1469 lines
70 KiB
C#
1469 lines
70 KiB
C#
// Copyright (c) Xenko contributors (https://xenko.com) and Silicon Studio Corp. (https://www.siliconstudio.co.jp)
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// Distributed under the MIT license. See the LICENSE.md file in the project root for more information.
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//
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// -----------------------------------------------------------------------------
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// Original code from SlimMath project. http://code.google.com/p/slimmath/
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// Greetings to SlimDX Group. Original code published with the following license:
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// -----------------------------------------------------------------------------
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/*
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* Copyright (c) 2007-2011 SlimDX Group
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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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
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* THE SOFTWARE.
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*/
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using System;
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using System.Globalization;
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using System.Runtime.CompilerServices;
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using System.Runtime.InteropServices;
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using System.Runtime.Serialization;
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namespace math
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{
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/// <summary>
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/// Represents a two dimensional mathematical vector.
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/// </summary>
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[DataContract( Name = "float2" )]
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[DataStyle( DataStyle.Compact )]
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[StructLayout( LayoutKind.Sequential, Pack = 4 )]
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public struct Vec2 : IEquatable<Vec2>, IFormattable
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{
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/// <summary>
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/// The size of the <see cref="math.Vec2"/> type, in bytes.
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/// </summary>
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public static readonly int SizeInBytes = lib.Util.SizeOf<Vec2>();
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/// <summary>
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/// A <see cref="math.Vec2"/> with all of its components set to zero.
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/// </summary>
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public static readonly Vec2 Zero = new Vec2();
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/// <summary>
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/// The X unit <see cref="math.Vec2"/> (1, 0).
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/// </summary>
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public static readonly Vec2 UnitX = new Vec2( 1.0f, 0.0f );
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/// <summary>
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/// The Y unit <see cref="math.Vec2"/> (0, 1).
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/// </summary>
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public static readonly Vec2 UnitY = new Vec2( 0.0f, 1.0f );
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/// <summary>
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/// A <see cref="math.Vec2"/> with all of its components set to one.
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/// </summary>
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public static readonly Vec2 One = new Vec2( 1.0f, 1.0f );
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/// <summary>
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/// The X component of the vector.
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/// </summary>
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[DataMember( Order = 0 )]
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public float X;
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/// <summary>
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/// The Y component of the vector.
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/// </summary>
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[DataMember( Order = 1 )]
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public float Y;
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Vec2"/> struct.
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/// </summary>
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/// <param name="value">The value that will be assigned to all components.</param>
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public Vec2( float value )
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{
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X = value;
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Y = value;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Vec2"/> struct.
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/// </summary>
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/// <param name="x">Initial value for the X component of the vector.</param>
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/// <param name="y">Initial value for the Y component of the vector.</param>
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public Vec2( float x, float y )
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{
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X = x;
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Y = y;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="math.Vec2"/> struct.
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/// </summary>
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/// <param name="values">The values to assign to the X and Y components of the vector. This must be an array with two elements.</param>
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/// <exception cref="ArgumentNullException">Thrown when <paramref name="values"/> is <c>null</c>.</exception>
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/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="values"/> contains more or less than two elements.</exception>
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public Vec2( float[] values )
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{
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if( values == null )
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throw new ArgumentNullException( "values" );
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if( values.Length != 2 )
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throw new ArgumentOutOfRangeException( "values", "There must be two and only two input values for Vector2." );
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X = values[0];
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Y = values[1];
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}
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/// <summary>
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/// Gets a value indicting whether this instance is normalized.
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/// </summary>
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public bool IsNormalized
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{
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get { return Math.Abs( ( X * X ) + ( Y * Y ) - 1f ) < MathUtil.ZeroTolerance; }
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}
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/// <summary>
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/// Gets or sets the component at the specified index.
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/// </summary>
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/// <value>The value of the X or Y component, depending on the index.</value>
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/// <param name="index">The index of the component to access. Use 0 for the X component and 1 for the Y component.</param>
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/// <returns>The value of the component at the specified index.</returns>
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/// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="index"/> is out of the range [0, 1].</exception>
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public float this[int index]
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{
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get
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{
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switch( index )
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{
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case 0:
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return X;
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case 1:
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return Y;
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}
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throw new ArgumentOutOfRangeException( "index", "Indices for Vector2 run from 0 to 1, inclusive." );
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}
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set
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{
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switch( index )
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{
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case 0:
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X = value;
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break;
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case 1:
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Y = value;
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break;
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default:
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throw new ArgumentOutOfRangeException( "index", "Indices for Vector2 run from 0 to 1, inclusive." );
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}
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}
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}
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/// <summary>
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/// Calculates the length of the vector.
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/// </summary>
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/// <returns>The length of the vector.</returns>
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/// <remarks>
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/// <see cref="math.Vec2.LengthSquared"/> may be preferred when only the relative length is needed
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/// and speed is of the essence.
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/// </remarks>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public float Length()
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{
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return (float)Math.Sqrt( ( X * X ) + ( Y * Y ) );
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}
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/// <summary>
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/// Calculates the squared length of the vector.
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/// </summary>
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/// <returns>The squared length of the vector.</returns>
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/// <remarks>
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/// This method may be preferred to <see cref="math.Vec2.Length"/> when only a relative length is needed
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/// and speed is of the essence.
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/// </remarks>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public float LengthSquared()
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{
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return ( X * X ) + ( Y * Y );
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}
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/// <summary>
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/// Converts the vector into a unit vector.
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/// </summary>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public void Normalize()
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{
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float length = Length();
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if( length > MathUtil.ZeroTolerance )
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{
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float inv = 1.0f / length;
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X *= inv;
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Y *= inv;
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}
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}
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/// <summary>
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/// Creates an array containing the elements of the vector.
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/// </summary>
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/// <returns>A two-element array containing the components of the vector.</returns>
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public float[] ToArray()
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{
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return new float[] { X, Y };
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}
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/// <summary>
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/// Adds two vectors.
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/// </summary>
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/// <param name="left">The first vector to add.</param>
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/// <param name="right">The second vector to add.</param>
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/// <param name="result">When the method completes, contains the sum of the two vectors.</param>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static void Add( ref Vec2 left, ref Vec2 right, out Vec2 result )
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{
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result = new Vec2( left.X + right.X, left.Y + right.Y );
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}
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/// <summary>
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/// Adds two vectors.
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/// </summary>
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/// <param name="left">The first vector to add.</param>
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/// <param name="right">The second vector to add.</param>
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/// <returns>The sum of the two vectors.</returns>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static Vec2 Add( Vec2 left, Vec2 right )
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{
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return new Vec2( left.X + right.X, left.Y + right.Y );
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}
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/// <summary>
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/// Subtracts two vectors.
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/// </summary>
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/// <param name="left">The first vector to subtract.</param>
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/// <param name="right">The second vector to subtract.</param>
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/// <param name="result">When the method completes, contains the difference of the two vectors.</param>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static void Subtract( ref Vec2 left, ref Vec2 right, out Vec2 result )
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{
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result = new Vec2( left.X - right.X, left.Y - right.Y );
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}
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/// <summary>
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/// Subtracts two vectors.
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/// </summary>
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/// <param name="left">The first vector to subtract.</param>
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/// <param name="right">The second vector to subtract.</param>
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/// <returns>The difference of the two vectors.</returns>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static Vec2 Subtract( Vec2 left, Vec2 right )
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{
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return new Vec2( left.X - right.X, left.Y - right.Y );
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}
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/// <summary>
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/// Scales a vector by the given value.
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/// </summary>
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/// <param name="value">The vector to scale.</param>
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/// <param name="scale">The amount by which to scale the vector.</param>
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/// <param name="result">When the method completes, contains the scaled vector.</param>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static void Multiply( ref Vec2 value, float scale, out Vec2 result )
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{
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result = new Vec2( value.X * scale, value.Y * scale );
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}
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/// <summary>
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/// Scales a vector by the given value.
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/// </summary>
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/// <param name="value">The vector to scale.</param>
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/// <param name="scale">The amount by which to scale the vector.</param>
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/// <returns>The scaled vector.</returns>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static Vec2 Multiply( Vec2 value, float scale )
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{
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return new Vec2( value.X * scale, value.Y * scale );
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}
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/// <summary>
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/// Modulates a vector with another by performing component-wise multiplication.
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/// </summary>
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/// <param name="left">The first vector to modulate.</param>
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/// <param name="right">The second vector to modulate.</param>
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/// <param name="result">When the method completes, contains the modulated vector.</param>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static void Modulate( ref Vec2 left, ref Vec2 right, out Vec2 result )
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{
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result = new Vec2( left.X * right.X, left.Y * right.Y );
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}
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/// <summary>
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/// Modulates a vector with another by performing component-wise multiplication.
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/// </summary>
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/// <param name="left">The first vector to modulate.</param>
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/// <param name="right">The second vector to modulate.</param>
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/// <returns>The modulated vector.</returns>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static Vec2 Modulate( Vec2 left, Vec2 right )
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{
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return new Vec2( left.X * right.X, left.Y * right.Y );
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}
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/// <summary>
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/// Scales a vector by the given value.
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/// </summary>
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/// <param name="value">The vector to scale.</param>
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/// <param name="scale">The amount by which to scale the vector.</param>
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/// <param name="result">When the method completes, contains the scaled vector.</param>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static void Divide( ref Vec2 value, float scale, out Vec2 result )
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{
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result = new Vec2( value.X / scale, value.Y / scale );
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}
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/// <summary>
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/// Scales a vector by the given value.
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/// </summary>
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/// <param name="value">The vector to scale.</param>
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/// <param name="scale">The amount by which to scale the vector.</param>
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/// <returns>The scaled vector.</returns>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static Vec2 Divide( Vec2 value, float scale )
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{
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return new Vec2( value.X / scale, value.Y / scale );
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}
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/// <summary>
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/// Demodulates a vector with another by performing component-wise division.
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/// </summary>
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/// <param name="left">The first vector to demodulate.</param>
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/// <param name="right">The second vector to demodulate.</param>
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/// <param name="result">When the method completes, contains the demodulated vector.</param>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static void Demodulate( ref Vec2 left, ref Vec2 right, out Vec2 result )
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{
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result = new Vec2( left.X / right.X, left.Y / right.Y );
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}
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/// <summary>
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/// Demodulates a vector with another by performing component-wise division.
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/// </summary>
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/// <param name="left">The first vector to demodulate.</param>
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/// <param name="right">The second vector to demodulate.</param>
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/// <returns>The demodulated vector.</returns>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static Vec2 Demodulate( Vec2 left, Vec2 right )
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{
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return new Vec2( left.X / right.X, left.Y / right.Y );
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}
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/// <summary>
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/// Reverses the direction of a given vector.
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/// </summary>
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/// <param name="value">The vector to negate.</param>
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/// <param name="result">When the method completes, contains a vector facing in the opposite direction.</param>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static void Negate( ref Vec2 value, out Vec2 result )
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{
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result = new Vec2( -value.X, -value.Y );
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}
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/// <summary>
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/// Reverses the direction of a given vector.
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/// </summary>
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/// <param name="value">The vector to negate.</param>
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/// <returns>A vector facing in the opposite direction.</returns>
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[MethodImpl( MethodImplOptions.AggressiveInlining )]
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public static Vec2 Negate( Vec2 value )
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{
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return new Vec2( -value.X, -value.Y );
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}
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/// <summary>
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/// Returns a <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 2D triangle.
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/// </summary>
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/// <param name="value1">A <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of vertex 1 of the triangle.</param>
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/// <param name="value2">A <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of vertex 2 of the triangle.</param>
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/// <param name="value3">A <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of vertex 3 of the triangle.</param>
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/// <param name="amount1">Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in <paramref name="value2"/>).</param>
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/// <param name="amount2">Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in <paramref name="value3"/>).</param>
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/// <param name="result">When the method completes, contains the 2D Cartesian coordinates of the specified point.</param>
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public static void Barycentric( ref Vec2 value1, ref Vec2 value2, ref Vec2 value3, float amount1, float amount2, out Vec2 result )
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{
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result = new Vec2(
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( value1.X + ( amount1 * ( value2.X - value1.X ) ) ) + ( amount2 * ( value3.X - value1.X ) ),
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( value1.Y + ( amount1 * ( value2.Y - value1.Y ) ) ) + ( amount2 * ( value3.Y - value1.Y ) ) );
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}
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/// <summary>
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/// Returns a <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 2D triangle.
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/// </summary>
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/// <param name="value1">A <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of vertex 1 of the triangle.</param>
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/// <param name="value2">A <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of vertex 2 of the triangle.</param>
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/// <param name="value3">A <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of vertex 3 of the triangle.</param>
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/// <param name="amount1">Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in <paramref name="value2"/>).</param>
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/// <param name="amount2">Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in <paramref name="value3"/>).</param>
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/// <returns>A new <see cref="math.Vec2"/> containing the 2D Cartesian coordinates of the specified point.</returns>
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public static Vec2 Barycentric( Vec2 value1, Vec2 value2, Vec2 value3, float amount1, float amount2 )
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{
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Vec2 result;
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Barycentric( ref value1, ref value2, ref value3, amount1, amount2, out result );
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return result;
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}
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/// <summary>
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/// Restricts a value to be within a specified range.
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/// </summary>
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/// <param name="value">The value to clamp.</param>
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/// <param name="min">The minimum value.</param>
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/// <param name="max">The maximum value.</param>
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/// <param name="result">When the method completes, contains the clamped value.</param>
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public static void Clamp( ref Vec2 value, ref Vec2 min, ref Vec2 max, out Vec2 result )
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{
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float x = value.X;
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x = ( x > max.X ) ? max.X : x;
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x = ( x < min.X ) ? min.X : x;
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float y = value.Y;
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y = ( y > max.Y ) ? max.Y : y;
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y = ( y < min.Y ) ? min.Y : y;
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result = new Vec2( x, y );
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}
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/// <summary>
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/// Restricts a value to be within a specified range.
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/// </summary>
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/// <param name="value">The value to clamp.</param>
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/// <param name="min">The minimum value.</param>
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/// <param name="max">The maximum value.</param>
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/// <returns>The clamped value.</returns>
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public static Vec2 Clamp( Vec2 value, Vec2 min, Vec2 max )
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{
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Vec2 result;
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Clamp( ref value, ref min, ref max, out result );
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return result;
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}
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/// <summary>
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/// Calculates the distance between two vectors.
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/// </summary>
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/// <param name="value1">The first vector.</param>
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/// <param name="value2">The second vector.</param>
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/// <param name="result">When the method completes, contains the distance between the two vectors.</param>
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/// <remarks>
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/// <see cref="math.Vec2.DistanceSquared(ref Vec2, ref Vec2, out float)"/> may be preferred when only the relative distance is needed
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/// and speed is of the essence.
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/// </remarks>
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public static void Distance( ref Vec2 value1, ref Vec2 value2, out float result )
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{
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float x = value1.X - value2.X;
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float y = value1.Y - value2.Y;
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|
|
result = (float)Math.Sqrt( ( x * x ) + ( y * y ) );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the distance between two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector.</param>
|
|
/// <returns>The distance between the two vectors.</returns>
|
|
/// <remarks>
|
|
/// <see cref="math.Vec2.DistanceSquared(Vec2, Vec2)"/> may be preferred when only the relative distance is needed
|
|
/// and speed is of the essence.
|
|
/// </remarks>
|
|
public static float Distance( Vec2 value1, Vec2 value2 )
|
|
{
|
|
float x = value1.X - value2.X;
|
|
float y = value1.Y - value2.Y;
|
|
|
|
return (float)Math.Sqrt( ( x * x ) + ( y * y ) );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the squared distance between two vectors.
|
|
/// </summary>
|
|
/// <param name="value1">The first vector.</param>
|
|
/// <param name="value2">The second vector</param>
|
|
/// <param name="result">When the method completes, contains the squared distance between the two vectors.</param>
|
|
/// <remarks>Distance squared is the value before taking the square root.
|
|
/// Distance squared can often be used in place of distance if relative comparisons are being made.
|
|
/// For example, consider three points A, B, and C. To determine whether B or C is further from A,
|
|
/// compare the distance between A and B to the distance between A and C. Calculating the two distances
|
|
/// involves two square roots, which are computationally expensive. However, using distance squared
|
|
/// provides the same information and avoids calculating two square roots.
|
|
/// </remarks>
|
|
public static void DistanceSquared( ref Vec2 value1, ref Vec2 value2, out float result )
|
|
{
|
|
float x = value1.X - value2.X;
|
|
float y = value1.Y - value2.Y;
|
|
|
|
result = ( x * x ) + ( y * y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates 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 the two vectors.</returns>
|
|
/// <remarks>Distance squared is the value before taking the square root.
|
|
/// Distance squared can often be used in place of distance if relative comparisons are being made.
|
|
/// For example, consider three points A, B, and C. To determine whether B or C is further from A,
|
|
/// compare the distance between A and B to the distance between A and C. Calculating the two distances
|
|
/// involves two square roots, which are computationally expensive. However, using distance squared
|
|
/// provides the same information and avoids calculating two square roots.
|
|
/// </remarks>
|
|
public static float DistanceSquared( Vec2 value1, Vec2 value2 )
|
|
{
|
|
float x = value1.X - value2.X;
|
|
float y = value1.Y - value2.Y;
|
|
|
|
return ( x * x ) + ( y * y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the dot product of two vectors.
|
|
/// </summary>
|
|
/// <param name="left">First source vector.</param>
|
|
/// <param name="right">Second source vector.</param>
|
|
/// <param name="result">When the method completes, contains the dot product of the two vectors.</param>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static void Dot( ref Vec2 left, ref Vec2 right, out float result )
|
|
{
|
|
result = ( left.X * right.X ) + ( left.Y * right.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the dot product of two vectors.
|
|
/// </summary>
|
|
/// <param name="left">First source vector.</param>
|
|
/// <param name="right">Second source vector.</param>
|
|
/// <returns>The dot product of the two vectors.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static float Dot( Vec2 left, Vec2 right )
|
|
{
|
|
return ( left.X * right.X ) + ( left.Y * right.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Converts the vector into a unit vector.
|
|
/// </summary>
|
|
/// <param name="value">The vector to normalize.</param>
|
|
/// <param name="result">When the method completes, contains the normalized vector.</param>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static void Normalize( ref Vec2 value, out Vec2 result )
|
|
{
|
|
result = value;
|
|
result.Normalize();
|
|
}
|
|
|
|
/// <summary>
|
|
/// Converts the vector into a unit vector.
|
|
/// </summary>
|
|
/// <param name="value">The vector to normalize.</param>
|
|
/// <returns>The normalized vector.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 Normalize( Vec2 value )
|
|
{
|
|
value.Normalize();
|
|
return value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a linear interpolation between two vectors.
|
|
/// </summary>
|
|
/// <param name="start">Start vector.</param>
|
|
/// <param name="end">End vector.</param>
|
|
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
|
|
/// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
|
|
/// <remarks>
|
|
/// This method performs the linear interpolation based on the following formula.
|
|
/// <code>start + (end - start) * amount</code>
|
|
/// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
|
|
/// </remarks>
|
|
public static void Lerp( ref Vec2 start, ref Vec2 end, float amount, out Vec2 result )
|
|
{
|
|
result.X = start.X + ( ( end.X - start.X ) * amount );
|
|
result.Y = start.Y + ( ( end.Y - start.Y ) * amount );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a linear interpolation between two vectors.
|
|
/// </summary>
|
|
/// <param name="start">Start vector.</param>
|
|
/// <param name="end">End vector.</param>
|
|
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
|
|
/// <returns>The linear interpolation of the two vectors.</returns>
|
|
/// <remarks>
|
|
/// This method performs the linear interpolation based on the following formula.
|
|
/// <code>start + (end - start) * amount</code>
|
|
/// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
|
|
/// </remarks>
|
|
public static Vec2 Lerp( Vec2 start, Vec2 end, float amount )
|
|
{
|
|
Vec2 result;
|
|
Lerp( ref start, ref end, amount, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a cubic interpolation between two vectors.
|
|
/// </summary>
|
|
/// <param name="start">Start vector.</param>
|
|
/// <param name="end">End vector.</param>
|
|
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
|
|
/// <param name="result">When the method completes, contains the cubic interpolation of the two vectors.</param>
|
|
public static void SmoothStep( ref Vec2 start, ref Vec2 end, float amount, out Vec2 result )
|
|
{
|
|
amount = ( amount > 1.0f ) ? 1.0f : ( ( amount < 0.0f ) ? 0.0f : amount );
|
|
amount = ( amount * amount ) * ( 3.0f - ( 2.0f * amount ) );
|
|
|
|
result.X = start.X + ( ( end.X - start.X ) * amount );
|
|
result.Y = start.Y + ( ( end.Y - start.Y ) * amount );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a cubic interpolation between two vectors.
|
|
/// </summary>
|
|
/// <param name="start">Start vector.</param>
|
|
/// <param name="end">End vector.</param>
|
|
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
|
|
/// <returns>The cubic interpolation of the two vectors.</returns>
|
|
public static Vec2 SmoothStep( Vec2 start, Vec2 end, float amount )
|
|
{
|
|
Vec2 result;
|
|
SmoothStep( ref start, ref end, amount, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a Hermite spline interpolation.
|
|
/// </summary>
|
|
/// <param name="value1">First source position vector.</param>
|
|
/// <param name="tangent1">First source tangent vector.</param>
|
|
/// <param name="value2">Second source position vector.</param>
|
|
/// <param name="tangent2">Second source tangent vector.</param>
|
|
/// <param name="amount">Weighting factor.</param>
|
|
/// <param name="result">When the method completes, contains the result of the Hermite spline interpolation.</param>
|
|
public static void Hermite( ref Vec2 value1, ref Vec2 tangent1, ref Vec2 value2, ref Vec2 tangent2, float amount, out Vec2 result )
|
|
{
|
|
float squared = amount * amount;
|
|
float cubed = amount * squared;
|
|
float part1 = ( ( 2.0f * cubed ) - ( 3.0f * squared ) ) + 1.0f;
|
|
float part2 = ( -2.0f * cubed ) + ( 3.0f * squared );
|
|
float part3 = ( cubed - ( 2.0f * squared ) ) + amount;
|
|
float part4 = cubed - squared;
|
|
|
|
result.X = ( ( ( value1.X * part1 ) + ( value2.X * part2 ) ) + ( tangent1.X * part3 ) ) + ( tangent2.X * part4 );
|
|
result.Y = ( ( ( value1.Y * part1 ) + ( value2.Y * part2 ) ) + ( tangent1.Y * part3 ) ) + ( tangent2.Y * part4 );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a Hermite spline interpolation.
|
|
/// </summary>
|
|
/// <param name="value1">First source position vector.</param>
|
|
/// <param name="tangent1">First source tangent vector.</param>
|
|
/// <param name="value2">Second source position vector.</param>
|
|
/// <param name="tangent2">Second source tangent vector.</param>
|
|
/// <param name="amount">Weighting factor.</param>
|
|
/// <returns>The result of the Hermite spline interpolation.</returns>
|
|
public static Vec2 Hermite( Vec2 value1, Vec2 tangent1, Vec2 value2, Vec2 tangent2, float amount )
|
|
{
|
|
Vec2 result;
|
|
Hermite( ref value1, ref tangent1, ref value2, ref tangent2, amount, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a Catmull-Rom interpolation using the specified positions.
|
|
/// </summary>
|
|
/// <param name="value1">The first position in the interpolation.</param>
|
|
/// <param name="value2">The second position in the interpolation.</param>
|
|
/// <param name="value3">The third position in the interpolation.</param>
|
|
/// <param name="value4">The fourth position in the interpolation.</param>
|
|
/// <param name="amount">Weighting factor.</param>
|
|
/// <param name="result">When the method completes, contains the result of the Catmull-Rom interpolation.</param>
|
|
public static void CatmullRom( ref Vec2 value1, ref Vec2 value2, ref Vec2 value3, ref Vec2 value4, float amount, out Vec2 result )
|
|
{
|
|
float squared = amount * amount;
|
|
float cubed = amount * squared;
|
|
|
|
result.X = 0.5f * ( ( ( ( 2.0f * value2.X ) + ( ( -value1.X + value3.X ) * amount ) ) +
|
|
( ( ( ( ( 2.0f * value1.X ) - ( 5.0f * value2.X ) ) + ( 4.0f * value3.X ) ) - value4.X ) * squared ) ) +
|
|
( ( ( ( -value1.X + ( 3.0f * value2.X ) ) - ( 3.0f * value3.X ) ) + value4.X ) * cubed ) );
|
|
|
|
result.Y = 0.5f * ( ( ( ( 2.0f * value2.Y ) + ( ( -value1.Y + value3.Y ) * amount ) ) +
|
|
( ( ( ( ( 2.0f * value1.Y ) - ( 5.0f * value2.Y ) ) + ( 4.0f * value3.Y ) ) - value4.Y ) * squared ) ) +
|
|
( ( ( ( -value1.Y + ( 3.0f * value2.Y ) ) - ( 3.0f * value3.Y ) ) + value4.Y ) * cubed ) );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a Catmull-Rom interpolation using the specified positions.
|
|
/// </summary>
|
|
/// <param name="value1">The first position in the interpolation.</param>
|
|
/// <param name="value2">The second position in the interpolation.</param>
|
|
/// <param name="value3">The third position in the interpolation.</param>
|
|
/// <param name="value4">The fourth position in the interpolation.</param>
|
|
/// <param name="amount">Weighting factor.</param>
|
|
/// <returns>A vector that is the result of the Catmull-Rom interpolation.</returns>
|
|
public static Vec2 CatmullRom( Vec2 value1, Vec2 value2, Vec2 value3, Vec2 value4, float amount )
|
|
{
|
|
Vec2 result;
|
|
CatmullRom( ref value1, ref value2, ref value3, ref value4, amount, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a vector containing the smallest components of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="left">The first source vector.</param>
|
|
/// <param name="right">The second source vector.</param>
|
|
/// <param name="result">When the method completes, contains an new vector composed of the largest components of the source vectors.</param>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static void Max( ref Vec2 left, ref Vec2 right, out Vec2 result )
|
|
{
|
|
result.X = ( left.X > right.X ) ? left.X : right.X;
|
|
result.Y = ( left.Y > right.Y ) ? left.Y : right.Y;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a vector containing the largest components of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="left">The first source vector.</param>
|
|
/// <param name="right">The second source vector.</param>
|
|
/// <returns>A vector containing the largest components of the source vectors.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 Max( Vec2 left, Vec2 right )
|
|
{
|
|
Vec2 result;
|
|
Max( ref left, ref right, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a vector containing the smallest components of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="left">The first source vector.</param>
|
|
/// <param name="right">The second source vector.</param>
|
|
/// <param name="result">When the method completes, contains an new vector composed of the smallest components of the source vectors.</param>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static void Min( ref Vec2 left, ref Vec2 right, out Vec2 result )
|
|
{
|
|
result.X = ( left.X < right.X ) ? left.X : right.X;
|
|
result.Y = ( left.Y < right.Y ) ? left.Y : right.Y;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a vector containing the smallest components of the specified vectors.
|
|
/// </summary>
|
|
/// <param name="left">The first source vector.</param>
|
|
/// <param name="right">The second source vector.</param>
|
|
/// <returns>A vector containing the smallest components of the source vectors.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 Min( Vec2 left, Vec2 right )
|
|
{
|
|
Vec2 result;
|
|
Min( ref left, ref right, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the reflection of a vector off a surface that has the specified normal.
|
|
/// </summary>
|
|
/// <param name="vector">The source vector.</param>
|
|
/// <param name="normal">Normal of the surface.</param>
|
|
/// <param name="result">When the method completes, contains the reflected vector.</param>
|
|
/// <remarks>Reflect only gives the direction of a reflection off a surface, it does not determine
|
|
/// whether the original vector was close enough to the surface to hit it.</remarks>
|
|
public static void Reflect( ref Vec2 vector, ref Vec2 normal, out Vec2 result )
|
|
{
|
|
float dot = ( vector.X * normal.X ) + ( vector.Y * normal.Y );
|
|
|
|
result.X = vector.X - ( ( 2.0f * dot ) * normal.X );
|
|
result.Y = vector.Y - ( ( 2.0f * dot ) * normal.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the reflection of a vector off a surface that has the specified normal.
|
|
/// </summary>
|
|
/// <param name="vector">The source vector.</param>
|
|
/// <param name="normal">Normal of the surface.</param>
|
|
/// <returns>The reflected vector.</returns>
|
|
/// <remarks>Reflect only gives the direction of a reflection off a surface, it does not determine
|
|
/// whether the original vector was close enough to the surface to hit it.</remarks>
|
|
public static Vec2 Reflect( Vec2 vector, Vec2 normal )
|
|
{
|
|
Vec2 result;
|
|
Reflect( ref vector, ref normal, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Orthogonalizes a list of vectors.
|
|
/// </summary>
|
|
/// <param name="destination">The list of orthogonalized vectors.</param>
|
|
/// <param name="source">The list of vectors to orthogonalize.</param>
|
|
/// <remarks>
|
|
/// <para>Orthogonalization is the process of making all vectors orthogonal to each other. This
|
|
/// means that any given vector in the list will be orthogonal to any other given vector in the
|
|
/// list.</para>
|
|
/// <para>Because this method uses the modified Gram-Schmidt process, the resulting vectors
|
|
/// tend to be numerically unstable. The numeric stability decreases according to the vectors
|
|
/// position in the list so that the first vector is the most stable and the last vector is the
|
|
/// least stable.</para>
|
|
/// </remarks>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
|
|
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
|
|
public static void Orthogonalize( Vec2[] destination, params Vec2[] source )
|
|
{
|
|
//Uses the modified Gram-Schmidt process.
|
|
//q1 = m1
|
|
//q2 = m2 - ((q1 ⋅ m2) / (q1 ⋅ q1)) * q1
|
|
//q3 = m3 - ((q1 ⋅ m3) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m3) / (q2 ⋅ q2)) * q2
|
|
//q4 = m4 - ((q1 ⋅ m4) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m4) / (q2 ⋅ q2)) * q2 - ((q3 ⋅ m4) / (q3 ⋅ q3)) * q3
|
|
//q5 = ...
|
|
|
|
if( source == null )
|
|
throw new ArgumentNullException( "_source" );
|
|
if( destination == null )
|
|
throw new ArgumentNullException( "destination" );
|
|
if( destination.Length < source.Length )
|
|
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
|
|
|
|
for( int i = 0; i < source.Length; ++i )
|
|
{
|
|
Vec2 newvector = source[i];
|
|
|
|
for( int r = 0; r < i; ++r )
|
|
{
|
|
newvector -= ( Vec2.Dot( destination[r], newvector ) / Vec2.Dot( destination[r], destination[r] ) ) * destination[r];
|
|
}
|
|
|
|
destination[i] = newvector;
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Orthonormalizes a list of vectors.
|
|
/// </summary>
|
|
/// <param name="destination">The list of orthonormalized vectors.</param>
|
|
/// <param name="source">The list of vectors to orthonormalize.</param>
|
|
/// <remarks>
|
|
/// <para>Orthonormalization is the process of making all vectors orthogonal to each
|
|
/// other and making all vectors of unit length. This means that any given vector will
|
|
/// be orthogonal to any other given vector in the list.</para>
|
|
/// <para>Because this method uses the modified Gram-Schmidt process, the resulting vectors
|
|
/// tend to be numerically unstable. The numeric stability decreases according to the vectors
|
|
/// position in the list so that the first vector is the most stable and the last vector is the
|
|
/// least stable.</para>
|
|
/// </remarks>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
|
|
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
|
|
public static void Orthonormalize( Vec2[] destination, params Vec2[] source )
|
|
{
|
|
//Uses the modified Gram-Schmidt process.
|
|
//Because we are making unit vectors, we can optimize the math for orthogonalization
|
|
//and simplify the projection operation to remove the division.
|
|
//q1 = m1 / |m1|
|
|
//q2 = (m2 - (q1 ⋅ m2) * q1) / |m2 - (q1 ⋅ m2) * q1|
|
|
//q3 = (m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2) / |m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2|
|
|
//q4 = (m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3) / |m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3|
|
|
//q5 = ...
|
|
|
|
if( source == null )
|
|
throw new ArgumentNullException( "_source" );
|
|
if( destination == null )
|
|
throw new ArgumentNullException( "destination" );
|
|
if( destination.Length < source.Length )
|
|
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
|
|
|
|
for( int i = 0; i < source.Length; ++i )
|
|
{
|
|
Vec2 newvector = source[i];
|
|
|
|
for( int r = 0; r < i; ++r )
|
|
{
|
|
newvector -= Vec2.Dot( destination[r], newvector ) * destination[r];
|
|
}
|
|
|
|
newvector.Normalize();
|
|
destination[i] = newvector;
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a 2D vector by the given <see cref="math.Quaternion"/> rotation.
|
|
/// </summary>
|
|
/// <param name="vector">The vector to rotate.</param>
|
|
/// <param name="rotation">The <see cref="math.Quaternion"/> rotation to apply.</param>
|
|
/// <param name="result">When the method completes, contains the transformed <see cref="math.Vec4"/>.</param>
|
|
public static void Transform( ref Vec2 vector, ref Quaternion rotation, out Vec2 result )
|
|
{
|
|
float x = rotation.X + rotation.X;
|
|
float y = rotation.Y + rotation.Y;
|
|
float z = rotation.Z + rotation.Z;
|
|
float wz = rotation.W * z;
|
|
float xx = rotation.X * x;
|
|
float xy = rotation.X * y;
|
|
float yy = rotation.Y * y;
|
|
float zz = rotation.Z * z;
|
|
|
|
result = new Vec2( ( vector.X * ( 1.0f - yy - zz ) ) + ( vector.Y * ( xy - wz ) ), ( vector.X * ( xy + wz ) ) + ( vector.Y * ( 1.0f - xx - zz ) ) );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a 2D vector by the given <see cref="math.Quaternion"/> rotation.
|
|
/// </summary>
|
|
/// <param name="vector">The vector to rotate.</param>
|
|
/// <param name="rotation">The <see cref="math.Quaternion"/> rotation to apply.</param>
|
|
/// <returns>The transformed <see cref="math.Vec4"/>.</returns>
|
|
public static Vec2 Transform( Vec2 vector, Quaternion rotation )
|
|
{
|
|
Vec2 result;
|
|
Transform( ref vector, ref rotation, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms an array of vectors by the given <see cref="math.Quaternion"/> rotation.
|
|
/// </summary>
|
|
/// <param name="source">The array of vectors to transform.</param>
|
|
/// <param name="rotation">The <see cref="math.Quaternion"/> rotation to apply.</param>
|
|
/// <param name="destination">The array for which the transformed vectors are stored.
|
|
/// This array may be the same array as <paramref name="source"/>.</param>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
|
|
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
|
|
public static void Transform( Vec2[] source, ref Quaternion rotation, Vec2[] destination )
|
|
{
|
|
if( source == null )
|
|
throw new ArgumentNullException( "_source" );
|
|
if( destination == null )
|
|
throw new ArgumentNullException( "destination" );
|
|
if( destination.Length < source.Length )
|
|
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
|
|
|
|
float x = rotation.X + rotation.X;
|
|
float y = rotation.Y + rotation.Y;
|
|
float z = rotation.Z + rotation.Z;
|
|
float wz = rotation.W * z;
|
|
float xx = rotation.X * x;
|
|
float xy = rotation.X * y;
|
|
float yy = rotation.Y * y;
|
|
float zz = rotation.Z * z;
|
|
|
|
float num1 = ( 1.0f - yy - zz );
|
|
float num2 = ( xy - wz );
|
|
float num3 = ( xy + wz );
|
|
float num4 = ( 1.0f - xx - zz );
|
|
|
|
for( int i = 0; i < source.Length; ++i )
|
|
{
|
|
destination[i] = new Vec2(
|
|
( source[i].X * num1 ) + ( source[i].Y * num2 ),
|
|
( source[i].X * num3 ) + ( source[i].Y * num4 ) );
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a 2D vector by the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="vector">The source vector.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <param name="result">When the method completes, contains the transformed <see cref="math.Vec4"/>.</param>
|
|
public static void Transform( ref Vec2 vector, ref Matrix transform, out Vec4 result )
|
|
{
|
|
result = new Vec4(
|
|
( vector.X * transform.M11 ) + ( vector.Y * transform.M21 ) + transform.M41,
|
|
( vector.X * transform.M12 ) + ( vector.Y * transform.M22 ) + transform.M42,
|
|
( vector.X * transform.M13 ) + ( vector.Y * transform.M23 ) + transform.M43,
|
|
( vector.X * transform.M14 ) + ( vector.Y * transform.M24 ) + transform.M44 );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a 2D vector by the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="vector">The source vector.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <returns>The transformed <see cref="math.Vec4"/>.</returns>
|
|
public static Vec4 Transform( Vec2 vector, Matrix transform )
|
|
{
|
|
Vec4 result;
|
|
Transform( ref vector, ref transform, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms an array of 2D vectors by the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="source">The array of vectors to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <param name="destination">The array for which the transformed vectors are stored.</param>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
|
|
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
|
|
public static void Transform( Vec2[] source, ref Matrix transform, Vec4[] destination )
|
|
{
|
|
if( source == null )
|
|
throw new ArgumentNullException( "_source" );
|
|
if( destination == null )
|
|
throw new ArgumentNullException( "destination" );
|
|
if( destination.Length < source.Length )
|
|
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
|
|
|
|
for( int i = 0; i < source.Length; ++i )
|
|
{
|
|
Transform( ref source[i], ref transform, out destination[i] );
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a coordinate transformation using the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="coordinate">The coordinate vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <param name="result">When the method completes, contains the transformed coordinates.</param>
|
|
/// <remarks>
|
|
/// A coordinate transform performs the transformation with the assumption that the w component
|
|
/// is one. The four dimensional vector obtained from the transformation operation has each
|
|
/// component in the vector divided by the w component. This forces the wcomponent to be one and
|
|
/// therefore makes the vector homogeneous. The homogeneous vector is often prefered when working
|
|
/// with coordinates as the w component can safely be ignored.
|
|
/// </remarks>
|
|
public static void TransformCoordinate( ref Vec2 coordinate, ref Matrix transform, out Vec2 result )
|
|
{
|
|
Vec4 vector = new Vec4();
|
|
vector.X = ( coordinate.X * transform.M11 ) + ( coordinate.Y * transform.M21 ) + transform.M41;
|
|
vector.Y = ( coordinate.X * transform.M12 ) + ( coordinate.Y * transform.M22 ) + transform.M42;
|
|
vector.Z = ( coordinate.X * transform.M13 ) + ( coordinate.Y * transform.M23 ) + transform.M43;
|
|
vector.W = 1f / ( ( coordinate.X * transform.M14 ) + ( coordinate.Y * transform.M24 ) + transform.M44 );
|
|
|
|
result = new Vec2( vector.X * vector.W, vector.Y * vector.W );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a coordinate transformation using the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="coordinate">The coordinate vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <returns>The transformed coordinates.</returns>
|
|
/// <remarks>
|
|
/// A coordinate transform performs the transformation with the assumption that the w component
|
|
/// is one. The four dimensional vector obtained from the transformation operation has each
|
|
/// component in the vector divided by the w component. This forces the wcomponent to be one and
|
|
/// therefore makes the vector homogeneous. The homogeneous vector is often prefered when working
|
|
/// with coordinates as the w component can safely be ignored.
|
|
/// </remarks>
|
|
public static Vec2 TransformCoordinate( Vec2 coordinate, Matrix transform )
|
|
{
|
|
Vec2 result;
|
|
TransformCoordinate( ref coordinate, ref transform, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a coordinate transformation on an array of vectors using the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="source">The array of coordinate vectors to trasnform.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <param name="destination">The array for which the transformed vectors are stored.
|
|
/// This array may be the same array as <paramref name="source"/>.</param>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
|
|
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
|
|
/// <remarks>
|
|
/// A coordinate transform performs the transformation with the assumption that the w component
|
|
/// is one. The four dimensional vector obtained from the transformation operation has each
|
|
/// component in the vector divided by the w component. This forces the wcomponent to be one and
|
|
/// therefore makes the vector homogeneous. The homogeneous vector is often prefered when working
|
|
/// with coordinates as the w component can safely be ignored.
|
|
/// </remarks>
|
|
public static void TransformCoordinate( Vec2[] source, ref Matrix transform, Vec2[] destination )
|
|
{
|
|
if( source == null )
|
|
throw new ArgumentNullException( "_source" );
|
|
if( destination == null )
|
|
throw new ArgumentNullException( "destination" );
|
|
if( destination.Length < source.Length )
|
|
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
|
|
|
|
for( int i = 0; i < source.Length; ++i )
|
|
{
|
|
TransformCoordinate( ref source[i], ref transform, out destination[i] );
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a normal transformation using the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="normal">The normal vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <param name="result">When the method completes, contains the transformed normal.</param>
|
|
/// <remarks>
|
|
/// A normal transform performs the transformation with the assumption that the w component
|
|
/// is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The
|
|
/// end result is a vector that is not translated, but all other transformation properties
|
|
/// apply. This is often prefered for normal vectors as normals purely represent direction
|
|
/// rather than location because normal vectors should not be translated.
|
|
/// </remarks>
|
|
public static void TransformNormal( ref Vec2 normal, ref Matrix transform, out Vec2 result )
|
|
{
|
|
result = new Vec2(
|
|
( normal.X * transform.M11 ) + ( normal.Y * transform.M21 ),
|
|
( normal.X * transform.M12 ) + ( normal.Y * transform.M22 ) );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a normal transformation using the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="normal">The normal vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <returns>The transformed normal.</returns>
|
|
/// <remarks>
|
|
/// A normal transform performs the transformation with the assumption that the w component
|
|
/// is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The
|
|
/// end result is a vector that is not translated, but all other transformation properties
|
|
/// apply. This is often prefered for normal vectors as normals purely represent direction
|
|
/// rather than location because normal vectors should not be translated.
|
|
/// </remarks>
|
|
public static Vec2 TransformNormal( Vec2 normal, Matrix transform )
|
|
{
|
|
Vec2 result;
|
|
TransformNormal( ref normal, ref transform, out result );
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a normal transformation on an array of vectors using the given <see cref="math.Matrix"/>.
|
|
/// </summary>
|
|
/// <param name="source">The array of normal vectors to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
|
|
/// <param name="destination">The array for which the transformed vectors are stored.
|
|
/// This array may be the same array as <paramref name="source"/>.</param>
|
|
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
|
|
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
|
|
/// <remarks>
|
|
/// A normal transform performs the transformation with the assumption that the w component
|
|
/// is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The
|
|
/// end result is a vector that is not translated, but all other transformation properties
|
|
/// apply. This is often prefered for normal vectors as normals purely represent direction
|
|
/// rather than location because normal vectors should not be translated.
|
|
/// </remarks>
|
|
public static void TransformNormal( Vec2[] source, ref Matrix transform, Vec2[] destination )
|
|
{
|
|
if( source == null )
|
|
throw new ArgumentNullException( "_source" );
|
|
if( destination == null )
|
|
throw new ArgumentNullException( "destination" );
|
|
if( destination.Length < source.Length )
|
|
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
|
|
|
|
for( int i = 0; i < source.Length; ++i )
|
|
{
|
|
TransformNormal( ref source[i], ref transform, out destination[i] );
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Adds two vectors.
|
|
/// </summary>
|
|
/// <param name="left">The first vector to add.</param>
|
|
/// <param name="right">The second vector to add.</param>
|
|
/// <returns>The sum of the two vectors.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator +( Vec2 left, Vec2 right )
|
|
{
|
|
return new Vec2( left.X + right.X, left.Y + right.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Assert a vector (return it unchanged).
|
|
/// </summary>
|
|
/// <param name="value">The vector to assert (unchange).</param>
|
|
/// <returns>The asserted (unchanged) vector.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator +( Vec2 value )
|
|
{
|
|
return value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Subtracts two vectors.
|
|
/// </summary>
|
|
/// <param name="left">The first vector to subtract.</param>
|
|
/// <param name="right">The second vector to subtract.</param>
|
|
/// <returns>The difference of the two vectors.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator -( Vec2 left, Vec2 right )
|
|
{
|
|
return new Vec2( left.X - right.X, left.Y - right.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Reverses the direction of a given vector.
|
|
/// </summary>
|
|
/// <param name="value">The vector to negate.</param>
|
|
/// <returns>A vector facing in the opposite direction.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator -( Vec2 value )
|
|
{
|
|
return new Vec2( -value.X, -value.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Modulates a vector with another by performing component-wise multiplication.
|
|
/// </summary>
|
|
/// <param name="left">The first vector to multiply.</param>
|
|
/// <param name="right">The second vector to multiply.</param>
|
|
/// <returns>The multiplication of the two vectors.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator *( Vec2 left, Vec2 right )
|
|
{
|
|
return new Vec2( left.X * right.X, left.Y * right.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scales a vector by the given value.
|
|
/// </summary>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <param name="scale">The amount by which to scale the vector.</param>
|
|
/// <returns>The scaled vector.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator *( float scale, Vec2 value )
|
|
{
|
|
return new Vec2( value.X * scale, value.Y * scale );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scales a vector by the given value.
|
|
/// </summary>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <param name="scale">The amount by which to scale the vector.</param>
|
|
/// <returns>The scaled vector.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator *( Vec2 value, float scale )
|
|
{
|
|
return new Vec2( value.X * scale, value.Y * scale );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scales a vector by the given value.
|
|
/// </summary>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <param name="scale">The amount by which to scale the vector.</param>
|
|
/// <returns>The scaled vector.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator /( Vec2 value, float scale )
|
|
{
|
|
return new Vec2( value.X / scale, value.Y / scale );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides a numerator by a vector.
|
|
/// </summary>
|
|
/// <param name="numerator">The numerator.</param>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The scaled vector.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator /( float numerator, Vec2 value )
|
|
{
|
|
return new Vec2( numerator / value.X, numerator / value.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides a vector by the given vector, component-wise.
|
|
/// </summary>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <param name="by">The by.</param>
|
|
/// <returns>The scaled vector.</returns>
|
|
[MethodImpl( MethodImplOptions.AggressiveInlining )]
|
|
public static Vec2 operator /( Vec2 value, Vec2 by )
|
|
{
|
|
return new Vec2( value.X / by.X, value.Y / by.Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Tests for equality between two objects.
|
|
/// </summary>
|
|
/// <param name="left">The first value to compare.</param>
|
|
/// <param name="right">The second value to compare.</param>
|
|
/// <returns><c>true</c> if <paramref name="left"/> has the same value as <paramref name="right"/>; otherwise, <c>false</c>.</returns>
|
|
public static bool operator ==( Vec2 left, Vec2 right )
|
|
{
|
|
return left.Equals( right );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Tests for inequality between two objects.
|
|
/// </summary>
|
|
/// <param name="left">The first value to compare.</param>
|
|
/// <param name="right">The second value to compare.</param>
|
|
/// <returns><c>true</c> if <paramref name="left"/> has a different value than <paramref name="right"/>; otherwise, <c>false</c>.</returns>
|
|
public static bool operator !=( Vec2 left, Vec2 right )
|
|
{
|
|
return !left.Equals( right );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an explicit conversion from <see cref="math.Vec2"/> to <see cref="math.Vec3"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static explicit operator Vec3( Vec2 value )
|
|
{
|
|
return new Vec3( value, 0.0f );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an explicit conversion from <see cref="math.Vec2"/> to <see cref="math.Vec4"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static explicit operator Vec4( Vec2 value )
|
|
{
|
|
return new Vec4( value, 0.0f, 0.0f );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public override string ToString()
|
|
{
|
|
return string.Format( CultureInfo.CurrentCulture, "X:{0} Y:{1}", X, Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="format">The format.</param>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public string ToString( string format )
|
|
{
|
|
if( format == null )
|
|
return ToString();
|
|
|
|
return string.Format( CultureInfo.CurrentCulture, "X:{0} Y:{1}", X.ToString( format, CultureInfo.CurrentCulture ), Y.ToString( format, CultureInfo.CurrentCulture ) );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="formatProvider">The format provider.</param>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public string ToString( IFormatProvider formatProvider )
|
|
{
|
|
return string.Format( formatProvider, "X:{0} Y:{1}", X, Y );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="string"/> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="format">The format.</param>
|
|
/// <param name="formatProvider">The format provider.</param>
|
|
/// <returns>
|
|
/// A <see cref="string"/> that represents this instance.
|
|
/// </returns>
|
|
public string ToString( string format, IFormatProvider formatProvider )
|
|
{
|
|
if( format == null )
|
|
ToString( formatProvider );
|
|
|
|
return string.Format( formatProvider, "X:{0} Y:{1}", X.ToString( format, formatProvider ), Y.ToString( format, formatProvider ) );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a hash code for this instance.
|
|
/// </summary>
|
|
/// <returns>
|
|
/// A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.
|
|
/// </returns>
|
|
public override int GetHashCode()
|
|
{
|
|
return X.GetHashCode() + Y.GetHashCode();
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="math.Vec2"/> is equal to this instance.
|
|
/// </summary>
|
|
/// <param name="other">The <see cref="math.Vec2"/> to compare with this instance.</param>
|
|
/// <returns>
|
|
/// <c>true</c> if the specified <see cref="math.Vec2"/> is equal to this instance; otherwise, <c>false</c>.
|
|
/// </returns>
|
|
public bool Equals( Vec2 other )
|
|
{
|
|
return ( (float)Math.Abs( other.X - X ) < MathUtil.ZeroTolerance &&
|
|
(float)Math.Abs( other.Y - Y ) < MathUtil.ZeroTolerance );
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="object"/> is equal to this instance.
|
|
/// </summary>
|
|
/// <param name="value">The <see cref="object"/> to compare with this instance.</param>
|
|
/// <returns>
|
|
/// <c>true</c> if the specified <see cref="object"/> is equal to this instance; otherwise, <c>false</c>.
|
|
/// </returns>
|
|
public override bool Equals( object value )
|
|
{
|
|
if( value == null )
|
|
return false;
|
|
|
|
if( value.GetType() != GetType() )
|
|
return false;
|
|
|
|
return Equals( (Vec2)value );
|
|
}
|
|
|
|
#if WPFInterop
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="math.Vector2"/> to <see cref="System.Windows.Point"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator System.Windows.Point(Vector2 value)
|
|
{
|
|
return new System.Windows.Point(value.X, value.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an explicit conversion from <see cref="System.Windows.Point"/> to <see cref="math.Vector2"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static explicit operator Vector2(System.Windows.Point value)
|
|
{
|
|
return new Vector2((float)value.X, (float)value.Y);
|
|
}
|
|
#endif
|
|
|
|
#if XnaInterop
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="math.Vector2"/> to <see cref="Microsoft.Xna.Framework.Vector2"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator Microsoft.Xna.Framework.Vector2(Vector2 value)
|
|
{
|
|
return new Microsoft.Xna.Framework.Vector2(value.X, value.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="Microsoft.Xna.Framework.Vector2"/> to <see cref="math.Vector2"/>.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator Vector2(Microsoft.Xna.Framework.Vector2 value)
|
|
{
|
|
return new Vector2(value.X, value.Y);
|
|
}
|
|
#endif
|
|
}
|
|
}
|