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800 lines
26 KiB
C#
800 lines
26 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 Quaternion.
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/// </summary>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Quaternion : IEquatable<Quaternion>
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{
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#region Fields
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Vector3 xyz;
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float w;
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#endregion
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#region Constructors
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/// <summary>
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/// Construct a new Quaternion 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 Quaternion(Vector3 v, float 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 Quaternion
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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 Quaternion(float x, float y, float z, float w)
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: this(new Vector3(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.Vector3 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 Vector3 XYZ { get { return Xyz; } set { Xyz = value; } }
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/// <summary>
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/// Gets or sets an OpenTK.Vector3 with the X, Y and Z components of this instance.
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/// </summary>
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public Vector3 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 float 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 float 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 float 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 float 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 Vector3 axis, out float angle)
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{
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Vector4 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 Vector4 ToAxisAngle()
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{
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Quaternion q = this;
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if (Math.Abs(q.W) > 1.0f)
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q.Normalize();
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Vector4 result = new Vector4();
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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 = Vector3.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 float Length
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/// <summary>
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/// Gets the length (magnitude) of the quaternion.
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/// </summary>
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/// <seealso cref="LengthSquared"/>
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public float Length
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{
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get
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{
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return (float)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 float LengthSquared
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/// <summary>
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/// Gets the square of the quaternion length (magnitude).
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/// </summary>
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public float 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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/// <summary>
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/// Returns a copy of the Quaternion scaled to unit length.
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/// </summary>
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public Quaternion Normalized()
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{
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Quaternion q = this;
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q.Normalize();
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return q;
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}
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/// <summary>
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/// Reverses the rotation angle of this Quaterniond.
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/// </summary>
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public void Invert()
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{
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W = -W;
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}
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/// <summary>
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/// Returns a copy of this Quaterniond with its rotation angle reversed.
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/// </summary>
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public Quaternion Inverted()
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{
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var q = this;
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q.Invert();
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return q;
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}
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#region public void Normalize()
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/// <summary>
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/// Scales the Quaternion to unit length.
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/// </summary>
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public void Normalize()
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{
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float 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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/// Inverts the Vector3 component of this Quaternion.
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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 static readonly Quaternion Identity = new Quaternion(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 Quaternion Add(Quaternion left, Quaternion right)
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{
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return new Quaternion(
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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 Quaternion left, ref Quaternion right, out Quaternion result)
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{
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result = new Quaternion(
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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 Quaternion Sub(Quaternion left, Quaternion right)
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{
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return new Quaternion(
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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 Quaternion left, ref Quaternion right, out Quaternion result)
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{
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result = new Quaternion(
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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 Quaternion Mult(Quaternion left, Quaternion right)
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{
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return new Quaternion(
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right.W * left.Xyz + left.W * right.Xyz + Vector3.Cross(left.Xyz, right.Xyz),
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left.W * right.W - Vector3.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 Quaternion left, ref Quaternion right, out Quaternion result)
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{
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result = new Quaternion(
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right.W * left.Xyz + left.W * right.Xyz + Vector3.Cross(left.Xyz, right.Xyz),
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left.W * right.W - Vector3.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 Quaternion Multiply(Quaternion left, Quaternion right)
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{
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Quaternion 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 Quaternion left, ref Quaternion right, out Quaternion result)
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{
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result = new Quaternion(
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right.W * left.Xyz + left.W * right.Xyz + Vector3.Cross(left.Xyz, right.Xyz),
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left.W * right.W - Vector3.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 Quaternion quaternion, float scale, out Quaternion result)
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{
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result = new Quaternion(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 Quaternion Multiply(Quaternion quaternion, float scale)
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{
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return new Quaternion(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 quaternion
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/// </summary>
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/// <param name="q">The quaternion</param>
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/// <returns>The conjugate of the given quaternion</returns>
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public static Quaternion Conjugate(Quaternion q)
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{
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return new Quaternion(-q.Xyz, q.W);
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}
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/// <summary>
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/// Get the conjugate of the given quaternion
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/// </summary>
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/// <param name="q">The quaternion</param>
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/// <param name="result">The conjugate of the given quaternion</param>
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public static void Conjugate(ref Quaternion q, out Quaternion result)
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{
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result = new Quaternion(-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 quaternion
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/// </summary>
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/// <param name="q">The quaternion to invert</param>
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/// <returns>The inverse of the given quaternion</returns>
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public static Quaternion Invert(Quaternion q)
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{
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Quaternion 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 quaternion
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/// </summary>
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/// <param name="q">The quaternion to invert</param>
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/// <param name="result">The inverse of the given quaternion</param>
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public static void Invert(ref Quaternion q, out Quaternion result)
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{
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float lengthSq = q.LengthSquared;
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if (lengthSq != 0.0)
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{
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float i = 1.0f / lengthSq;
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result = new Quaternion(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 quaternion to unit length
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/// </summary>
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/// <param name="q">The quaternion to normalize</param>
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/// <returns>The normalized quaternion</returns>
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public static Quaternion Normalize(Quaternion q)
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{
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Quaternion 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 quaternion to unit length
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/// </summary>
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/// <param name="q">The quaternion to normalize</param>
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/// <param name="result">The normalized quaternion</param>
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public static void Normalize(ref Quaternion q, out Quaternion result)
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{
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float scale = 1.0f / q.Length;
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result = new Quaternion(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 quaternion 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>The equivalent quaternion</returns>
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public static Quaternion FromAxisAngle(Vector3 axis, float angle)
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{
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if (axis.LengthSquared == 0.0f)
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return Identity;
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Quaternion result = Identity;
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angle *= 0.5f;
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axis.Normalize();
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result.Xyz = axis * (float)System.Math.Sin(angle);
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result.W = (float)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 FromMatrix
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/// <summary>
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/// Builds a quaternion from the given rotation matrix
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/// </summary>
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/// <param name="matrix">A rotation matrix</param>
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/// <returns>The equivalent quaternion</returns>
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public static Quaternion FromMatrix(Matrix3 matrix)
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{
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Quaternion result;
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FromMatrix(ref matrix, out result);
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return result;
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}
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/// <summary>
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/// Builds a quaternion from the given rotation matrix
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/// </summary>
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/// <param name="matrix">A rotation matrix</param>
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/// <param name="result">The equivalent quaternion</param>
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public static void FromMatrix(ref Matrix3 matrix, out Quaternion result)
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{
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float trace = matrix.Trace;
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if (trace > 0)
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{
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float s = (float)Math.Sqrt(trace + 1) * 2;
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float invS = 1f / s;
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result.w = s * 0.25f;
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result.xyz.X = (matrix.Row2.Y - matrix.Row1.Z) * invS;
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result.xyz.Y = (matrix.Row0.Z - matrix.Row2.X) * invS;
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result.xyz.Z = (matrix.Row1.X - matrix.Row0.Y) * invS;
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}
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else
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{
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float m00 = matrix.Row0.X, m11 = matrix.Row1.Y, m22 = matrix.Row2.Z;
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if (m00 > m11 && m00 > m22)
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{
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float s = (float)Math.Sqrt(1 + m00 - m11 - m22) * 2;
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float invS = 1f / s;
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result.w = (matrix.Row2.Y - matrix.Row1.Z) * invS;
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result.xyz.X = s * 0.25f;
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result.xyz.Y = (matrix.Row0.Y + matrix.Row1.X) * invS;
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result.xyz.Z = (matrix.Row0.Z + matrix.Row2.X) * invS;
|
|
}
|
|
else if (m11 > m22)
|
|
{
|
|
float s = (float)Math.Sqrt(1 + m11 - m00 - m22) * 2;
|
|
float invS = 1f / s;
|
|
|
|
result.w = (matrix.Row0.Z - matrix.Row2.X) * invS;
|
|
result.xyz.X = (matrix.Row0.Y + matrix.Row1.X) * invS;
|
|
result.xyz.Y = s * 0.25f;
|
|
result.xyz.Z = (matrix.Row1.Z + matrix.Row2.Y) * invS;
|
|
}
|
|
else
|
|
{
|
|
float s = (float)Math.Sqrt(1 + m22 - m00 - m11) * 2;
|
|
float invS = 1f / s;
|
|
|
|
result.w = (matrix.Row1.X - matrix.Row0.Y) * invS;
|
|
result.xyz.X = (matrix.Row0.Z + matrix.Row2.X) * invS;
|
|
result.xyz.Y = (matrix.Row1.Z + matrix.Row2.Y) * invS;
|
|
result.xyz.Z = s * 0.25f;
|
|
}
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Slerp
|
|
|
|
/// <summary>
|
|
/// Do Spherical linear interpolation between two quaternions
|
|
/// </summary>
|
|
/// <param name="q1">The first quaternion</param>
|
|
/// <param name="q2">The second quaternion</param>
|
|
/// <param name="blend">The blend factor</param>
|
|
/// <returns>A smooth blend between the given quaternions</returns>
|
|
public static Quaternion Slerp(Quaternion q1, Quaternion q2, float blend)
|
|
{
|
|
// if either input is zero, return the other.
|
|
if (q1.LengthSquared == 0.0f)
|
|
{
|
|
if (q2.LengthSquared == 0.0f)
|
|
{
|
|
return Identity;
|
|
}
|
|
return q2;
|
|
}
|
|
else if (q2.LengthSquared == 0.0f)
|
|
{
|
|
return q1;
|
|
}
|
|
|
|
|
|
float cosHalfAngle = q1.W * q2.W + Vector3.Dot(q1.Xyz, q2.Xyz);
|
|
|
|
if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f)
|
|
{
|
|
// angle = 0.0f, so just return one input.
|
|
return q1;
|
|
}
|
|
else if (cosHalfAngle < 0.0f)
|
|
{
|
|
q2.Xyz = -q2.Xyz;
|
|
q2.W = -q2.W;
|
|
cosHalfAngle = -cosHalfAngle;
|
|
}
|
|
|
|
float blendA;
|
|
float blendB;
|
|
if (cosHalfAngle < 0.99f)
|
|
{
|
|
// do proper slerp for big angles
|
|
float halfAngle = (float)System.Math.Acos(cosHalfAngle);
|
|
float sinHalfAngle = (float)System.Math.Sin(halfAngle);
|
|
float oneOverSinHalfAngle = 1.0f / sinHalfAngle;
|
|
blendA = (float)System.Math.Sin(halfAngle * (1.0f - blend)) * oneOverSinHalfAngle;
|
|
blendB = (float)System.Math.Sin(halfAngle * blend) * oneOverSinHalfAngle;
|
|
}
|
|
else
|
|
{
|
|
// do lerp if angle is really small.
|
|
blendA = 1.0f - blend;
|
|
blendB = blend;
|
|
}
|
|
|
|
Quaternion result = new Quaternion(blendA * q1.Xyz + blendB * q2.Xyz, blendA * q1.W + blendB * q2.W);
|
|
if (result.LengthSquared > 0.0f)
|
|
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 Quaternion operator +(Quaternion left, Quaternion 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 Quaternion operator -(Quaternion left, Quaternion 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 Quaternion operator *(Quaternion left, Quaternion 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 Quaternion operator *(Quaternion quaternion, float 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 Quaternion operator *(float scale, Quaternion quaternion)
|
|
{
|
|
return new Quaternion(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 ==(Quaternion left, Quaternion 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 !=(Quaternion left, Quaternion right)
|
|
{
|
|
return !left.Equals(right);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Overrides
|
|
|
|
#region public override string ToString()
|
|
|
|
/// <summary>
|
|
/// Returns a System.String that represents the current Quaternion.
|
|
/// </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 Quaternion == false) return false;
|
|
return this == (Quaternion)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
|
|
|
|
#region IEquatable<Quaternion> Members
|
|
|
|
/// <summary>
|
|
/// Compares this Quaternion instance to another Quaternion for equality.
|
|
/// </summary>
|
|
/// <param name="other">The other Quaternion to be used in the comparison.</param>
|
|
/// <returns>True if both instances are equal; false otherwise.</returns>
|
|
public bool Equals(Quaternion other)
|
|
{
|
|
return Xyz == other.Xyz && W == other.W;
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
}
|