1682 lines
75 KiB
C#
1682 lines
75 KiB
C#
// Copyright (c) 2012-2024 Wojciech Figat. All rights reserved.
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// -----------------------------------------------------------------------------
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// Original code from SharpDX project. https://github.com/sharpdx/SharpDX/
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// Greetings to Alexandre Mutel. Original code published with the following license:
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// -----------------------------------------------------------------------------
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// Copyright (c) 2010-2014 SharpDX - Alexandre Mutel
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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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// 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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namespace FlaxEngine
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{
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[Serializable]
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#if FLAX_EDITOR
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[System.ComponentModel.TypeConverter(typeof(TypeConverters.Float2Converter))]
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#endif
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partial struct Float2 : IEquatable<Float2>, IFormattable
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{
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private static readonly string _formatString = "X:{0:F2} Y:{1:F2}";
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/// <summary>
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/// The size of the <see cref="Float2" /> type, in bytes.
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/// </summary>
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public static readonly int SizeInBytes = Marshal.SizeOf(typeof(Float2));
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/// <summary>
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/// A <see cref="Float2" /> with all of its components set to zero.
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/// </summary>
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public static readonly Float2 Zero;
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/// <summary>
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/// The X unit <see cref="Float2" /> (1, 0).
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/// </summary>
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public static readonly Float2 UnitX = new Float2(1.0f, 0.0f);
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/// <summary>
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/// The Y unit <see cref="Float2" /> (0, 1).
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/// </summary>
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public static readonly Float2 UnitY = new Float2(0.0f, 1.0f);
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/// <summary>
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/// A <see cref="Float2" /> with all of its components set to half.
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/// </summary>
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public static readonly Float2 Half = new Float2(0.5f, 0.5f);
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/// <summary>
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/// A <see cref="Float2" /> with all of its components set to one.
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/// </summary>
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public static readonly Float2 One = new Float2(1.0f, 1.0f);
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/// <summary>
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/// A <see cref="Float2" /> with all components equal to <see cref="float.MinValue"/>.
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/// </summary>
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public static readonly Float2 Minimum = new Float2(float.MinValue);
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/// <summary>
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/// A <see cref="Float2" /> with all components equal to <see cref="float.MaxValue"/>.
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/// </summary>
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public static readonly Float2 Maximum = new Float2(float.MaxValue);
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/// <summary>
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/// Initializes a new instance of the <see cref="Float2" /> 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 Float2(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="Float2" /> 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 Float2(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="Float2" /> struct.
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/// </summary>
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/// <param name="value">A vector containing the values with which to initialize the X, Y and Z components.</param>
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public Float2(Vector2 value)
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{
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X = (float)value.X;
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Y = (float)value.Y;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="Float2" /> struct.
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/// </summary>
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/// <param name="value">A vector containing the values with which to initialize the X, Y and Z components.</param>
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public Float2(Double2 value)
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{
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X = (float)value.X;
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Y = (float)value.Y;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="Float2" /> struct.
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/// </summary>
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/// <param name="value">A vector containing the values with which to initialize the X and Y components.</param>
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public Float2(Float3 value)
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{
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X = value.X;
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Y = value.Y;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="Float2" /> struct.
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/// </summary>
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/// <param name="value">A vector containing the values with which to initialize the X and Y components.</param>
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public Float2(Float4 value)
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{
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X = value.X;
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Y = value.Y;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="Float2" /> 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 Float2(float[] values)
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{
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if (values == null)
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throw new ArgumentNullException(nameof(values));
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if (values.Length != 2)
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throw new ArgumentOutOfRangeException(nameof(values), "There must be two and only two input values for Float2.");
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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 => Mathf.IsOne(X * X + Y * Y);
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/// <summary>
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/// Gets a value indicting whether this vector is zero
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/// </summary>
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public bool IsZero => Mathf.IsZero(X) && Mathf.IsZero(Y);
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/// <summary>
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/// Gets a minimum component value
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/// </summary>
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public float MinValue => Mathf.Min(X, Y);
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/// <summary>
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/// Gets a maximum component value
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/// </summary>
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public float MaxValue => Mathf.Max(X, Y);
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/// <summary>
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/// Gets an arithmetic average value of all vector components.
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/// </summary>
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public float AvgValue => (X + Y) * (1.0f / 2.0f);
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/// <summary>
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/// Gets a sum of the component values.
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/// </summary>
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public float ValuesSum => X + Y;
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/// <summary>
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/// Gets a vector with values being absolute values of that vector.
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/// </summary>
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public Float2 Absolute => new Float2(Mathf.Abs(X), Mathf.Abs(Y));
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/// <summary>
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/// Gets a vector with values being opposite to values of that vector.
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/// </summary>
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public Float2 Negative => new Float2(-X, -Y);
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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: return X;
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case 1: return Y;
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}
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throw new ArgumentOutOfRangeException(nameof(index), "Indices for Float2 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: throw new ArgumentOutOfRangeException(nameof(index), "Indices for Float2 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><see cref="Float2.LengthSquared" /> may be preferred when only the relative length is needed and speed is of the essence.</remarks>
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public float Length => (float)Math.Sqrt(X * X + Y * Y);
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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>This method may be preferred to <see cref="Float2.Length" /> when only a relative length is needed and speed is of the essence.</remarks>
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public float LengthSquared => X * X + Y * Y;
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/// <summary>
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/// Gets the normalized vector. Returned vector has length equal 1.
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/// </summary>
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public Float2 Normalized
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{
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get
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{
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Float2 result = this;
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result.Normalize();
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return result;
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}
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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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public void Normalize()
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{
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float length = Length;
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if (length >= Mathf.Epsilon)
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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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public float[] ToArray()
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{
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return new[] { 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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public static void Add(ref Float2 left, ref Float2 right, out Float2 result)
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{
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result = new Float2(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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public static Float2 Add(Float2 left, Float2 right)
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{
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return new Float2(left.X + right.X, left.Y + right.Y);
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}
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/// <summary>
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/// Performs a component-wise addition.
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/// </summary>
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/// <param name="left">The input vector</param>
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/// <param name="right">The scalar value to be added to elements</param>
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/// <param name="result">The vector with added scalar for each element.</param>
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public static void Add(ref Float2 left, ref float right, out Float2 result)
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{
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result = new Float2(left.X + right, left.Y + right);
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}
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/// <summary>
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/// Performs a component-wise addition.
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/// </summary>
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/// <param name="left">The input vector</param>
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/// <param name="right">The scalar value to be added to elements</param>
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/// <returns>The vector with added scalar for each element.</returns>
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public static Float2 Add(Float2 left, float right)
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{
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return new Float2(left.X + right, left.Y + right);
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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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public static void Subtract(ref Float2 left, ref Float2 right, out Float2 result)
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{
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result = new Float2(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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public static Float2 Subtract(Float2 left, Float2 right)
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{
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return new Float2(left.X - right.X, left.Y - right.Y);
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}
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/// <summary>
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/// Performs a component-wise subtraction.
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/// </summary>
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/// <param name="left">The input vector</param>
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/// <param name="right">The scalar value to be subtracted from elements</param>
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/// <param name="result">The vector with subtracted scalar for each element.</param>
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public static void Subtract(ref Float2 left, ref float right, out Float2 result)
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{
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result = new Float2(left.X - right, left.Y - right);
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}
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/// <summary>
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/// Performs a component-wise subtraction.
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/// </summary>
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/// <param name="left">The input vector</param>
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/// <param name="right">The scalar value to be subtracted from elements</param>
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/// <returns>The vector with subtracted scalar for each element.</returns>
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public static Float2 Subtract(Float2 left, float right)
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{
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return new Float2(left.X - right, left.Y - right);
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}
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/// <summary>
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/// Performs a component-wise subtraction.
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/// </summary>
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/// <param name="left">The scalar value to be subtracted from elements</param>
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/// <param name="right">The input vector</param>
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/// <param name="result">The vector with subtracted scalar for each element.</param>
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public static void Subtract(ref float left, ref Float2 right, out Float2 result)
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{
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result = new Float2(left - right.X, left - right.Y);
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}
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/// <summary>
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/// Performs a component-wise subtraction.
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/// </summary>
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/// <param name="left">The scalar value to be subtracted from elements</param>
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/// <param name="right">The input vector</param>
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/// <returns>The vector with subtracted scalar for each element.</returns>
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public static Float2 Subtract(float left, Float2 right)
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{
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return new Float2(left - right.X, left - 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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public static void Multiply(ref Float2 value, float scale, out Float2 result)
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{
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result = new Float2(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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public static Float2 Multiply(Float2 value, float scale)
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{
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return new Float2(value.X * scale, value.Y * scale);
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}
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/// <summary>
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/// Multiplies 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 multiply.</param>
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/// <param name="right">The second vector to multiply.</param>
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/// <param name="result">When the method completes, contains the multiplied vector.</param>
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public static void Multiply(ref Float2 left, ref Float2 right, out Float2 result)
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{
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result = new Float2(left.X * right.X, left.Y * right.Y);
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}
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/// <summary>
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/// Multiplies 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 multiply.</param>
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/// <param name="right">The second vector to multiply.</param>
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/// <returns>The multiplied vector.</returns>
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public static Float2 Multiply(Float2 left, Float2 right)
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{
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return new Float2(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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public static void Divide(ref Float2 value, float scale, out Float2 result)
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{
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result = new Float2(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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public static Float2 Divide(Float2 value, float scale)
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{
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return new Float2(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="scale">The amount by which to scale the vector.</param>
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/// <param name="value">The vector to scale.</param>
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/// <param name="result">When the method completes, contains the scaled vector.</param>
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public static void Divide(float scale, ref Float2 value, out Float2 result)
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{
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result = new Float2(scale / value.X, scale / value.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>
|
|
/// <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>
|
|
public static Float2 Divide(float scale, Float2 value)
|
|
{
|
|
return new Float2(scale / value.X, scale / value.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Reverses the direction of a given vector.
|
|
/// </summary>
|
|
/// <param name="value">The vector to negate.</param>
|
|
/// <param name="result">When the method completes, contains a vector facing in the opposite direction.</param>
|
|
public static void Negate(ref Float2 value, out Float2 result)
|
|
{
|
|
result = new Float2(-value.X, -value.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>
|
|
public static Float2 Negate(Float2 value)
|
|
{
|
|
return new Float2(-value.X, -value.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="Float2" /> containing the 2D Cartesian coordinates of a point specified in Barycentric
|
|
/// coordinates relative to a 2D triangle.
|
|
/// </summary>
|
|
/// <param name="value1">A <see cref="Float2" /> containing the 2D Cartesian coordinates of vertex 1 of the triangle.</param>
|
|
/// <param name="value2">A <see cref="Float2" /> containing the 2D Cartesian coordinates of vertex 2 of the triangle.</param>
|
|
/// <param name="value3">A <see cref="Float2" /> containing the 2D Cartesian coordinates of vertex 3 of the triangle.</param>
|
|
/// <param name="amount1">Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in <paramref name="value2" />).</param>
|
|
/// <param name="amount2">Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in <paramref name="value3" />).</param>
|
|
/// <param name="result">When the method completes, contains the 2D Cartesian coordinates of the specified point.</param>
|
|
public static void Barycentric(ref Float2 value1, ref Float2 value2, ref Float2 value3, float amount1, float amount2, out Float2 result)
|
|
{
|
|
result = new Float2(value1.X + amount1 * (value2.X - value1.X) + amount2 * (value3.X - value1.X),
|
|
value1.Y + amount1 * (value2.Y - value1.Y) + amount2 * (value3.Y - value1.Y));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="Float2" /> containing the 2D Cartesian coordinates of a point specified in Barycentric
|
|
/// coordinates relative to a 2D triangle.
|
|
/// </summary>
|
|
/// <param name="value1">A <see cref="Float2" /> containing the 2D Cartesian coordinates of vertex 1 of the triangle.</param>
|
|
/// <param name="value2">A <see cref="Float2" /> containing the 2D Cartesian coordinates of vertex 2 of the triangle.</param>
|
|
/// <param name="value3">A <see cref="Float2" /> containing the 2D Cartesian coordinates of vertex 3 of the triangle.</param>
|
|
/// <param name="amount1">Barycentric coordinate b2, which expresses the weighting factor toward vertex 2 (specified in <paramref name="value2" />).</param>
|
|
/// <param name="amount2">Barycentric coordinate b3, which expresses the weighting factor toward vertex 3 (specified in <paramref name="value3" />).</param>
|
|
/// <returns>A new <see cref="Float2" /> containing the 2D Cartesian coordinates of the specified point.</returns>
|
|
public static Float2 Barycentric(Float2 value1, Float2 value2, Float2 value3, float amount1, float amount2)
|
|
{
|
|
Barycentric(ref value1, ref value2, ref value3, amount1, amount2, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Restricts a value to be within a specified range.
|
|
/// </summary>
|
|
/// <param name="value">The value to clamp.</param>
|
|
/// <param name="min">The minimum value.</param>
|
|
/// <param name="max">The maximum value.</param>
|
|
/// <param name="result">When the method completes, contains the clamped value.</param>
|
|
public static void Clamp(ref Float2 value, ref Float2 min, ref Float2 max, out Float2 result)
|
|
{
|
|
float x = value.X;
|
|
x = x > max.X ? max.X : x;
|
|
x = x < min.X ? min.X : x;
|
|
float y = value.Y;
|
|
y = y > max.Y ? max.Y : y;
|
|
y = y < min.Y ? min.Y : y;
|
|
result = new Float2(x, y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Restricts a value to be within a specified range.
|
|
/// </summary>
|
|
/// <param name="value">The value to clamp.</param>
|
|
/// <param name="min">The minimum value.</param>
|
|
/// <param name="max">The maximum value.</param>
|
|
/// <returns>The clamped value.</returns>
|
|
public static Float2 Clamp(Float2 value, Float2 min, Float2 max)
|
|
{
|
|
Clamp(ref value, ref min, ref max, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Saturates this instance in the range [0,1].
|
|
/// </summary>
|
|
public void Saturate()
|
|
{
|
|
X = X < 0.0f ? 0.0f : X > 1.0f ? 1.0f : X;
|
|
Y = Y < 0.0f ? 0.0f : Y > 1.0f ? 1.0f : Y;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the area of the triangle.
|
|
/// </summary>
|
|
/// <param name="v0">The first triangle vertex.</param>
|
|
/// <param name="v1">The second triangle vertex.</param>
|
|
/// <param name="v2">The third triangle vertex.</param>
|
|
/// <returns>The triangle area.</returns>
|
|
public static float TriangleArea(ref Float2 v0, ref Float2 v1, ref Float2 v2)
|
|
{
|
|
return Mathf.Abs((v0.X * (v1.Y - v2.Y) + v1.X * (v2.Y - v0.Y) + v2.X * (v0.Y - v1.Y)) / 2);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the 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 distance between the two vectors.</param>
|
|
/// <remarks><see cref="Float2.DistanceSquared(ref Float2, ref Float2, out float)" /> may be preferred when only the relative distance is needed and speed is of the essence.</remarks>
|
|
public static void Distance(ref Float2 value1, ref Float2 value2, out float result)
|
|
{
|
|
float x = value1.X - value2.X;
|
|
float y = value1.Y - value2.Y;
|
|
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="Float2.DistanceSquared(Float2, Float2)" /> may be preferred when only the relative distance is needed and speed is of the essence.</remarks>
|
|
public static float Distance(Float2 value1, Float2 value2)
|
|
{
|
|
float x = value1.X - value2.X;
|
|
float y = value1.Y - value2.Y;
|
|
return (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="Float2.DistanceSquared(ref Float2, ref Float2, out float)" /> may be preferred when only the relative distance is needed and speed is of the essence.</remarks>
|
|
public static float Distance(ref Float2 value1, ref Float2 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>
|
|
public static void DistanceSquared(ref Float2 value1, ref Float2 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>
|
|
public static float DistanceSquared(ref Float2 value1, ref Float2 value2)
|
|
{
|
|
float x = value1.X - value2.X;
|
|
float y = value1.Y - value2.Y;
|
|
return 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>
|
|
public static float DistanceSquared(Float2 value1, Float2 value2)
|
|
{
|
|
float x = value1.X - value2.X;
|
|
float y = value1.Y - value2.Y;
|
|
return x * x + y * y;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Tests whether one vector is near another vector.
|
|
/// </summary>
|
|
/// <param name="left">The left vector.</param>
|
|
/// <param name="right">The right vector.</param>
|
|
/// <param name="epsilon">The epsilon.</param>
|
|
/// <returns><c>true</c> if left and right are near, <c>false</c> otherwise</returns>
|
|
public static bool NearEqual(Float2 left, Float2 right, float epsilon = Mathf.Epsilon)
|
|
{
|
|
return NearEqual(ref left, ref right, epsilon);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Tests whether one vector is near another vector.
|
|
/// </summary>
|
|
/// <param name="left">The left vector.</param>
|
|
/// <param name="right">The right vector.</param>
|
|
/// <param name="epsilon">The epsilon.</param>
|
|
/// <returns><c>true</c> if left and right are near another, <c>false</c> otherwise</returns>
|
|
public static bool NearEqual(ref Float2 left, ref Float2 right, float epsilon = Mathf.Epsilon)
|
|
{
|
|
return Mathf.WithinEpsilon(left.X, right.X, epsilon) && Mathf.WithinEpsilon(left.Y, right.Y, epsilon);
|
|
}
|
|
|
|
/// <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>
|
|
public static void Dot(ref Float2 left, ref Float2 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>
|
|
public static float Dot(ref Float2 left, ref Float2 right)
|
|
{
|
|
return 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>
|
|
public static float Dot(Float2 left, Float2 right)
|
|
{
|
|
return left.X * right.X + left.Y * right.Y;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the cross 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 cross product of the two vectors.</param>
|
|
public static void Cross(ref Float2 left, ref Float2 right, out float result)
|
|
{
|
|
result = left.X * right.Y - left.Y * right.X;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the cross product of two vectors.
|
|
/// </summary>
|
|
/// <param name="left">First source vector.</param>
|
|
/// <param name="right">Second source vector.</param>
|
|
/// <returns>The cross product of the two vectors.</returns>
|
|
public static float Cross(ref Float2 left, ref Float2 right)
|
|
{
|
|
return left.X * right.Y - left.Y * right.X;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the cross product of two vectors.
|
|
/// </summary>
|
|
/// <param name="left">First source vector.</param>
|
|
/// <param name="right">Second source vector.</param>
|
|
/// <returns>The cross product of the two vectors.</returns>
|
|
public static float Cross(Float2 left, Float2 right)
|
|
{
|
|
return left.X * right.Y - left.Y * right.X;
|
|
}
|
|
|
|
/// <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>
|
|
public static void Normalize(ref Float2 value, out Float2 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>
|
|
public static Float2 Normalize(Float2 value)
|
|
{
|
|
value.Normalize();
|
|
return value;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Makes sure that Length of the output vector is always below max and above 0.
|
|
/// </summary>
|
|
/// <param name="vector">Input vector.</param>
|
|
/// <param name="max">Max Length</param>
|
|
public static Float2 ClampLength(Float2 vector, float max)
|
|
{
|
|
return ClampLength(vector, 0, max);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Makes sure that Length of the output vector is always below max and above min.
|
|
/// </summary>
|
|
/// <param name="vector">Input vector.</param>
|
|
/// <param name="min">Min Length</param>
|
|
/// <param name="max">Max Length</param>
|
|
public static Float2 ClampLength(Float2 vector, float min, float max)
|
|
{
|
|
ClampLength(vector, min, max, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Makes sure that Length of the output vector is always below max and above min.
|
|
/// </summary>
|
|
/// <param name="vector">Input vector.</param>
|
|
/// <param name="min">Min Length</param>
|
|
/// <param name="max">Max Length</param>
|
|
/// <param name="result">The result value.</param>
|
|
public static void ClampLength(Float2 vector, float min, float max, out Float2 result)
|
|
{
|
|
result = vector;
|
|
float lenSq = result.LengthSquared;
|
|
if (lenSq > max * max)
|
|
{
|
|
float scaleFactor = max / (float)Math.Sqrt(lenSq);
|
|
result.X *= scaleFactor;
|
|
result.Y *= scaleFactor;
|
|
}
|
|
if (lenSq < min * min)
|
|
{
|
|
float scaleFactor = min / (float)Math.Sqrt(lenSq);
|
|
result.X *= scaleFactor;
|
|
result.Y *= scaleFactor;
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the vector with components rounded to the nearest integer.
|
|
/// </summary>
|
|
/// <param name="v">The value.</param>
|
|
/// <returns>The result.</returns>
|
|
public static Float2 Round(Float2 v)
|
|
{
|
|
return new Float2(Mathf.Round(v.X), Mathf.Round(v.Y));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the vector with components containing the smallest integer greater to or equal to the original value.
|
|
/// </summary>
|
|
/// <param name="v">The value.</param>
|
|
/// <returns>The result.</returns>
|
|
public static Float2 Ceil(Float2 v)
|
|
{
|
|
return new Float2(Mathf.Ceil(v.X), Mathf.Ceil(v.Y));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Breaks the components of the vector into an integral and a fractional part. Returns vector made of fractional parts.
|
|
/// </summary>
|
|
/// <param name="v">The value.</param>
|
|
/// <returns>The result.</returns>
|
|
public static Float2 Mod(Float2 v)
|
|
{
|
|
return new Float2(v.X - (int)v.X, v.Y - (int)v.Y);
|
|
}
|
|
|
|
/// <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>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 Float2 start, ref Float2 end, float amount, out Float2 result)
|
|
{
|
|
result.X = Mathf.Lerp(start.X, end.X, amount);
|
|
result.Y = Mathf.Lerp(start.Y, end.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>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 Float2 Lerp(Float2 start, Float2 end, float amount)
|
|
{
|
|
Lerp(ref start, ref end, amount, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <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>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 Float2 start, ref Float2 end, ref Float2 amount, out Float2 result)
|
|
{
|
|
result.X = Mathf.Lerp(start.X, end.X, amount.X);
|
|
result.Y = Mathf.Lerp(start.Y, end.Y, amount.Y);
|
|
}
|
|
|
|
/// <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>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 Float2 Lerp(Float2 start, Float2 end, Float2 amount)
|
|
{
|
|
Lerp(ref start, ref end, ref amount, out Float2 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 Float2 start, ref Float2 end, float amount, out Float2 result)
|
|
{
|
|
amount = Mathf.SmoothStep(amount);
|
|
Lerp(ref start, ref end, amount, out 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>
|
|
/// <returns>The cubic interpolation of the two vectors.</returns>
|
|
public static Float2 SmoothStep(Float2 start, Float2 end, float amount)
|
|
{
|
|
SmoothStep(ref start, ref end, amount, out Float2 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 Float2 value1, ref Float2 tangent1, ref Float2 value2, ref Float2 tangent2, float amount, out Float2 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 Float2 Hermite(Float2 value1, Float2 tangent1, Float2 value2, Float2 tangent2, float amount)
|
|
{
|
|
Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the 2D vector perpendicular to the given 2D vector. The result is always rotated 90-degrees in a counter-clockwise direction for a 2D coordinate system where the positive Y axis goes up.
|
|
/// </summary>
|
|
/// <param name="inDirection">The input direction.</param>
|
|
/// <returns>The result.</returns>
|
|
public static Float2 Perpendicular(Float2 inDirection)
|
|
{
|
|
return new Float2(-inDirection.Y, inDirection.X);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculates the 2D vector perpendicular to the given 2D vector. The result is always rotated 90-degrees in a counter-clockwise direction for a 2D coordinate system where the positive Y axis goes up.
|
|
/// </summary>
|
|
/// <param name="inDirection">The in direction.</param>
|
|
/// <param name="result">When the method completes, contains the result of the calculation.</param>
|
|
public static void Perpendicular(ref Float2 inDirection, out Float2 result)
|
|
{
|
|
result = new Float2(-inDirection.Y, inDirection.X);
|
|
}
|
|
|
|
/// <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 Float2 value1, ref Float2 value2, ref Float2 value3, ref Float2 value4, float amount, out Float2 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 Float2 CatmullRom(Float2 value1, Float2 value2, Float2 value3, Float2 value4, float amount)
|
|
{
|
|
CatmullRom(ref value1, ref value2, ref value3, ref value4, amount, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <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>
|
|
/// <param name="result">When the method completes, contains an new vector composed of the largest components of the source vectors.</param>
|
|
public static void Max(ref Float2 left, ref Float2 right, out Float2 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>
|
|
public static Float2 Max(Float2 left, Float2 right)
|
|
{
|
|
Max(ref left, ref right, out Float2 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>
|
|
public static void Min(ref Float2 left, ref Float2 right, out Float2 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>
|
|
public static Float2 Min(Float2 left, Float2 right)
|
|
{
|
|
Min(ref left, ref right, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns the absolute value of a vector.
|
|
/// </summary>
|
|
/// <param name="v">The value.</param>
|
|
/// <returns> A vector which components are less or equal to 0.</returns>
|
|
public static Float2 Abs(Float2 v)
|
|
{
|
|
return new Float2(Math.Abs(v.X), Math.Abs(v.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>
|
|
/// <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 Float2 vector, ref Float2 normal, out Float2 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 Float2 Reflect(Float2 vector, Float2 normal)
|
|
{
|
|
Reflect(ref vector, ref normal, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a 2D vector by the given <see cref="Quaternion" /> rotation.
|
|
/// </summary>
|
|
/// <param name="vector">The vector to rotate.</param>
|
|
/// <param name="rotation">The <see cref="Quaternion" /> rotation to apply.</param>
|
|
/// <param name="result">When the method completes, contains the transformed <see cref="Float2" />.</param>
|
|
public static void Transform(ref Float2 vector, ref Quaternion rotation, out Float2 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 Float2(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="Quaternion" /> rotation.
|
|
/// </summary>
|
|
/// <param name="vector">The vector to rotate.</param>
|
|
/// <param name="rotation">The <see cref="Quaternion" /> rotation to apply.</param>
|
|
/// <returns>The transformed <see cref="Float2" />.</returns>
|
|
public static Float2 Transform(Float2 vector, Quaternion rotation)
|
|
{
|
|
Transform(ref vector, ref rotation, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Transforms a 2D vector by the given <see cref="Matrix" />.
|
|
/// </summary>
|
|
/// <param name="vector">The source vector.</param>
|
|
/// <param name="transform">The transformation <see cref="Matrix" />.</param>
|
|
/// <param name="result">When the method completes, contains the transformed <see cref="Float4" />.</param>
|
|
public static void Transform(ref Float2 vector, ref Matrix transform, out Float4 result)
|
|
{
|
|
result = new Float4(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="Matrix" />.
|
|
/// </summary>
|
|
/// <param name="vector">The source vector.</param>
|
|
/// <param name="transform">The transformation <see cref="Matrix" />.</param>
|
|
/// <returns>The transformed <see cref="Float4" />.</returns>
|
|
public static Float4 Transform(Float2 vector, Matrix transform)
|
|
{
|
|
Transform(ref vector, ref transform, out Float4 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a coordinate transformation using the given <see cref="Matrix" />.
|
|
/// </summary>
|
|
/// <param name="coordinate">The coordinate vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="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 w component to be one and
|
|
/// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
|
|
/// with coordinates as the w component can safely be ignored.
|
|
/// </remarks>
|
|
public static void TransformCoordinate(ref Float2 coordinate, ref Matrix transform, out Float2 result)
|
|
{
|
|
var vector = new Float4
|
|
{
|
|
X = coordinate.X * transform.M11 + coordinate.Y * transform.M21 + transform.M41,
|
|
Y = coordinate.X * transform.M12 + coordinate.Y * transform.M22 + transform.M42,
|
|
Z = coordinate.X * transform.M13 + coordinate.Y * transform.M23 + transform.M43,
|
|
W = 1f / (coordinate.X * transform.M14 + coordinate.Y * transform.M24 + transform.M44)
|
|
};
|
|
result = new Float2(vector.X * vector.W, vector.Y * vector.W);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a coordinate transformation using the given <see cref="Matrix" />.
|
|
/// </summary>
|
|
/// <param name="coordinate">The coordinate vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="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 w component to be one and
|
|
/// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
|
|
/// with coordinates as the w component can safely be ignored.
|
|
/// </remarks>
|
|
public static Float2 TransformCoordinate(Float2 coordinate, Matrix transform)
|
|
{
|
|
TransformCoordinate(ref coordinate, ref transform, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a normal transformation using the given <see cref="Matrix" />.
|
|
/// </summary>
|
|
/// <param name="normal">The normal vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="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 column 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 preferred for normal vectors as normals purely represent direction
|
|
/// rather than location because normal vectors should not be translated.
|
|
/// </remarks>
|
|
public static void TransformNormal(ref Float2 normal, ref Matrix transform, out Float2 result)
|
|
{
|
|
result = new Float2(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="Matrix" />.
|
|
/// </summary>
|
|
/// <param name="normal">The normal vector to transform.</param>
|
|
/// <param name="transform">The transformation <see cref="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 column 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 preferred for normal vectors as normals purely represent direction
|
|
/// rather than location because normal vectors should not be translated.
|
|
/// </remarks>
|
|
public static Float2 TransformNormal(Float2 normal, Matrix transform)
|
|
{
|
|
TransformNormal(ref normal, ref transform, out Float2 result);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Snaps the input position into the grid.
|
|
/// </summary>
|
|
/// <param name="pos">The position to snap.</param>
|
|
/// <param name="gridSize">The size of the grid.</param>
|
|
/// <returns>The position snapped to the grid.</returns>
|
|
public static Float2 SnapToGrid(Float2 pos, Float2 gridSize)
|
|
{
|
|
pos.X = Mathf.Ceil((pos.X - (gridSize.X * 0.5f)) / gridSize.X) * gridSize.X;
|
|
pos.Y = Mathf.Ceil((pos.Y - (gridSize.Y * 0.5f)) / gridSize.Y) * gridSize.Y;
|
|
return pos;
|
|
}
|
|
|
|
/// <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>
|
|
public static Float2 operator +(Float2 left, Float2 right)
|
|
{
|
|
return new Float2(left.X + right.X, left.Y + right.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Multiplies a vector with another by performing component-wise multiplication equivalent to <see cref="Multiply(ref Float2,ref Float2,out Float2)" />.
|
|
/// </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>
|
|
public static Float2 operator *(Float2 left, Float2 right)
|
|
{
|
|
return new Float2(left.X * right.X, left.Y * right.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Assert a vector (return it unchanged).
|
|
/// </summary>
|
|
/// <param name="value">The vector to assert (unchanged).</param>
|
|
/// <returns>The asserted (unchanged) vector.</returns>
|
|
public static Float2 operator +(Float2 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>
|
|
public static Float2 operator -(Float2 left, Float2 right)
|
|
{
|
|
return new Float2(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>
|
|
public static Float2 operator -(Float2 value)
|
|
{
|
|
return new Float2(-value.X, -value.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>
|
|
public static Float2 operator *(float scale, Float2 value)
|
|
{
|
|
return new Float2(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>
|
|
public static Float2 operator *(Float2 value, float scale)
|
|
{
|
|
return new Float2(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>
|
|
public static Float2 operator /(Float2 value, float scale)
|
|
{
|
|
return new Float2(value.X / scale, value.Y / scale);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scales a vector by the given value.
|
|
/// </summary>
|
|
/// <param name="scale">The amount by which to scale the vector.</param>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <returns>The scaled vector.</returns>
|
|
public static Float2 operator /(float scale, Float2 value)
|
|
{
|
|
return new Float2(scale / value.X, scale / value.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>
|
|
public static Float2 operator *(double scale, Float2 value)
|
|
{
|
|
var s = (float)scale;
|
|
return new Float2(value.X * s, value.Y * s);
|
|
}
|
|
|
|
/// <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>
|
|
public static Float2 operator *(Float2 value, double scale)
|
|
{
|
|
var s = (float)scale;
|
|
return new Float2(value.X * s, value.Y * s);
|
|
}
|
|
|
|
/// <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>
|
|
public static Float2 operator /(Float2 value, double scale)
|
|
{
|
|
var s = (float)scale;
|
|
return new Float2(value.X / s, value.Y / s);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Scales a vector by the given value.
|
|
/// </summary>
|
|
/// <param name="scale">The amount by which to scale the vector.</param>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <returns>The scaled vector.</returns>
|
|
public static Float2 operator /(double scale, Float2 value)
|
|
{
|
|
var s = (float)scale;
|
|
return new Float2(s / value.X, s / value.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>
|
|
public static Float2 operator /(Float2 value, Float2 scale)
|
|
{
|
|
return new Float2(value.X / scale.X, value.Y / scale.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Remainder of value divided by scale.
|
|
/// </summary>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <param name="scale">The amount by which to scale the vector.</param>
|
|
/// <returns>The remained vector.</returns>
|
|
public static Float2 operator %(Float2 value, float scale)
|
|
{
|
|
return new Float2(value.X % scale, value.Y % scale);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Remainder of value divided by scale.
|
|
/// </summary>
|
|
/// <param name="value">The amount by which to scale the vector.</param>
|
|
/// <param name="scale">The vector to scale.</param>
|
|
/// <returns>The remained vector.</returns>
|
|
public static Float2 operator %(float value, Float2 scale)
|
|
{
|
|
return new Float2(value % scale.X, value % scale.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Remainder of value divided by scale.
|
|
/// </summary>
|
|
/// <param name="value">The vector to scale.</param>
|
|
/// <param name="scale">The amount by which to scale the vector.</param>
|
|
/// <returns>The remained vector.</returns>
|
|
public static Float2 operator %(Float2 value, Float2 scale)
|
|
{
|
|
return new Float2(value.X % scale.X, value.Y % scale.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a component-wise addition.
|
|
/// </summary>
|
|
/// <param name="value">The input vector.</param>
|
|
/// <param name="scalar">The scalar value to be added on elements</param>
|
|
/// <returns>The vector with added scalar for each element.</returns>
|
|
public static Float2 operator +(Float2 value, float scalar)
|
|
{
|
|
return new Float2(value.X + scalar, value.Y + scalar);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a component-wise addition.
|
|
/// </summary>
|
|
/// <param name="value">The input vector.</param>
|
|
/// <param name="scalar">The scalar value to be added on elements</param>
|
|
/// <returns>The vector with added scalar for each element.</returns>
|
|
public static Float2 operator +(float scalar, Float2 value)
|
|
{
|
|
return new Float2(scalar + value.X, scalar + value.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a component-wise subtraction.
|
|
/// </summary>
|
|
/// <param name="value">The input vector.</param>
|
|
/// <param name="scalar">The scalar value to be subtracted from elements</param>
|
|
/// <returns>The vector with subtracted scalar from each element.</returns>
|
|
public static Float2 operator -(Float2 value, float scalar)
|
|
{
|
|
return new Float2(value.X - scalar, value.Y - scalar);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs a component-wise subtraction.
|
|
/// </summary>
|
|
/// <param name="value">The input vector.</param>
|
|
/// <param name="scalar">The scalar value to be subtracted from elements</param>
|
|
/// <returns>The vector with subtracted scalar from each element.</returns>
|
|
public static Float2 operator -(float scalar, Float2 value)
|
|
{
|
|
return new Float2(scalar - value.X, scalar - value.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>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static bool operator ==(Float2 left, Float2 right)
|
|
{
|
|
return Mathf.NearEqual(left.X, right.X) && Mathf.NearEqual(left.Y, right.Y);
|
|
}
|
|
|
|
/// <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>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public static bool operator !=(Float2 left, Float2 right)
|
|
{
|
|
return !Mathf.NearEqual(left.X, right.X) || !Mathf.NearEqual(left.Y, right.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="Float2" /> to <see cref="Vector2" />.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator Vector2(Float2 value)
|
|
{
|
|
return new Vector2(value.X, value.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an implicit conversion from <see cref="Float2" /> to <see cref="Double2" />.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static implicit operator Double2(Float2 value)
|
|
{
|
|
return new Double2(value.X, value.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an explicit conversion from <see cref="Float2" /> to <see cref="Float3" />.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static explicit operator Float3(Float2 value)
|
|
{
|
|
return new Float3(value, 0.0f);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Performs an explicit conversion from <see cref="Float2" /> to <see cref="Float4" />.
|
|
/// </summary>
|
|
/// <param name="value">The value.</param>
|
|
/// <returns>The result of the conversion.</returns>
|
|
public static explicit operator Float4(Float2 value)
|
|
{
|
|
return new Float4(value, 0.0f, 0.0f);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="System.String" /> that represents this instance.
|
|
/// </summary>
|
|
/// <returns>A <see cref="System.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="System.String" /> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="format">The format.</param>
|
|
/// <returns>A <see cref="System.String" /> that represents this instance.</returns>
|
|
public string ToString(string format)
|
|
{
|
|
if (format == null)
|
|
return ToString();
|
|
return string.Format(CultureInfo.CurrentCulture, _formatString, X.ToString(format, CultureInfo.CurrentCulture), Y.ToString(format, CultureInfo.CurrentCulture));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="System.String" /> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="formatProvider">The format provider.</param>
|
|
/// <returns>A <see cref="System.String" /> that represents this instance.</returns>
|
|
public string ToString(IFormatProvider formatProvider)
|
|
{
|
|
return string.Format(formatProvider, _formatString, X, Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a <see cref="System.String" /> that represents this instance.
|
|
/// </summary>
|
|
/// <param name="format">The format.</param>
|
|
/// <param name="formatProvider">The format provider.</param>
|
|
/// <returns>A <see cref="System.String" /> that represents this instance.</returns>
|
|
public string ToString(string format, IFormatProvider formatProvider)
|
|
{
|
|
if (format == null)
|
|
return ToString(formatProvider);
|
|
return string.Format(formatProvider, _formatString, X.ToString(format, formatProvider), Y.ToString(format, formatProvider));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Returns a hash code for this instance.
|
|
/// </summary>
|
|
public override int GetHashCode()
|
|
{
|
|
unchecked
|
|
{
|
|
return (X.GetHashCode() * 397) ^ Y.GetHashCode();
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="Float2" /> is equal to this instance.
|
|
/// </summary>
|
|
/// <param name="other">The <see cref="Float2" /> to compare with this instance.</param>
|
|
/// <returns><c>true</c> if the specified <see cref="Float2" /> is equal to this instance; otherwise, <c>false</c>.</returns>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public bool Equals(ref Float2 other)
|
|
{
|
|
return Mathf.NearEqual(other.X, X) && Mathf.NearEqual(other.Y, Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="Float2"/> are equal.
|
|
/// </summary>
|
|
public static bool Equals(ref Float2 a, ref Float2 b)
|
|
{
|
|
return Mathf.NearEqual(a.X, b.X) && Mathf.NearEqual(a.Y, b.Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="Float2" /> is equal to this instance.
|
|
/// </summary>
|
|
/// <param name="other">The <see cref="Float2" /> to compare with this instance.</param>
|
|
/// <returns><c>true</c> if the specified <see cref="Float2" /> is equal to this instance; otherwise, <c>false</c>.</returns>
|
|
[MethodImpl(MethodImplOptions.AggressiveInlining)]
|
|
public bool Equals(Float2 other)
|
|
{
|
|
return Mathf.NearEqual(other.X, X) && Mathf.NearEqual(other.Y, Y);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Determines whether the specified <see cref="System.Object" /> is equal to this instance.
|
|
/// </summary>
|
|
/// <param name="value">The <see cref="System.Object" /> to compare with this instance.</param>
|
|
/// <returns><c>true</c> if the specified <see cref="System.Object" /> is equal to this instance; otherwise, <c>false</c>.</returns>
|
|
public override bool Equals(object value)
|
|
{
|
|
return value is Float2 other && Mathf.NearEqual(other.X, X) && Mathf.NearEqual(other.Y, Y);
|
|
}
|
|
}
|
|
}
|