix[2, 2])) / 2;
|
|
Y = System.Math.Sqrt(System.Math.Max(0, scale - matrix[0, 0] + matrix[1, 1] - matrix[2, 2])) / 2;
|
|
Z = System.Math.Sqrt(System.Math.Max(0, scale - matrix[0, 0] - matrix[1, 1] + matrix[2, 2])) / 2;
|
|
if( matrix[2,1] - matrix[1,2] < 0 ) X = -X;
|
|
if( matrix[0,2] - matrix[2,0] < 0 ) Y = -Y;
|
|
if( matrix[1,0] - matrix[0,1] < 0 ) Z = -Z;
|
|
}
|
|
|
|
public Quaterniond(ref Matrix3d matrix)
|
|
{
|
|
double scale = System.Math.Pow(matrix.Determinant, 1.0d / 3.0d);
|
|
|
|
W = System.Math.Sqrt(System.Math.Max(0, scale + matrix[0, 0] + matrix[1, 1] + matrix[2, 2])) / 2;
|
|
X = System.Math.Sqrt(System.Math.Max(0, scale + matrix[0, 0] - matrix[1, 1] - matrix[2, 2])) / 2;
|
|
Y = System.Math.Sqrt(System.Math.Max(0, scale - matrix[0, 0] + matrix[1, 1] - matrix[2, 2])) / 2;
|
|
Z = System.Math.Sqrt(System.Math.Max(0, scale - matrix[0, 0] - matrix[1, 1] + matrix[2, 2])) / 2;
|
|
if (matrix[2, 1] - matrix[1, 2] < 0) X = -X;
|
|
if (matrix[0, 2] - matrix[2, 0] < 0) Y = -Y;
|
|
if (matrix[1, 0] - matrix[0, 1] < 0) Z = -Z;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Arithmetic Operators
|
|
|
|
public void Add(ref Quaterniond Quaterniond)
|
|
{
|
|
W = W + Quaterniond.W;
|
|
X = X + Quaterniond.X;
|
|
Y = Y + Quaterniond.Y;
|
|
Z = Z + Quaterniond.Z;
|
|
}
|
|
public void Add(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
result.W = W + Quaterniond.W;
|
|
result.X = X + Quaterniond.X;
|
|
result.Y = Y + Quaterniond.Y;
|
|
result.Z = Z + Quaterniond.Z;
|
|
}
|
|
public static void Add(ref Quaterniond left, ref Quaterniond right, out Quaterniond result)
|
|
{
|
|
result.W = left.W + right.W;
|
|
result.X = left.X + right.X;
|
|
result.Y = left.Y + right.Y;
|
|
result.Z = left.Z + right.Z;
|
|
}
|
|
|
|
public void Subtract(ref Quaterniond Quaterniond)
|
|
{
|
|
W = W - Quaterniond.W;
|
|
X = X - Quaterniond.X;
|
|
Y = Y - Quaterniond.Y;
|
|
Z = Z - Quaterniond.Z;
|
|
}
|
|
public void Subtract(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
result.W = W - Quaterniond.W;
|
|
result.X = X - Quaterniond.X;
|
|
result.Y = Y - Quaterniond.Y;
|
|
result.Z = Z - Quaterniond.Z;
|
|
}
|
|
public static void Subtract(ref Quaterniond left, ref Quaterniond right, out Quaterniond result)
|
|
{
|
|
result.W = left.W - right.W;
|
|
result.X = left.X - right.X;
|
|
result.Y = left.Y - right.Y;
|
|
result.Z = left.Z - right.Z;
|
|
}
|
|
|
|
public void Multiply(ref Quaterniond Quaterniond)
|
|
{
|
|
double w = W * Quaterniond.W - X * Quaterniond.X - Y * Quaterniond.Y - Z * Quaterniond.Z;
|
|
double x = W * Quaterniond.X + X * Quaterniond.W + Y * Quaterniond.Z - Z * Quaterniond.Y;
|
|
double y = W * Quaterniond.Y + Y * Quaterniond.W + Z * Quaterniond.X - X * Quaterniond.Z;
|
|
Z = W * Quaterniond.Z + Z * Quaterniond.W + X * Quaterniond.Y - Y * Quaterniond.X;
|
|
W = w;
|
|
X = x;
|
|
Y = y;
|
|
}
|
|
public void Multiply(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
result.W = W * Quaterniond.W - X * Quaterniond.X - Y * Quaterniond.Y - Z * Quaterniond.Z;
|
|
result.X = W * Quaterniond.X + X * Quaterniond.W + Y * Quaterniond.Z - Z * Quaterniond.Y;
|
|
result.Y = W * Quaterniond.Y + Y * Quaterniond.W + Z * Quaterniond.X - X * Quaterniond.Z;
|
|
result.Z = W * Quaterniond.Z + Z * Quaterniond.W + X * Quaterniond.Y - Y * Quaterniond.X;
|
|
}
|
|
public static void Multiply(ref Quaterniond left, ref Quaterniond right, out Quaterniond result)
|
|
{
|
|
result.W = left.W * right.W - left.X * right.X - left.Y * right.Y - left.Z * right.Z;
|
|
result.X = left.W * right.X + left.X * right.W + left.Y * right.Z - left.Z * right.Y;
|
|
result.Y = left.W * right.Y + left.Y * right.W + left.Z * right.X - left.X * right.Z;
|
|
result.Z = left.W * right.Z + left.Z * right.W + left.X * right.Y - left.Y * right.X;
|
|
}
|
|
|
|
public void Multiply(double scalar)
|
|
{
|
|
W = W * scalar;
|
|
X = X * scalar;
|
|
Y = Y * scalar;
|
|
Z = Z * scalar;
|
|
}
|
|
public void Multiply(double scalar, out Quaterniond result)
|
|
{
|
|
result.W = W * scalar;
|
|
result.X = X * scalar;
|
|
result.Y = Y * scalar;
|
|
result.Z = Z * scalar;
|
|
}
|
|
public static void Multiply(ref Quaterniond Quaterniond, double scalar, out Quaterniond result)
|
|
{
|
|
result.W = Quaterniond.W * scalar;
|
|
result.X = Quaterniond.X * scalar;
|
|
result.Y = Quaterniond.Y * scalar;
|
|
result.Z = Quaterniond.Z * scalar;
|
|
}
|
|
|
|
public void Divide(double scalar)
|
|
{
|
|
if (scalar == 0) throw new DivideByZeroException();
|
|
W = W / scalar;
|
|
X = X / scalar;
|
|
Y = Y / scalar;
|
|
Z = Z / scalar;
|
|
}
|
|
public void Divide(double scalar, out Quaterniond result)
|
|
{
|
|
if (scalar == 0) throw new DivideByZeroException();
|
|
result.W = W / scalar;
|
|
result.X = X / scalar;
|
|
result.Y = Y / scalar;
|
|
result.Z = Z / scalar;
|
|
}
|
|
public static void Divide(ref Quaterniond Quaterniond, double scalar, out Quaterniond result)
|
|
{
|
|
if (scalar == 0) throw new DivideByZeroException();
|
|
result.W = Quaterniond.W / scalar;
|
|
result.X = Quaterniond.X / scalar;
|
|
result.Y = Quaterniond.Y / scalar;
|
|
result.Z = Quaterniond.Z / scalar;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Functions
|
|
|
|
public double Modulus
|
|
{
|
|
get
|
|
{
|
|
return System.Math.Sqrt(W * W + X * X + Y * Y + Z * Z);
|
|
}
|
|
}
|
|
public double ModulusSquared
|
|
{
|
|
get
|
|
{
|
|
return W * W + X * X + Y * Y + Z * Z;
|
|
}
|
|
}
|
|
|
|
public static double DotProduct(Quaterniond left, Quaterniond right)
|
|
{
|
|
return left.W * right.W + left.X * right.X + left.Y * right.Y + left.Z * right.Z;
|
|
}
|
|
|
|
public void Normalize()
|
|
{
|
|
double modulus = System.Math.Sqrt(W * W + X * X + Y * Y + Z * Z);
|
|
if (modulus == 0) throw new DivideByZeroException();
|
|
W = W / modulus;
|
|
X = X / modulus;
|
|
Y = Y / modulus;
|
|
Z = Z / modulus;
|
|
}
|
|
public void Normalize( out Quaterniond result )
|
|
{
|
|
double modulus = System.Math.Sqrt(W * W + X * X + Y * Y + Z * Z);
|
|
if (modulus == 0) throw new DivideByZeroException();
|
|
result.W = W / modulus;
|
|
result.X = X / modulus;
|
|
result.Y = Y / modulus;
|
|
result.Z = Z / modulus;
|
|
}
|
|
public static void Normalize(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
double modulus = System.Math.Sqrt(Quaterniond.W * Quaterniond.W + Quaterniond.X * Quaterniond.X + Quaterniond.Y * Quaterniond.Y + Quaterniond.Z * Quaterniond.Z);
|
|
if (modulus == 0) throw new DivideByZeroException();
|
|
result.W = Quaterniond.W / modulus;
|
|
result.X = Quaterniond.X / modulus;
|
|
result.Y = Quaterniond.Y / modulus;
|
|
result.Z = Quaterniond.Z / modulus;
|
|
}
|
|
|
|
public void Conjugate()
|
|
{
|
|
X = -X;
|
|
Y = -Y;
|
|
Z = -Z;
|
|
}
|
|
public void Conjugate( out Quaterniond result )
|
|
{
|
|
result.W = W;
|
|
result.X = -X;
|
|
result.Y = -Y;
|
|
result.Z = -Z;
|
|
}
|
|
public static void Conjugate(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
result.W = Quaterniond.W;
|
|
result.X = -Quaterniond.X;
|
|
result.Y = -Quaterniond.Y;
|
|
result.Z = -Quaterniond.Z;
|
|
}
|
|
|
|
public void Inverse()
|
|
{
|
|
double modulusSquared = W * W + X * X + Y * Y + Z * Z;
|
|
if (modulusSquared <= 0) throw new InvalidOperationException();
|
|
double inverseModulusSquared = 1.0 / modulusSquared;
|
|
W = W * inverseModulusSquared;
|
|
X = X * -inverseModulusSquared;
|
|
Y = Y * -inverseModulusSquared;
|
|
Z = Z * -inverseModulusSquared;
|
|
}
|
|
public void Inverse( out Quaterniond result )
|
|
{
|
|
double modulusSquared = W * W + X * X + Y * Y + Z * Z;
|
|
if (modulusSquared <= 0) throw new InvalidOperationException();
|
|
double inverseModulusSquared = 1.0 / modulusSquared;
|
|
result.W = W * inverseModulusSquared;
|
|
result.X = X * -inverseModulusSquared;
|
|
result.Y = Y * -inverseModulusSquared;
|
|
result.Z = Z * -inverseModulusSquared;
|
|
}
|
|
public static void Inverse(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
double modulusSquared = Quaterniond.W * Quaterniond.W + Quaterniond.X * Quaterniond.X + Quaterniond.Y * Quaterniond.Y + Quaterniond.Z * Quaterniond.Z;
|
|
if (modulusSquared <= 0) throw new InvalidOperationException();
|
|
double inverseModulusSquared = 1.0 / modulusSquared;
|
|
result.W = Quaterniond.W * inverseModulusSquared;
|
|
result.X = Quaterniond.X * -inverseModulusSquared;
|
|
result.Y = Quaterniond.Y * -inverseModulusSquared;
|
|
result.Z = Quaterniond.Z * -inverseModulusSquared;
|
|
}
|
|
|
|
public void Log()
|
|
{
|
|
if (System.Math.Abs(W) < 1.0)
|
|
{
|
|
double angle = System.Math.Acos(W);
|
|
double sin = System.Math.Sin(angle);
|
|
|
|
if (System.Math.Abs(sin) >= 0)
|
|
{
|
|
double coefficient = angle / sin;
|
|
X = X * coefficient;
|
|
Y = Y * coefficient;
|
|
Z = Z * coefficient;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
X = 0;
|
|
Y = 0;
|
|
Z = 0;
|
|
}
|
|
|
|
W = 0;
|
|
}
|
|
public void Log( out Quaterniond result )
|
|
{
|
|
if (System.Math.Abs(W) < 1.0)
|
|
{
|
|
double angle = System.Math.Acos(W);
|
|
double sin = System.Math.Sin(angle);
|
|
|
|
if (System.Math.Abs(sin) >= 0)
|
|
{
|
|
double coefficient = angle / sin;
|
|
result.X = X * coefficient;
|
|
result.Y = Y * coefficient;
|
|
result.Z = Z * coefficient;
|
|
}
|
|
else
|
|
{
|
|
result.X = X;
|
|
result.Y = Y;
|
|
result.Z = Z;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
result.X = 0;
|
|
result.Y = 0;
|
|
result.Z = 0;
|
|
}
|
|
|
|
result.W = 0;
|
|
}
|
|
public static void Log(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
if (System.Math.Abs(Quaterniond.W) < 1.0)
|
|
{
|
|
double angle = System.Math.Acos(Quaterniond.W);
|
|
double sin = System.Math.Sin(angle);
|
|
|
|
if (System.Math.Abs(sin) >= 0)
|
|
{
|
|
double coefficient = angle / sin;
|
|
result.X = Quaterniond.X * coefficient;
|
|
result.Y = Quaterniond.Y * coefficient;
|
|
result.Z = Quaterniond.Z * coefficient;
|
|
}
|
|
else
|
|
{
|
|
result.X = Quaterniond.X;
|
|
result.Y = Quaterniond.Y;
|
|
result.Z = Quaterniond.Z;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
result.X = 0;
|
|
result.Y = 0;
|
|
result.Z = 0;
|
|
}
|
|
|
|
result.W = 0;
|
|
}
|
|
|
|
public void Exp()
|
|
{
|
|
double angle = System.Math.Sqrt(X * X + Y * Y + Z * Z);
|
|
double sin = System.Math.Sin(angle);
|
|
|
|
if (System.Math.Abs(sin) > 0)
|
|
{
|
|
double coefficient = angle / sin;
|
|
W = 0;
|
|
X = X * coefficient;
|
|
Y = Y * coefficient;
|
|
Z = Z * coefficient;
|
|
}
|
|
else
|
|
{
|
|
W = 0;
|
|
}
|
|
}
|
|
public void Exp(out Quaterniond result)
|
|
{
|
|
double angle = System.Math.Sqrt(X * X + Y * Y + Z * Z);
|
|
double sin = System.Math.Sin(angle);
|
|
|
|
if (System.Math.Abs(sin) > 0)
|
|
{
|
|
double coefficient = angle / sin;
|
|
result.W = 0;
|
|
result.X = X * coefficient;
|
|
result.Y = Y * coefficient;
|
|
result.Z = Z * coefficient;
|
|
}
|
|
else
|
|
{
|
|
result.W = 0;
|
|
result.X = X;
|
|
result.Y = Y;
|
|
result.Z = Z;
|
|
}
|
|
}
|
|
public static void Exp(ref Quaterniond Quaterniond, out Quaterniond result)
|
|
{
|
|
double angle = System.Math.Sqrt(Quaterniond.X * Quaterniond.X + Quaterniond.Y * Quaterniond.Y + Quaterniond.Z * Quaterniond.Z);
|
|
double sin = System.Math.Sin(angle);
|
|
|
|
if (System.Math.Abs(sin) > 0)
|
|
{
|
|
double coefficient = angle / sin;
|
|
result.W = 0;
|
|
result.X = Quaterniond.X * coefficient;
|
|
result.Y = Quaterniond.Y * coefficient;
|
|
result.Z = Quaterniond.Z * coefficient;
|
|
}
|
|
else
|
|
{
|
|
result.W = 0;
|
|
result.X = Quaterniond.X;
|
|
result.Y = Quaterniond.Y;
|
|
result.Z = Quaterniond.Z;
|
|
}
|
|
}
|
|
|
|
/// <summary>Returns left matrix for this Quaterniond.</summary>
|
|
public void Matrix4d(out Matrix4d result)
|
|
{
|
|
// TODO Expand
|
|
result = new Matrix4d(ref this);
|
|
}
|
|
|
|
public void GetAxisAndAngle(out Vector3d axis, out double angle)
|
|
{
|
|
Quaterniond Quaterniond;
|
|
Normalize(out Quaterniond);
|
|
double cos = Quaterniond.W;
|
|
angle = System.Math.Acos(cos) * 2 * Functions.RTOD;
|
|
double sin = System.Math.Sqrt( 1.0d - cos * cos );
|
|
if ( System.Math.Abs( sin ) < 0.0001 ) sin = 1;
|
|
axis = new Vector3d(X / sin, Y / sin, Z / sin);
|
|
}
|
|
|
|
public static void Slerp(ref Quaterniond start, ref Quaterniond end, double blend, out Quaterniond result)
|
|
{
|
|
if (start.W == 0 && start.X == 0 && start.Y == 0 && start.Z == 0)
|
|
{
|
|
if (end.W == 0 && end.X == 0 && end.Y == 0 && end.Z == 0)
|
|
{
|
|
result.W = 1;
|
|
result.X = 0;
|
|
result.Y = 0;
|
|
result.Z = 0;
|
|
}
|
|
else
|
|
{
|
|
result = end;
|
|
}
|
|
}
|
|
else if (end.W == 0 && end.X == 0 && end.Y == 0 && end.Z == 0)
|
|
{
|
|
result = start;
|
|
}
|
|
|
|
Vector3d startVector = new Vector3d(start.X, start.Y, start.Z);
|
|
Vector3d endVector = new Vector3d(end.X, end.Y, end.Z);
|
|
double cosHalfAngle = start.W * end.W + Vector3d.Dot(startVector, endVector);
|
|
|
|
if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f)
|
|
{
|
|
// angle = 0.0f, so just return one input.
|
|
result = start;
|
|
}
|
|
else if (cosHalfAngle < 0.0f)
|
|
{
|
|
end.W = -end.W;
|
|
end.X = -end.X;
|
|
end.Y = -end.Y;
|
|
end.Z = -end.Z;
|
|
cosHalfAngle = -cosHalfAngle;
|
|
}
|
|
|
|
double blendA;
|
|
double blendB;
|
|
if (cosHalfAngle < 0.99f)
|
|
{
|
|
// do proper slerp for big angles
|
|
double halfAngle = (double)System.Math.Acos(cosHalfAngle);
|
|
double sinHalfAngle = (double)System.Math.Sin(halfAngle);
|
|
double oneOverSinHalfAngle = 1.0f / sinHalfAngle;
|
|
blendA = (double)System.Math.Sin(halfAngle * (1.0f - blend)) * oneOverSinHalfAngle;
|
|
blendB = (double)System.Math.Sin(halfAngle * blend) * oneOverSinHalfAngle;
|
|
}
|
|
else
|
|
{
|
|
// do lerp if angle is really small.
|
|
blendA = 1.0f - blend;
|
|
blendB = blend;
|
|
}
|
|
|
|
result.W = blendA * start.W + blendB * end.W;
|
|
result.X = blendA * start.X + blendB * end.X;
|
|
result.Y = blendA * start.Y + blendB * end.Y;
|
|
result.Z = blendA * start.Z + blendB * end.Z;
|
|
|
|
if (result.W != 0 || result.X != 0 || result.Y != 0 || result.Z != 0)
|
|
{
|
|
result.Normalize();
|
|
}
|
|
else
|
|
{
|
|
result.W = 1;
|
|
result.X = 0;
|
|
result.Y = 0;
|
|
result.Z = 0;
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region HashCode
|
|
|
|
/// <summary>Returns the hash code for this instance.</summary>
|
|
/// <returns>A 32-bit signed integer that is the hash code for this instance.</returns>
|
|
public override int GetHashCode()
|
|
{
|
|
base.GetHashCode();
|
|
return W.GetHashCode() ^ X.GetHashCode() ^ Y.GetHashCode() ^ Z.GetHashCode();
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region String and Parse
|
|
|
|
/// <summary>Returns the fully qualified type name of this instance.</summary>
|
|
/// <returns>A System.String containing left fully qualified type name.</returns>
|
|
public override string ToString()
|
|
{
|
|
return string.Format("({0}, {1}, {2}, {3})", W, X, Y, Z);
|
|
}
|
|
|
|
/// <summary>Parses left string, converting it to left Quaterniond.</summary>
|
|
/// <param name="str">The string to parse.</param>
|
|
/// <returns>The Quaterniond represented by the string.</returns>
|
|
public static void Parse(string str, out Quaterniond result)
|
|
{
|
|
Match match = new Regex(@"\((?<w>.*),(?<x>.*),(?<y>.*),(?<z>.*)\)", RegexOptions.None).Match(str);
|
|
if (!match.Success) throw new Exception("Parse failed!");
|
|
|
|
result.W = double.Parse(match.Result("${w}"));
|
|
result.X = double.Parse(match.Result("${x}"));
|
|
result.Y = double.Parse(match.Result("${y}"));
|
|
result.Z = double.Parse(match.Result("${z}"));
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Constants
|
|
|
|
/// <summary>A quaterion with all zero components.</summary>
|
|
public static readonly Quaterniond Zero = new Quaterniond(0, 0, 0, 0);
|
|
|
|
/// <summary>A quaterion representing an identity.</summary>
|
|
public static readonly Quaterniond Identity = new Quaterniond(1, 0, 0, 0);
|
|
|
|
/// <summary>A quaterion representing the W axis.</summary>
|
|
public static readonly Quaterniond WAxis = new Quaterniond(1, 0, 0, 0);
|
|
|
|
/// <summary>A quaterion representing the X axis.</summary>
|
|
public static readonly Quaterniond XAxis = new Quaterniond(0, 1, 0, 0);
|
|
|
|
/// <summary>A quaterion representing the Y axis.</summary>
|
|
public static readonly Quaterniond YAxis = new Quaterniond(0, 0, 1, 0);
|
|
|
|
/// <summary>A quaterion representing the Z axis.</summary>
|
|
public static readonly Quaterniond ZAxis = new Quaterniond(0, 0, 0, 1);
|
|
|
|
#endregion
|
|
|
|
#endif
|
|
|
|
#region IEquatable<Quaterniond> Members
|
|
|
|
/// <summary>
|
|
/// Compares this Quaterniond instance to another Quaterniond for equality.
|
|
/// </summary>
|
|
/// <param name="other">The other Quaterniond to be used in the comparison.</param>
|
|
/// <returns>True if both instances are equal; false otherwise.</returns>
|
|
public bool Equals(Quaterniond other)
|
|
{
|
|
return Xyz == other.Xyz && W == other.W;
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
} |