1515 lines
52 KiB
C#
1515 lines
52 KiB
C#
#region License
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/* MoonWorks - Game Development Framework
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* Copyright 2021 Evan Hemsley
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*/
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/* Derived from code by Ethan Lee (Copyright 2009-2021).
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* Released under the Microsoft Public License.
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* See fna.LICENSE for details.
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* Derived from code by the Mono.Xna Team (Copyright 2006).
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* Released under the MIT License. See monoxna.LICENSE for details.
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*/
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#endregion
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#region Using Statements
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using System;
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using System.Diagnostics;
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using System.Runtime.InteropServices;
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using System.Text;
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#endregion
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namespace MoonWorks.Math
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{
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/// <summary>
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/// Describes a 3D-vector.
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/// </summary>
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[Serializable]
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[DebuggerDisplay("{DebugDisplayString,nq}")]
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[StructLayout(LayoutKind.Explicit)]
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public struct Vector3 : IEquatable<Vector3>
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{
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#region Public Static Properties
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 0, 0, 0.
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/// </summary>
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public static Vector3 Zero
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{
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get
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{
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return zero;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 1, 1, 1.
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/// </summary>
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public static Vector3 One
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{
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get
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{
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return one;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 1, 0, 0.
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/// </summary>
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public static Vector3 UnitX
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{
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get
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{
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return unitX;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 0, 1, 0.
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/// </summary>
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public static Vector3 UnitY
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{
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get
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{
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return unitY;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 0, 0, 1.
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/// </summary>
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public static Vector3 UnitZ
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{
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get
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{
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return unitZ;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 0, 1, 0.
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/// </summary>
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public static Vector3 Up
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{
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get
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{
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return up;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 0, -1, 0.
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/// </summary>
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public static Vector3 Down
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{
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get
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{
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return down;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 1, 0, 0.
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/// </summary>
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public static Vector3 Right
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{
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get
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{
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return right;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components -1, 0, 0.
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/// </summary>
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public static Vector3 Left
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{
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get
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{
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return left;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 0, 0, -1.
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/// </summary>
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public static Vector3 Forward
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{
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get
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{
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return forward;
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}
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}
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/// <summary>
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/// Returns a <see cref="Vector3"/> with components 0, 0, 1.
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/// </summary>
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public static Vector3 Backward
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{
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get
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{
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return backward;
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}
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}
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#endregion
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#region Internal Properties
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internal string DebugDisplayString
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{
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get
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{
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return string.Concat(
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X.ToString(), " ",
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Y.ToString(), " ",
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Z.ToString()
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);
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}
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}
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#endregion
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#region Private Static Fields
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private static Vector3 zero = new Vector3(0f, 0f, 0f); // Not readonly for performance -flibit
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private static readonly Vector3 one = new Vector3(1f, 1f, 1f);
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private static readonly Vector3 unitX = new Vector3(1f, 0f, 0f);
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private static readonly Vector3 unitY = new Vector3(0f, 1f, 0f);
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private static readonly Vector3 unitZ = new Vector3(0f, 0f, 1f);
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private static readonly Vector3 up = new Vector3(0f, 1f, 0f);
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private static readonly Vector3 down = new Vector3(0f, -1f, 0f);
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private static readonly Vector3 right = new Vector3(1f, 0f, 0f);
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private static readonly Vector3 left = new Vector3(-1f, 0f, 0f);
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private static readonly Vector3 forward = new Vector3(0f, 0f, -1f);
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private static readonly Vector3 backward = new Vector3(0f, 0f, 1f);
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#endregion
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#region Public Fields
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/// <summary>
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/// The x coordinate of this <see cref="Vector3"/>.
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/// </summary>
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[FieldOffset(0)]
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public float X;
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/// <summary>
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/// The y coordinate of this <see cref="Vector3"/>.
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/// </summary>
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[FieldOffset(4)]
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public float Y;
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/// <summary>
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/// The z coordinate of this <see cref="Vector3"/>.
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/// </summary>
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[FieldOffset(8)]
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public float Z;
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#endregion
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#region Public Constructors
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/// <summary>
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/// Constructs a 3d vector with X, Y and Z from three values.
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/// </summary>
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/// <param name="x">The x coordinate in 3d-space.</param>
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/// <param name="y">The y coordinate in 3d-space.</param>
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/// <param name="z">The z coordinate in 3d-space.</param>
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public Vector3(float x, float y, float z)
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{
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this.X = x;
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this.Y = y;
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this.Z = z;
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}
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/// <summary>
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/// Constructs a 3d vector with X, Y and Z set to the same value.
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/// </summary>
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/// <param name="value">The x, y and z coordinates in 3d-space.</param>
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public Vector3(float value)
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{
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this.X = value;
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this.Y = value;
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this.Z = value;
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}
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/// <summary>
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/// Constructs a 3d vector with X, Y from <see cref="Vector2"/> and Z from a scalar.
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/// </summary>
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/// <param name="value">The x and y coordinates in 3d-space.</param>
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/// <param name="z">The z coordinate in 3d-space.</param>
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public Vector3(Vector2 value, float z)
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{
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this.X = value.X;
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this.Y = value.Y;
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this.Z = z;
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}
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#endregion
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#region Public Methods
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/// <summary>
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/// Compares whether current instance is equal to specified <see cref="Object"/>.
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/// </summary>
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/// <param name="obj">The <see cref="Object"/> to compare.</param>
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/// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
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public override bool Equals(object obj)
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{
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return (obj is Vector3) && Equals((Vector3) obj);
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}
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/// <summary>
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/// Compares whether current instance is equal to specified <see cref="Vector3"/>.
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/// </summary>
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/// <param name="other">The <see cref="Vector3"/> to compare.</param>
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/// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
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public bool Equals(Vector3 other)
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{
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return ( X == other.X &&
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Y == other.Y &&
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Z == other.Z );
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}
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/// <summary>
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/// Gets the hash code of this <see cref="Vector3"/>.
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/// </summary>
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/// <returns>Hash code of this <see cref="Vector3"/>.</returns>
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public override int GetHashCode()
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{
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return X.GetHashCode() + Y.GetHashCode() + Z.GetHashCode();
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}
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/// <summary>
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/// Returns the length of this <see cref="Vector3"/>.
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/// </summary>
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/// <returns>The length of this <see cref="Vector3"/>.</returns>
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public float Length()
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{
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return (float) System.Math.Sqrt((X * X) + (Y * Y) + (Z * Z));
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}
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/// <summary>
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/// Returns the squared length of this <see cref="Vector3"/>.
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/// </summary>
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/// <returns>The squared length of this <see cref="Vector3"/>.</returns>
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public float LengthSquared()
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{
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return (X * X) + (Y * Y) + (Z * Z);
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}
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/// <summary>
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/// Turns this <see cref="Vector3"/> to a unit vector with the same direction.
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/// </summary>
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public void Normalize()
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{
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float factor = 1.0f / (float) System.Math.Sqrt(
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(X * X) +
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(Y * Y) +
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(Z * Z)
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);
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X *= factor;
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Y *= factor;
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Z *= factor;
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}
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/// <summary>
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/// Returns a <see cref="String"/> representation of this <see cref="Vector3"/> in the format:
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/// {X:[<see cref="X"/>] Y:[<see cref="Y"/>] Z:[<see cref="Z"/>]}
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/// </summary>
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/// <returns>A <see cref="String"/> representation of this <see cref="Vector3"/>.</returns>
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public override string ToString()
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{
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StringBuilder sb = new StringBuilder(32);
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sb.Append("{X:");
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sb.Append(this.X);
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sb.Append(" Y:");
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sb.Append(this.Y);
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sb.Append(" Z:");
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sb.Append(this.Z);
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sb.Append("}");
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return sb.ToString();
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}
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#endregion
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#region Public Static Methods
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/// <summary>
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/// Performs vector addition on <paramref name="value1"/> and <paramref name="value2"/>.
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/// </summary>
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/// <param name="value1">The first vector to add.</param>
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/// <param name="value2">The second vector to add.</param>
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/// <returns>The result of the vector addition.</returns>
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public static Vector3 Add(Vector3 value1, Vector3 value2)
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{
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value1.X += value2.X;
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value1.Y += value2.Y;
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value1.Z += value2.Z;
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return value1;
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}
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/// <summary>
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/// Performs vector addition on <paramref name="value1"/> and
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/// <paramref name="value2"/>, storing the result of the
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/// addition in <paramref name="result"/>.
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/// </summary>
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/// <param name="value1">The first vector to add.</param>
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/// <param name="value2">The second vector to add.</param>
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/// <param name="result">The result of the vector addition.</param>
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public static void Add(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
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{
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result.X = value1.X + value2.X;
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result.Y = value1.Y + value2.Y;
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result.Z = value1.Z + value2.Z;
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}
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/// <summary>
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/// Creates a new <see cref="Vector3"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 3d-triangle.
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/// </summary>
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/// <param name="value1">The first vector of 3d-triangle.</param>
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/// <param name="value2">The second vector of 3d-triangle.</param>
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/// <param name="value3">The third vector of 3d-triangle.</param>
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/// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 3d-triangle.</param>
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/// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 3d-triangle.</param>
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/// <returns>The cartesian translation of barycentric coordinates.</returns>
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public static Vector3 Barycentric(
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Vector3 value1,
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Vector3 value2,
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Vector3 value3,
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float amount1,
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float amount2
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) {
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return new Vector3(
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MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
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MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2),
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MathHelper.Barycentric(value1.Z, value2.Z, value3.Z, amount1, amount2)
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);
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}
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/// <summary>
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/// Creates a new <see cref="Vector3"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 3d-triangle.
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/// </summary>
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/// <param name="value1">The first vector of 3d-triangle.</param>
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/// <param name="value2">The second vector of 3d-triangle.</param>
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/// <param name="value3">The third vector of 3d-triangle.</param>
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/// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 3d-triangle.</param>
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/// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 3d-triangle.</param>
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/// <param name="result">The cartesian translation of barycentric coordinates as an output parameter.</param>
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public static void Barycentric(
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ref Vector3 value1,
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ref Vector3 value2,
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ref Vector3 value3,
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float amount1,
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float amount2,
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out Vector3 result
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) {
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result.X = MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2);
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result.Y = MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2);
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result.Z = MathHelper.Barycentric(value1.Z, value2.Z, value3.Z, amount1, amount2);
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}
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/// <summary>
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/// Creates a new <see cref="Vector3"/> that contains CatmullRom interpolation of the specified vectors.
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/// </summary>
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/// <param name="value1">The first vector in interpolation.</param>
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/// <param name="value2">The second vector in interpolation.</param>
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/// <param name="value3">The third vector in interpolation.</param>
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/// <param name="value4">The fourth vector in interpolation.</param>
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/// <param name="amount">Weighting factor.</param>
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/// <returns>The result of CatmullRom interpolation.</returns>
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public static Vector3 CatmullRom(
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Vector3 value1,
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Vector3 value2,
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Vector3 value3,
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Vector3 value4,
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float amount
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) {
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return new Vector3(
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MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
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MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount),
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MathHelper.CatmullRom(value1.Z, value2.Z, value3.Z, value4.Z, amount)
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);
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}
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/// <summary>
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/// Creates a new <see cref="Vector3"/> that contains CatmullRom interpolation of the specified vectors.
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/// </summary>
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/// <param name="value1">The first vector in interpolation.</param>
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/// <param name="value2">The second vector in interpolation.</param>
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/// <param name="value3">The third vector in interpolation.</param>
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/// <param name="value4">The fourth vector in interpolation.</param>
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/// <param name="amount">Weighting factor.</param>
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/// <param name="result">The result of CatmullRom interpolation as an output parameter.</param>
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public static void CatmullRom(
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ref Vector3 value1,
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ref Vector3 value2,
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ref Vector3 value3,
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ref Vector3 value4,
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float amount,
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out Vector3 result
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) {
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result.X = MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount);
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result.Y = MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount);
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result.Z = MathHelper.CatmullRom(value1.Z, value2.Z, value3.Z, value4.Z, amount);
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}
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/// <summary>
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/// Clamps the specified value within a range.
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/// </summary>
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/// <param name="value1">The value to clamp.</param>
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/// <param name="min">The min value.</param>
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/// <param name="max">The max value.</param>
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/// <returns>The clamped value.</returns>
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public static Vector3 Clamp(Vector3 value1, Vector3 min, Vector3 max)
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{
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return new Vector3(
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MathHelper.Clamp(value1.X, min.X, max.X),
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MathHelper.Clamp(value1.Y, min.Y, max.Y),
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MathHelper.Clamp(value1.Z, min.Z, max.Z)
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);
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}
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/// <summary>
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/// Clamps the specified value within a range.
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/// </summary>
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/// <param name="value1">The value to clamp.</param>
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/// <param name="min">The min value.</param>
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/// <param name="max">The max value.</param>
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/// <param name="result">The clamped value as an output parameter.</param>
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public static void Clamp(
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ref Vector3 value1,
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ref Vector3 min,
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ref Vector3 max,
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out Vector3 result
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) {
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result.X = MathHelper.Clamp(value1.X, min.X, max.X);
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result.Y = MathHelper.Clamp(value1.Y, min.Y, max.Y);
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result.Z = MathHelper.Clamp(value1.Z, min.Z, max.Z);
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}
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/// <summary>
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/// Computes the cross product of two vectors.
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/// </summary>
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/// <param name="vector1">The first vector.</param>
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/// <param name="vector2">The second vector.</param>
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/// <returns>The cross product of two vectors.</returns>
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public static Vector3 Cross(Vector3 vector1, Vector3 vector2)
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{
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Cross(ref vector1, ref vector2, out vector1);
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return vector1;
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}
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/// <summary>
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/// Computes the cross product of two vectors.
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/// </summary>
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/// <param name="vector1">The first vector.</param>
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/// <param name="vector2">The second vector.</param>
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/// <param name="result">The cross product of two vectors as an output parameter.</param>
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public static void Cross(ref Vector3 vector1, ref Vector3 vector2, out Vector3 result)
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{
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float x = vector1.Y * vector2.Z - vector2.Y * vector1.Z;
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float y = -(vector1.X * vector2.Z - vector2.X * vector1.Z);
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float z = vector1.X * vector2.Y - vector2.X * vector1.Y;
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result.X = x;
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result.Y = y;
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result.Z = z;
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}
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/// <summary>
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/// Returns the distance between two vectors.
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/// </summary>
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|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <returns>The distance between two vectors.</returns>
|
|
public static float Distance(Vector3 vector1, Vector3 vector2)
|
|
{
|
|
float result;
|
|
DistanceSquared(ref vector1, ref vector2, out result);
|
|
return (float) System.Math.Sqrt(result);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the distance between two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <param name="result">The distance between two vectors as an output parameter.</param>
|
|
public static void Distance(ref Vector3 value1, ref Vector3 value2, out float result)
|
|
{
|
|
DistanceSquared(ref value1, ref value2, out result);
|
|
result = (float) System.Math.Sqrt(result);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the squared distance between two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <returns>The squared distance between two vectors.</returns>
|
|
public static float DistanceSquared(Vector3 value1, Vector3 value2)
|
|
{
|
|
return (
|
|
(value1.X - value2.X) * (value1.X - value2.X) +
|
|
(value1.Y - value2.Y) * (value1.Y - value2.Y) +
|
|
(value1.Z - value2.Z) * (value1.Z - value2.Z)
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the squared distance between two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <param name="result">The squared distance between two vectors as an output parameter.</param>
|
|
public static void DistanceSquared(
|
|
ref Vector3 value1,
|
|
ref Vector3 value2,
|
|
out float result
|
|
) {
|
|
result = (
|
|
(value1.X - value2.X) * (value1.X - value2.X) +
|
|
(value1.Y - value2.Y) * (value1.Y - value2.Y) +
|
|
(value1.Z - value2.Z) * (value1.Z - value2.Z)
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides the components of a <see cref="Vector3"/> by the components of another <see cref="Vector3"/>.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Divisor <see cref="Vector3"/>.</param>
|
|
/// <returns>The result of dividing the vectors.</returns>
|
|
public static Vector3 Divide(Vector3 value1, Vector3 value2)
|
|
{
|
|
value1.X /= value2.X;
|
|
value1.Y /= value2.Y;
|
|
value1.Z /= value2.Z;
|
|
return value1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides the components of a <see cref="Vector3"/> by the components of another <see cref="Vector3"/>.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Divisor <see cref="Vector3"/>.</param>
|
|
/// <param name="result">The result of dividing the vectors as an output parameter.</param>
|
|
public static void Divide(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
|
|
{
|
|
result.X = value1.X / value2.X;
|
|
result.Y = value1.Y / value2.Y;
|
|
result.Z = value1.Z / value2.Z;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides the components of a <see cref="Vector3"/> by a scalar.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Divisor scalar.</param>
|
|
/// <returns>The result of dividing a vector by a scalar.</returns>
|
|
public static Vector3 Divide(Vector3 value1, float value2)
|
|
{
|
|
float factor = 1 / value2;
|
|
value1.X *= factor;
|
|
value1.Y *= factor;
|
|
value1.Z *= factor;
|
|
return value1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides the components of a <see cref="Vector3"/> by a scalar.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Divisor scalar.</param>
|
|
/// <param name="result">The result of dividing a vector by a scalar as an output parameter.</param>
|
|
public static void Divide(ref Vector3 value1, float value2, out Vector3 result)
|
|
{
|
|
float factor = 1 / value2;
|
|
result.X = value1.X * factor;
|
|
result.Y = value1.Y * factor;
|
|
result.Z = value1.Z * factor;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a dot product of two vectors.
|
|
/// </summary>
|
|
/// <param name="vector1">The first vector.</param>
|
|
/// <param name="vector2">The second vector.</param>
|
|
/// <returns>The dot product of two vectors.</returns>
|
|
public static float Dot(Vector3 vector1, Vector3 vector2)
|
|
{
|
|
return vector1.X * vector2.X + vector1.Y * vector2.Y + vector1.Z * vector2.Z;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a dot product of two vectors.
|
|
/// </summary>
|
|
/// <param name="vector1">The first vector.</param>
|
|
/// <param name="vector2">The second vector.</param>
|
|
/// <param name="result">The dot product of two vectors as an output parameter.</param>
|
|
public static void Dot(ref Vector3 vector1, ref Vector3 vector2, out float result)
|
|
{
|
|
result = (
|
|
(vector1.X * vector2.X) +
|
|
(vector1.Y * vector2.Y) +
|
|
(vector1.Z * vector2.Z)
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains hermite spline interpolation.
|
|
/// </summary>
|
|
/// <param name="value1">The first position vector.</param>
|
|
/// <param name="tangent1">The first tangent vector.</param>
|
|
/// <param name="value2">The second position vector.</param>
|
|
/// <param name="tangent2">The second tangent vector.</param>
|
|
/// <param name="amount">Weighting factor.</param>
|
|
/// <returns>The hermite spline interpolation vector.</returns>
|
|
public static Vector3 Hermite(
|
|
Vector3 value1,
|
|
Vector3 tangent1,
|
|
Vector3 value2,
|
|
Vector3 tangent2,
|
|
float amount
|
|
) {
|
|
Vector3 result = new Vector3();
|
|
Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains hermite spline interpolation.
|
|
/// </summary>
|
|
/// <param name="value1">The first position vector.</param>
|
|
/// <param name="tangent1">The first tangent vector.</param>
|
|
/// <param name="value2">The second position vector.</param>
|
|
/// <param name="tangent2">The second tangent vector.</param>
|
|
/// <param name="amount">Weighting factor.</param>
|
|
/// <param name="result">The hermite spline interpolation vector as an output parameter.</param>
|
|
public static void Hermite(
|
|
ref Vector3 value1,
|
|
ref Vector3 tangent1,
|
|
ref Vector3 value2,
|
|
ref Vector3 tangent2,
|
|
float amount,
|
|
out Vector3 result
|
|
) {
|
|
result.X = MathHelper.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount);
|
|
result.Y = MathHelper.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount);
|
|
result.Z = MathHelper.Hermite(value1.Z, tangent1.Z, value2.Z, tangent2.Z, amount);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains linear interpolation of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <param name="amount">Weighting value(between 0.0 and 1.0).</param>
|
|
/// <returns>The result of linear interpolation of the specified vectors.</returns>
|
|
public static Vector3 Lerp(Vector3 value1, Vector3 value2, float amount)
|
|
{
|
|
return new Vector3(
|
|
MathHelper.Lerp(value1.X, value2.X, amount),
|
|
MathHelper.Lerp(value1.Y, value2.Y, amount),
|
|
MathHelper.Lerp(value1.Z, value2.Z, amount)
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains linear interpolation of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <param name="amount">Weighting value(between 0.0 and 1.0).</param>
|
|
/// <param name="result">The result of linear interpolation of the specified vectors as an output parameter.</param>
|
|
public static void Lerp(
|
|
ref Vector3 value1,
|
|
ref Vector3 value2,
|
|
float amount,
|
|
out Vector3 result
|
|
) {
|
|
result.X = MathHelper.Lerp(value1.X, value2.X, amount);
|
|
result.Y = MathHelper.Lerp(value1.Y, value2.Y, amount);
|
|
result.Z = MathHelper.Lerp(value1.Z, value2.Z, amount);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a maximal values from the two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <returns>The <see cref="Vector3"/> with maximal values from the two vectors.</returns>
|
|
public static Vector3 Max(Vector3 value1, Vector3 value2)
|
|
{
|
|
return new Vector3(
|
|
MathHelper.Max(value1.X, value2.X),
|
|
MathHelper.Max(value1.Y, value2.Y),
|
|
MathHelper.Max(value1.Z, value2.Z)
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a maximal values from the two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <param name="result">The <see cref="Vector3"/> with maximal values from the two vectors as an output parameter.</param>
|
|
public static void Max(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
|
|
{
|
|
result.X = MathHelper.Max(value1.X, value2.X);
|
|
result.Y = MathHelper.Max(value1.Y, value2.Y);
|
|
result.Z = MathHelper.Max(value1.Z, value2.Z);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a minimal values from the two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <returns>The <see cref="Vector3"/> with minimal values from the two vectors.</returns>
|
|
public static Vector3 Min(Vector3 value1, Vector3 value2)
|
|
{
|
|
return new Vector3(
|
|
MathHelper.Min(value1.X, value2.X),
|
|
MathHelper.Min(value1.Y, value2.Y),
|
|
MathHelper.Min(value1.Z, value2.Z)
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a minimal values from the two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <param name="result">The <see cref="Vector3"/> with minimal values from the two vectors as an output parameter.</param>
|
|
public static void Min(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
|
|
{
|
|
result.X = MathHelper.Min(value1.X, value2.X);
|
|
result.Y = MathHelper.Min(value1.Y, value2.Y);
|
|
result.Z = MathHelper.Min(value1.Z, value2.Z);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a multiplication of two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/>.</param>
|
|
/// <returns>The result of the vector multiplication.</returns>
|
|
public static Vector3 Multiply(Vector3 value1, Vector3 value2)
|
|
{
|
|
value1.X *= value2.X;
|
|
value1.Y *= value2.Y;
|
|
value1.Z *= value2.Z;
|
|
return value1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a multiplication of <see cref="Vector3"/> and a scalar.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="scaleFactor">Scalar value.</param>
|
|
/// <returns>The result of the vector multiplication with a scalar.</returns>
|
|
public static Vector3 Multiply(Vector3 value1, float scaleFactor)
|
|
{
|
|
value1.X *= scaleFactor;
|
|
value1.Y *= scaleFactor;
|
|
value1.Z *= scaleFactor;
|
|
return value1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a multiplication of <see cref="Vector3"/> and a scalar.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="scaleFactor">Scalar value.</param>
|
|
/// <param name="result">The result of the multiplication with a scalar as an output parameter.</param>
|
|
public static void Multiply(ref Vector3 value1, float scaleFactor, out Vector3 result)
|
|
{
|
|
result.X = value1.X * scaleFactor;
|
|
result.Y = value1.Y * scaleFactor;
|
|
result.Z = value1.Z * scaleFactor;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a multiplication of two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="result">The result of the vector multiplication as an output parameter.</param>
|
|
public static void Multiply(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
|
|
{
|
|
result.X = value1.X * value2.X;
|
|
result.Y = value1.Y * value2.Y;
|
|
result.Z = value1.Z * value2.Z;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains the specified vector inversion.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/>.</param>
|
|
/// <returns>The result of the vector inversion.</returns>
|
|
public static Vector3 Negate(Vector3 value)
|
|
{
|
|
value = new Vector3(-value.X, -value.Y, -value.Z);
|
|
return value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains the specified vector inversion.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="result">The result of the vector inversion as an output parameter.</param>
|
|
public static void Negate(ref Vector3 value, out Vector3 result)
|
|
{
|
|
result.X = -value.X;
|
|
result.Y = -value.Y;
|
|
result.Z = -value.Z;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a normalized values from another vector.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/>.</param>
|
|
/// <returns>Unit vector.</returns>
|
|
public static Vector3 Normalize(Vector3 value)
|
|
{
|
|
float factor = 1.0f / (float) System.Math.Sqrt(
|
|
(value.X * value.X) +
|
|
(value.Y * value.Y) +
|
|
(value.Z * value.Z)
|
|
);
|
|
return new Vector3(
|
|
value.X * factor,
|
|
value.Y * factor,
|
|
value.Z * factor
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a normalized values from another vector.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="result">Unit vector as an output parameter.</param>
|
|
public static void Normalize(ref Vector3 value, out Vector3 result)
|
|
{
|
|
float factor = 1.0f / (float) System.Math.Sqrt(
|
|
(value.X * value.X) +
|
|
(value.Y * value.Y) +
|
|
(value.Z * value.Z)
|
|
);
|
|
result.X = value.X * factor;
|
|
result.Y = value.Y * factor;
|
|
result.Z = value.Z * factor;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains reflect vector of the given vector and normal.
|
|
/// </summary>
|
|
/// <param name="vector">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="normal">Reflection normal.</param>
|
|
/// <returns>Reflected vector.</returns>
|
|
public static Vector3 Reflect(Vector3 vector, Vector3 normal)
|
|
{
|
|
/* I is the original array.
|
|
* N is the normal of the incident plane.
|
|
* R = I - (2 * N * ( DotProduct[ I,N] ))
|
|
*/
|
|
Vector3 reflectedVector;
|
|
// Inline the dotProduct here instead of calling method
|
|
float dotProduct = ((vector.X * normal.X) + (vector.Y * normal.Y)) +
|
|
(vector.Z * normal.Z);
|
|
reflectedVector.X = vector.X - (2.0f * normal.X) * dotProduct;
|
|
reflectedVector.Y = vector.Y - (2.0f * normal.Y) * dotProduct;
|
|
reflectedVector.Z = vector.Z - (2.0f * normal.Z) * dotProduct;
|
|
|
|
return reflectedVector;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains reflect vector of the given vector and normal.
|
|
/// </summary>
|
|
/// <param name="vector">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="normal">Reflection normal.</param>
|
|
/// <param name="result">Reflected vector as an output parameter.</param>
|
|
public static void Reflect(ref Vector3 vector, ref Vector3 normal, out Vector3 result)
|
|
{
|
|
/* I is the original array.
|
|
* N is the normal of the incident plane.
|
|
* R = I - (2 * N * ( DotProduct[ I,N] ))
|
|
*/
|
|
|
|
// Inline the dotProduct here instead of calling method.
|
|
float dotProduct = ((vector.X * normal.X) + (vector.Y * normal.Y)) +
|
|
(vector.Z * normal.Z);
|
|
result.X = vector.X - (2.0f * normal.X) * dotProduct;
|
|
result.Y = vector.Y - (2.0f * normal.Y) * dotProduct;
|
|
result.Z = vector.Z - (2.0f * normal.Z) * dotProduct;
|
|
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains cubic interpolation of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="amount">Weighting value.</param>
|
|
/// <returns>Cubic interpolation of the specified vectors.</returns>
|
|
public static Vector3 SmoothStep(Vector3 value1, Vector3 value2, float amount)
|
|
{
|
|
return new Vector3(
|
|
MathHelper.SmoothStep(value1.X, value2.X, amount),
|
|
MathHelper.SmoothStep(value1.Y, value2.Y, amount),
|
|
MathHelper.SmoothStep(value1.Z, value2.Z, amount)
|
|
);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains cubic interpolation of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="amount">Weighting value.</param>
|
|
/// <param name="result">Cubic interpolation of the specified vectors as an output parameter.</param>
|
|
public static void SmoothStep(
|
|
ref Vector3 value1,
|
|
ref Vector3 value2,
|
|
float amount,
|
|
out Vector3 result
|
|
) {
|
|
result.X = MathHelper.SmoothStep(value1.X, value2.X, amount);
|
|
result.Y = MathHelper.SmoothStep(value1.Y, value2.Y, amount);
|
|
result.Z = MathHelper.SmoothStep(value1.Z, value2.Z, amount);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains subtraction of on <see cref="Vector3"/> from a another.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/>.</param>
|
|
/// <returns>The result of the vector subtraction.</returns>
|
|
public static Vector3 Subtract(Vector3 value1, Vector3 value2)
|
|
{
|
|
value1.X -= value2.X;
|
|
value1.Y -= value2.Y;
|
|
value1.Z -= value2.Z;
|
|
return value1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains subtraction of on <see cref="Vector3"/> from a another.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="result">The result of the vector subtraction as an output parameter.</param>
|
|
public static void Subtract(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
|
|
{
|
|
result.X = value1.X - value2.X;
|
|
result.Y = value1.Y - value2.Y;
|
|
result.Z = value1.Z - value2.Z;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Matrix4x4"/>.
|
|
/// </summary>
|
|
/// <param name="position">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <returns>Transformed <see cref="Vector3"/>.</returns>
|
|
public static Vector3 Transform(Vector3 position, Matrix4x4 matrix)
|
|
{
|
|
Transform(ref position, ref matrix, out position);
|
|
return position;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Matrix4x4"/>.
|
|
/// </summary>
|
|
/// <param name="position">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <param name="result">Transformed <see cref="Vector3"/> as an output parameter.</param>
|
|
public static void Transform(
|
|
ref Vector3 position,
|
|
ref Matrix4x4 matrix,
|
|
out Vector3 result
|
|
) {
|
|
float x = (
|
|
(position.X * matrix.M11) +
|
|
(position.Y * matrix.M21) +
|
|
(position.Z * matrix.M31) +
|
|
matrix.M41
|
|
);
|
|
float y = (
|
|
(position.X * matrix.M12) +
|
|
(position.Y * matrix.M22) +
|
|
(position.Z * matrix.M32) +
|
|
matrix.M42
|
|
);
|
|
float z = (
|
|
(position.X * matrix.M13) +
|
|
(position.Y * matrix.M23) +
|
|
(position.Z * matrix.M33) +
|
|
matrix.M43
|
|
);
|
|
result.X = x;
|
|
result.Y = y;
|
|
result.Z = z;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Apply transformation on all vectors within array of <see cref="Vector3"/> by the specified <see cref="Matrix4x4"/> and places the results in an another array.
|
|
/// </summary>
|
|
/// <param name="sourceArray">Source array.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <param name="destinationArray">Destination array.</param>
|
|
public static void Transform(
|
|
Vector3[] sourceArray,
|
|
ref Matrix4x4 matrix,
|
|
Vector3[] destinationArray
|
|
) {
|
|
Debug.Assert(
|
|
destinationArray.Length >= sourceArray.Length,
|
|
"The destination array is smaller than the source array."
|
|
);
|
|
|
|
/* TODO: Are there options on some platforms to implement
|
|
* a vectorized version of this?
|
|
*/
|
|
|
|
for (int i = 0; i < sourceArray.Length; i += 1)
|
|
{
|
|
Vector3 position = sourceArray[i];
|
|
destinationArray[i] = new Vector3(
|
|
(position.X * matrix.M11) + (position.Y * matrix.M21) +
|
|
(position.Z * matrix.M31) + matrix.M41,
|
|
(position.X * matrix.M12) + (position.Y * matrix.M22) +
|
|
(position.Z * matrix.M32) + matrix.M42,
|
|
(position.X * matrix.M13) + (position.Y * matrix.M23) +
|
|
(position.Z * matrix.M33) + matrix.M43
|
|
);
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Apply transformation on vectors within array of <see cref="Vector3"/> by the specified <see cref="Matrix4x4"/> and places the results in an another array.
|
|
/// </summary>
|
|
/// <param name="sourceArray">Source array.</param>
|
|
/// <param name="sourceIndex">The starting index of transformation in the source array.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <param name="destinationArray">Destination array.</param>
|
|
/// <param name="destinationIndex">The starting index in the destination array, where the first <see cref="Vector3"/> should be written.</param>
|
|
/// <param name="length">The number of vectors to be transformed.</param>
|
|
public static void Transform(
|
|
Vector3[] sourceArray,
|
|
int sourceIndex,
|
|
ref Matrix4x4 matrix,
|
|
Vector3[] destinationArray,
|
|
int destinationIndex,
|
|
int length
|
|
) {
|
|
Debug.Assert(
|
|
sourceArray.Length - sourceIndex >= length,
|
|
"The source array is too small for the given sourceIndex and length."
|
|
);
|
|
Debug.Assert(
|
|
destinationArray.Length - destinationIndex >= length,
|
|
"The destination array is too small for " +
|
|
"the given destinationIndex and length."
|
|
);
|
|
|
|
/* TODO: Are there options on some platforms to implement a
|
|
* vectorized version of this?
|
|
*/
|
|
|
|
for (int i = 0; i < length; i += 1)
|
|
{
|
|
Vector3 position = sourceArray[sourceIndex + i];
|
|
destinationArray[destinationIndex + i] = new Vector3(
|
|
(position.X * matrix.M11) + (position.Y * matrix.M21) +
|
|
(position.Z * matrix.M31) + matrix.M41,
|
|
(position.X * matrix.M12) + (position.Y * matrix.M22) +
|
|
(position.Z * matrix.M32) + matrix.M42,
|
|
(position.X * matrix.M13) + (position.Y * matrix.M23) +
|
|
(position.Z * matrix.M33) + matrix.M43
|
|
);
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Quaternion"/>, representing the rotation.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
|
|
/// <returns>Transformed <see cref="Vector3"/>.</returns>
|
|
public static Vector3 Transform(Vector3 value, Quaternion rotation)
|
|
{
|
|
Vector3 result;
|
|
Transform(ref value, ref rotation, out result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Quaternion"/>, representing the rotation.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/>.</param>
|
|
/// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
|
|
/// <param name="result">Transformed <see cref="Vector3"/> as an output parameter.</param>
|
|
public static void Transform(
|
|
ref Vector3 value,
|
|
ref Quaternion rotation,
|
|
out Vector3 result
|
|
) {
|
|
float x = 2 * (rotation.Y * value.Z - rotation.Z * value.Y);
|
|
float y = 2 * (rotation.Z * value.X - rotation.X * value.Z);
|
|
float z = 2 * (rotation.X * value.Y - rotation.Y * value.X);
|
|
|
|
result.X = value.X + x * rotation.W + (rotation.Y * z - rotation.Z * y);
|
|
result.Y = value.Y + y * rotation.W + (rotation.Z * x - rotation.X * z);
|
|
result.Z = value.Z + z * rotation.W + (rotation.X * y - rotation.Y * x);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Apply transformation on all vectors within array of <see cref="Vector3"/> by the specified <see cref="Quaternion"/> and places the results in an another array.
|
|
/// </summary>
|
|
/// <param name="sourceArray">Source array.</param>
|
|
/// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
|
|
/// <param name="destinationArray">Destination array.</param>
|
|
public static void Transform(
|
|
Vector3[] sourceArray,
|
|
ref Quaternion rotation,
|
|
Vector3[] destinationArray
|
|
) {
|
|
Debug.Assert(
|
|
destinationArray.Length >= sourceArray.Length,
|
|
"The destination array is smaller than the source array."
|
|
);
|
|
|
|
/* TODO: Are there options on some platforms to implement
|
|
* a vectorized version of this?
|
|
*/
|
|
|
|
for (int i = 0; i < sourceArray.Length; i += 1)
|
|
{
|
|
Vector3 position = sourceArray[i];
|
|
|
|
float x = 2 * (rotation.Y * position.Z - rotation.Z * position.Y);
|
|
float y = 2 * (rotation.Z * position.X - rotation.X * position.Z);
|
|
float z = 2 * (rotation.X * position.Y - rotation.Y * position.X);
|
|
|
|
destinationArray[i] = new Vector3(
|
|
position.X + x * rotation.W + (rotation.Y * z - rotation.Z * y),
|
|
position.Y + y * rotation.W + (rotation.Z * x - rotation.X * z),
|
|
position.Z + z * rotation.W + (rotation.X * y - rotation.Y * x)
|
|
);
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
|
|
/// Apply transformation on vectors within array of <see cref="Vector3"/> by the specified <see cref="Quaternion"/> and places the results in an another array.
|
|
/// </summary>
|
|
/// <param name="sourceArray">Source array.</param>
|
|
/// <param name="sourceIndex">The starting index of transformation in the source array.</param>
|
|
/// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
|
|
/// <param name="destinationArray">Destination array.</param>
|
|
/// <param name="destinationIndex">The starting index in the destination array, where the first <see cref="Vector3"/> should be written.</param>
|
|
/// <param name="length">The number of vectors to be transformed.</param>
|
|
public static void Transform(
|
|
Vector3[] sourceArray,
|
|
int sourceIndex,
|
|
ref Quaternion rotation,
|
|
Vector3[] destinationArray,
|
|
int destinationIndex,
|
|
int length
|
|
) {
|
|
Debug.Assert(
|
|
sourceArray.Length - sourceIndex >= length,
|
|
"The source array is too small for the given sourceIndex and length."
|
|
);
|
|
Debug.Assert(
|
|
destinationArray.Length - destinationIndex >= length,
|
|
"The destination array is too small for the " +
|
|
"given destinationIndex and length."
|
|
);
|
|
|
|
/* TODO: Are there options on some platforms to implement
|
|
* a vectorized version of this?
|
|
*/
|
|
|
|
for (int i = 0; i < length; i += 1)
|
|
{
|
|
Vector3 position = sourceArray[sourceIndex + i];
|
|
|
|
float x = 2 * (rotation.Y * position.Z - rotation.Z * position.Y);
|
|
float y = 2 * (rotation.Z * position.X - rotation.X * position.Z);
|
|
float z = 2 * (rotation.X * position.Y - rotation.Y * position.X);
|
|
|
|
destinationArray[destinationIndex + i] = new Vector3(
|
|
position.X + x * rotation.W + (rotation.Y * z - rotation.Z * y),
|
|
position.Y + y * rotation.W + (rotation.Z * x - rotation.X * z),
|
|
position.Z + z * rotation.W + (rotation.X * y - rotation.Y * x)
|
|
);
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a transformation of the specified normal by the specified <see cref="Matrix4x4"/>.
|
|
/// </summary>
|
|
/// <param name="normal">Source <see cref="Vector3"/> which represents a normal vector.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <returns>Transformed normal.</returns>
|
|
public static Vector3 TransformNormal(Vector3 normal, Matrix4x4 matrix)
|
|
{
|
|
TransformNormal(ref normal, ref matrix, out normal);
|
|
return normal;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a new <see cref="Vector3"/> that contains a transformation of the specified normal by the specified <see cref="Matrix4x4"/>.
|
|
/// </summary>
|
|
/// <param name="normal">Source <see cref="Vector3"/> which represents a normal vector.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <param name="result">Transformed normal as an output parameter.</param>
|
|
public static void TransformNormal(
|
|
ref Vector3 normal,
|
|
ref Matrix4x4 matrix,
|
|
out Vector3 result
|
|
) {
|
|
float x = (normal.X * matrix.M11) + (normal.Y * matrix.M21) + (normal.Z * matrix.M31);
|
|
float y = (normal.X * matrix.M12) + (normal.Y * matrix.M22) + (normal.Z * matrix.M32);
|
|
float z = (normal.X * matrix.M13) + (normal.Y * matrix.M23) + (normal.Z * matrix.M33);
|
|
result.X = x;
|
|
result.Y = y;
|
|
result.Z = z;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Apply transformation on all normals within array of <see cref="Vector3"/> by the specified <see cref="Matrix4x4"/> and places the results in an another array.
|
|
/// </summary>
|
|
/// <param name="sourceArray">Source array.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <param name="destinationArray">Destination array.</param>
|
|
public static void TransformNormal(
|
|
Vector3[] sourceArray,
|
|
ref Matrix4x4 matrix,
|
|
Vector3[] destinationArray
|
|
) {
|
|
Debug.Assert(
|
|
destinationArray.Length >= sourceArray.Length,
|
|
"The destination array is smaller than the source array."
|
|
);
|
|
|
|
for (int i = 0; i < sourceArray.Length; i += 1)
|
|
{
|
|
Vector3 normal = sourceArray[i];
|
|
destinationArray[i].X = (normal.X * matrix.M11) + (normal.Y * matrix.M21) + (normal.Z * matrix.M31);
|
|
destinationArray[i].Y = (normal.X * matrix.M12) + (normal.Y * matrix.M22) + (normal.Z * matrix.M32);
|
|
destinationArray[i].Z = (normal.X * matrix.M13) + (normal.Y * matrix.M23) + (normal.Z * matrix.M33);
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Apply transformation on normals within array of <see cref="Vector3"/> by the specified <see cref="Matrix4x4"/> and places the results in an another array.
|
|
/// </summary>
|
|
/// <param name="sourceArray">Source array.</param>
|
|
/// <param name="sourceIndex">The starting index of transformation in the source array.</param>
|
|
/// <param name="matrix">The transformation <see cref="Matrix4x4"/>.</param>
|
|
/// <param name="destinationArray">Destination array.</param>
|
|
/// <param name="destinationIndex">The starting index in the destination array, where the first <see cref="Vector3"/> should be written.</param>
|
|
/// <param name="length">The number of normals to be transformed.</param>
|
|
public static void TransformNormal(
|
|
Vector3[] sourceArray,
|
|
int sourceIndex,
|
|
ref Matrix4x4 matrix,
|
|
Vector3[] destinationArray,
|
|
int destinationIndex,
|
|
int length
|
|
) {
|
|
if (sourceArray == null)
|
|
{
|
|
throw new ArgumentNullException("sourceArray");
|
|
}
|
|
if (destinationArray == null)
|
|
{
|
|
throw new ArgumentNullException("destinationArray");
|
|
}
|
|
if ((sourceIndex + length) > sourceArray.Length)
|
|
{
|
|
throw new ArgumentException(
|
|
"the combination of sourceIndex and " +
|
|
"length was greater than sourceArray.Length"
|
|
);
|
|
}
|
|
if ((destinationIndex + length) > destinationArray.Length)
|
|
{
|
|
throw new ArgumentException(
|
|
"destinationArray is too small to " +
|
|
"contain the result"
|
|
);
|
|
}
|
|
|
|
for (int i = 0; i < length; i += 1)
|
|
{
|
|
Vector3 normal = sourceArray[i + sourceIndex];
|
|
destinationArray[i + destinationIndex].X = (
|
|
(normal.X * matrix.M11) +
|
|
(normal.Y * matrix.M21) +
|
|
(normal.Z * matrix.M31)
|
|
);
|
|
destinationArray[i + destinationIndex].Y = (
|
|
(normal.X * matrix.M12) +
|
|
(normal.Y * matrix.M22) +
|
|
(normal.Z * matrix.M32)
|
|
);
|
|
destinationArray[i + destinationIndex].Z = (
|
|
(normal.X * matrix.M13) +
|
|
(normal.Y * matrix.M23) +
|
|
(normal.Z * matrix.M33)
|
|
);
|
|
}
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Public Static Operators
|
|
|
|
/// <summary>
|
|
/// Compares whether two <see cref="Vector3"/> instances are equal.
|
|
/// </summary>
|
|
/// <param name="value1"><see cref="Vector3"/> instance on the left of the equal sign.</param>
|
|
/// <param name="value2"><see cref="Vector3"/> instance on the right of the equal sign.</param>
|
|
/// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
|
|
public static bool operator ==(Vector3 value1, Vector3 value2)
|
|
{
|
|
return ( value1.X == value2.X &&
|
|
value1.Y == value2.Y &&
|
|
value1.Z == value2.Z );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Compares whether two <see cref="Vector3"/> instances are not equal.
|
|
/// </summary>
|
|
/// <param name="value1"><see cref="Vector3"/> instance on the left of the not equal sign.</param>
|
|
/// <param name="value2"><see cref="Vector3"/> instance on the right of the not equal sign.</param>
|
|
/// <returns><c>true</c> if the instances are not equal; <c>false</c> otherwise.</returns>
|
|
public static bool operator !=(Vector3 value1, Vector3 value2)
|
|
{
|
|
return !(value1 == value2);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Adds two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/> on the left of the add sign.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/> on the right of the add sign.</param>
|
|
/// <returns>Sum of the vectors.</returns>
|
|
public static Vector3 operator +(Vector3 value1, Vector3 value2)
|
|
{
|
|
value1.X += value2.X;
|
|
value1.Y += value2.Y;
|
|
value1.Z += value2.Z;
|
|
return value1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Inverts values in the specified <see cref="Vector3"/>.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/> on the right of the sub sign.</param>
|
|
/// <returns>Result of the inversion.</returns>
|
|
public static Vector3 operator -(Vector3 value)
|
|
{
|
|
value = new Vector3(-value.X, -value.Y, -value.Z);
|
|
return value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Subtracts a <see cref="Vector3"/> from a <see cref="Vector3"/>.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/> on the left of the sub sign.</param>
|
|
/// <param name="value2">Source <see cref="Vector3"/> on the right of the sub sign.</param>
|
|
/// <returns>Result of the vector subtraction.</returns>
|
|
public static Vector3 operator -(Vector3 value1, Vector3 value2)
|
|
{
|
|
value1.X -= value2.X;
|
|
value1.Y -= value2.Y;
|
|
value1.Z -= value2.Z;
|
|
return value1;
|
|
}
|
|
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/// <summary>
|
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/// Multiplies the components of two vectors by each other.
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/// </summary>
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/// <param name="value1">Source <see cref="Vector3"/> on the left of the mul sign.</param>
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/// <param name="value2">Source <see cref="Vector3"/> on the right of the mul sign.</param>
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/// <returns>Result of the vector multiplication.</returns>
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|
public static Vector3 operator *(Vector3 value1, Vector3 value2)
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|
{
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|
value1.X *= value2.X;
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|
value1.Y *= value2.Y;
|
|
value1.Z *= value2.Z;
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|
return value1;
|
|
}
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|
|
|
/// <summary>
|
|
/// Multiplies the components of vector by a scalar.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/> on the left of the mul sign.</param>
|
|
/// <param name="scaleFactor">Scalar value on the right of the mul sign.</param>
|
|
/// <returns>Result of the vector multiplication with a scalar.</returns>
|
|
public static Vector3 operator *(Vector3 value, float scaleFactor)
|
|
{
|
|
value.X *= scaleFactor;
|
|
value.Y *= scaleFactor;
|
|
value.Z *= scaleFactor;
|
|
return value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Multiplies the components of vector by a scalar.
|
|
/// </summary>
|
|
/// <param name="scaleFactor">Scalar value on the left of the mul sign.</param>
|
|
/// <param name="value">Source <see cref="Vector3"/> on the right of the mul sign.</param>
|
|
/// <returns>Result of the vector multiplication with a scalar.</returns>
|
|
public static Vector3 operator *(float scaleFactor, Vector3 value)
|
|
{
|
|
value.X *= scaleFactor;
|
|
value.Y *= scaleFactor;
|
|
value.Z *= scaleFactor;
|
|
return value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides the components of a <see cref="Vector3"/> by the components of another <see cref="Vector3"/>.
|
|
/// </summary>
|
|
/// <param name="value1">Source <see cref="Vector3"/> on the left of the div sign.</param>
|
|
/// <param name="value2">Divisor <see cref="Vector3"/> on the right of the div sign.</param>
|
|
/// <returns>The result of dividing the vectors.</returns>
|
|
public static Vector3 operator /(Vector3 value1, Vector3 value2)
|
|
{
|
|
value1.X /= value2.X;
|
|
value1.Y /= value2.Y;
|
|
value1.Z /= value2.Z;
|
|
return value1;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides the components of a <see cref="Vector3"/> by a scalar.
|
|
/// </summary>
|
|
/// <param name="value">Source <see cref="Vector3"/> on the left of the div sign.</param>
|
|
/// <param name="divider">Divisor scalar on the right of the div sign.</param>
|
|
/// <returns>The result of dividing a vector by a scalar.</returns>
|
|
public static Vector3 operator /(Vector3 value, float divider)
|
|
{
|
|
float factor = 1 / divider;
|
|
value.X *= factor;
|
|
value.Y *= factor;
|
|
value.Z *= factor;
|
|
return value;
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
}
|