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FlaxEngine/Source/Engine/Core/Math/Float3.cs
Wojtek Figat b85184eee0 Optimize vectors normalization
2023-04-17 11:10:14 +02:00

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// Copyright (c) 2012-2023 Wojciech Figat. All rights reserved.
// -----------------------------------------------------------------------------
// Original code from SharpDX project. https://github.com/sharpdx/SharpDX/
// Greetings to Alexandre Mutel. Original code published with the following license:
// -----------------------------------------------------------------------------
// Copyright (c) 2010-2014 SharpDX - Alexandre Mutel
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.
// -----------------------------------------------------------------------------
// Original code from SlimMath project. http://code.google.com/p/slimmath/
// Greetings to SlimDX Group. Original code published with the following license:
// -----------------------------------------------------------------------------
/*
* Copyright (c) 2007-2011 SlimDX Group
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
using System;
using System.ComponentModel;
using System.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
namespace FlaxEngine
{
[Serializable]
[TypeConverter(typeof(TypeConverters.Float3Converter))]
partial struct Float3 : IEquatable<Float3>, IFormattable
{
private static readonly string _formatString = "X:{0:F2} Y:{1:F2} Z:{2:F2}";
/// <summary>
/// The size of the <see cref="Float3" /> type, in bytes.
/// </summary>
public static readonly int SizeInBytes = Marshal.SizeOf(typeof(Float3));
/// <summary>
/// A <see cref="Float3" /> with all of its components set to zero.
/// </summary>
public static readonly Float3 Zero;
/// <summary>
/// The X unit <see cref="Float3" /> (1, 0, 0).
/// </summary>
public static readonly Float3 UnitX = new Float3(1.0f, 0.0f, 0.0f);
/// <summary>
/// The Y unit <see cref="Float3" /> (0, 1, 0).
/// </summary>
public static readonly Float3 UnitY = new Float3(0.0f, 1.0f, 0.0f);
/// <summary>
/// The Z unit <see cref="Float3" /> (0, 0, 1).
/// </summary>
public static readonly Float3 UnitZ = new Float3(0.0f, 0.0f, 1.0f);
/// <summary>
/// A <see cref="Float3" /> with all of its components set to one.
/// </summary>
public static readonly Float3 One = new Float3(1.0f, 1.0f, 1.0f);
/// <summary>
/// A <see cref="Float3" /> with all of its components set to half.
/// </summary>
public static readonly Float3 Half = new Float3(0.5f, 0.5f, 0.5f);
/// <summary>
/// A unit <see cref="Float3" /> designating up (0, 1, 0).
/// </summary>
public static readonly Float3 Up = new Float3(0.0f, 1.0f, 0.0f);
/// <summary>
/// A unit <see cref="Float3" /> designating down (0, -1, 0).
/// </summary>
public static readonly Float3 Down = new Float3(0.0f, -1.0f, 0.0f);
/// <summary>
/// A unit <see cref="Float3" /> designating left (-1, 0, 0).
/// </summary>
public static readonly Float3 Left = new Float3(-1.0f, 0.0f, 0.0f);
/// <summary>
/// A unit <see cref="Float3" /> designating right (1, 0, 0).
/// </summary>
public static readonly Float3 Right = new Float3(1.0f, 0.0f, 0.0f);
/// <summary>
/// A unit <see cref="Float3" /> designating forward in a left-handed coordinate system (0, 0, 1).
/// </summary>
public static readonly Float3 Forward = new Float3(0.0f, 0.0f, 1.0f);
/// <summary>
/// A unit <see cref="Float3" /> designating backward in a left-handed coordinate system (0, 0, -1).
/// </summary>
public static readonly Float3 Backward = new Float3(0.0f, 0.0f, -1.0f);
/// <summary>
/// A <see cref="Float3" /> with all components equal to <see cref="float.MinValue"/>.
/// </summary>
public static readonly Float3 Minimum = new Float3(float.MinValue);
/// <summary>
/// A <see cref="Float3" /> with all components equal to <see cref="float.MaxValue"/>.
/// </summary>
public static readonly Float3 Maximum = new Float3(float.MaxValue);
/// <summary>
/// Initializes a new instance of the <see cref="Float3" /> struct.
/// </summary>
/// <param name="value">The value that will be assigned to all components.</param>
public Float3(float value)
{
X = value;
Y = value;
Z = value;
}
/// <summary>
/// Initializes a new instance of the <see cref="Float3" /> struct.
/// </summary>
/// <param name="x">Initial value for the X component of the vector.</param>
/// <param name="y">Initial value for the Y component of the vector.</param>
/// <param name="z">Initial value for the Z component of the vector.</param>
public Float3(float x, float y, float z)
{
X = x;
Y = y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Float3" /> struct.
/// </summary>
/// <param name="value">A vector containing the values with which to initialize the X and Y components.</param>
/// <param name="z">Initial value for the Z component of the vector.</param>
public Float3(Float2 value, float z)
{
X = value.X;
Y = value.Y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Float3" /> struct.
/// </summary>
/// <param name="value">A vector containing the values with which to initialize the X, Y and Z components.</param>
public Float3(Vector3 value)
{
X = (float)value.X;
Y = (float)value.Y;
Z = (float)value.Z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Float3" /> struct.
/// </summary>
/// <param name="value">A vector containing the values with which to initialize the X, Y and Z components.</param>
public Float3(Double3 value)
{
X = (float)value.X;
Y = (float)value.Y;
Z = (float)value.Z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Float3" /> struct.
/// </summary>
/// <param name="value">A vector containing the values with which to initialize the X, Y and Z components.</param>
public Float3(Float4 value)
{
X = value.X;
Y = value.Y;
Z = value.Z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Float3" /> struct.
/// </summary>
/// <param name="values">The values to assign to the X, Y, and Z components of the vector. This must be an array with three elements.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="values" /> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException"> Thrown when <paramref name="values" /> contains more or less than three elements.</exception>
public Float3(float[] values)
{
if (values == null)
throw new ArgumentNullException(nameof(values));
if (values.Length != 3)
throw new ArgumentOutOfRangeException(nameof(values), "There must be three and only three input values for Float3.");
X = values[0];
Y = values[1];
Z = values[2];
}
/// <summary>
/// Gets a value indicting whether this instance is normalized.
/// </summary>
public bool IsNormalized => Mathf.IsOne(X * X + Y * Y + Z * Z);
/// <summary>
/// Gets the normalized vector. Returned vector has length equal 1.
/// </summary>
public Float3 Normalized
{
get
{
Float3 result = this;
result.Normalize();
return result;
}
}
/// <summary>
/// Gets a value indicting whether this vector is zero
/// </summary>
public bool IsZero => Mathf.IsZero(X) && Mathf.IsZero(Y) && Mathf.IsZero(Z);
/// <summary>
/// Gets a value indicting whether this vector is one
/// </summary>
public bool IsOne => Mathf.IsOne(X) && Mathf.IsOne(Y) && Mathf.IsOne(Z);
/// <summary>
/// Gets a minimum component value
/// </summary>
public float MinValue => Mathf.Min(X, Mathf.Min(Y, Z));
/// <summary>
/// Gets a maximum component value
/// </summary>
public float MaxValue => Mathf.Max(X, Mathf.Max(Y, Z));
/// <summary>
/// Gets an arithmetic average value of all vector components.
/// </summary>
public float AvgValue => (X + Y + Z) * (1.0f / 3.0f);
/// <summary>
/// Gets a sum of the component values.
/// </summary>
public float ValuesSum => X + Y + Z;
/// <summary>
/// Gets a vector with values being absolute values of that vector.
/// </summary>
public Float3 Absolute => new Float3(Mathf.Abs(X), Mathf.Abs(Y), Mathf.Abs(Z));
/// <summary>
/// Gets a vector with values being opposite to values of that vector.
/// </summary>
public Float3 Negative => new Float3(-X, -Y, -Z);
/// <summary>
/// Gets or sets the component at the specified index.
/// </summary>
/// <value>The value of the X, Y, or Z component, depending on the index.</value>
/// <param name="index">The index of the component to access. Use 0 for the X component, 1 for the Y component, and 2 for the Z component.</param>
/// <returns>The value of the component at the specified index.</returns>
/// <exception cref="System.ArgumentOutOfRangeException">Thrown when the <paramref name="index" /> is out of the range [0, 2].</exception>
public float this[int index]
{
get
{
switch (index)
{
case 0: return X;
case 1: return Y;
case 2: return Z;
}
throw new ArgumentOutOfRangeException(nameof(index), "Indices for Float3 run from 0 to 2, inclusive.");
}
set
{
switch (index)
{
case 0:
X = value;
break;
case 1:
Y = value;
break;
case 2:
Z = value;
break;
default: throw new ArgumentOutOfRangeException(nameof(index), "Indices for Float3 run from 0 to 2, inclusive.");
}
}
}
/// <summary>
/// Calculates the length of the vector.
/// </summary>
/// <returns>The length of the vector.</returns>
/// <remarks><see cref="Float3.LengthSquared" /> may be preferred when only the relative length is needed and speed is of the essence.</remarks>
public float Length => (float)Math.Sqrt(X * X + Y * Y + Z * Z);
/// <summary>
/// Calculates the squared length of the vector.
/// </summary>
/// <returns>The squared length of the vector.</returns>
/// <remarks>This method may be preferred to <see cref="Float3.Length" /> when only a relative length is needed and speed is of the essence.</remarks>
public float LengthSquared => X * X + Y * Y + Z * Z;
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
public void Normalize()
{
float length = Length;
if (length >= Mathf.Epsilon)
{
float inv = 1.0f / length;
X *= inv;
Y *= inv;
Z *= inv;
}
}
/// <summary>
/// Creates an array containing the elements of the vector.
/// </summary>
/// <returns>A three-element array containing the components of the vector.</returns>
public float[] ToArray()
{
return new[] { X, Y, Z };
}
/// <summary>
/// Adds two vectors.
/// </summary>
/// <param name="left">The first vector to add.</param>
/// <param name="right">The second vector to add.</param>
/// <param name="result">When the method completes, contains the sum of the two vectors.</param>
public static void Add(ref Float3 left, ref Float3 right, out Float3 result)
{
result = new Float3(left.X + right.X, left.Y + right.Y, left.Z + right.Z);
}
/// <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 Float3 Add(Float3 left, Float3 right)
{
return new Float3(left.X + right.X, left.Y + right.Y, left.Z + right.Z);
}
/// <summary>
/// Performs a component-wise addition.
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be added to elements</param>
/// <param name="result">The vector with added scalar for each element.</param>
public static void Add(ref Float3 left, ref float right, out Float3 result)
{
result = new Float3(left.X + right, left.Y + right, left.Z + right);
}
/// <summary>
/// Performs a component-wise addition.
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be added to elements</param>
/// <returns>The vector with added scalar for each element.</returns>
public static Float3 Add(Float3 left, float right)
{
return new Float3(left.X + right, left.Y + right, left.Z + right);
}
/// <summary>
/// Subtracts two vectors.
/// </summary>
/// <param name="left">The first vector to subtract.</param>
/// <param name="right">The second vector to subtract.</param>
/// <param name="result">When the method completes, contains the difference of the two vectors.</param>
public static void Subtract(ref Float3 left, ref Float3 right, out Float3 result)
{
result = new Float3(left.X - right.X, left.Y - right.Y, left.Z - right.Z);
}
/// <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 Float3 Subtract(Float3 left, Float3 right)
{
return new Float3(left.X - right.X, left.Y - right.Y, left.Z - right.Z);
}
/// <summary>
/// Performs a component-wise subtraction.
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be subtracted from elements</param>
/// <param name="result">The vector with subtracted scalar for each element.</param>
public static void Subtract(ref Float3 left, ref float right, out Float3 result)
{
result = new Float3(left.X - right, left.Y - right, left.Z - right);
}
/// <summary>
/// Performs a component-wise subtraction.
/// </summary>
/// <param name="left">The input vector</param>
/// <param name="right">The scalar value to be subtracted from elements</param>
/// <returns>The vector with subtracted scalar for each element.</returns>
public static Float3 Subtract(Float3 left, float right)
{
return new Float3(left.X - right, left.Y - right, left.Z - right);
}
/// <summary>
/// Performs a component-wise subtraction.
/// </summary>
/// <param name="left">The scalar value to be subtracted from elements</param>
/// <param name="right">The input vector.</param>
/// <param name="result">The vector with subtracted scalar for each element.</param>
public static void Subtract(ref float left, ref Float3 right, out Float3 result)
{
result = new Float3(left - right.X, left - right.Y, left - right.Z);
}
/// <summary>
/// Performs a component-wise subtraction.
/// </summary>
/// <param name="left">The scalar value to be subtracted from elements</param>
/// <param name="right">The input vector.</param>
/// <returns>The vector with subtracted scalar for each element.</returns>
public static Float3 Subtract(float left, Float3 right)
{
return new Float3(left - right.X, left - right.Y, left - right.Z);
}
/// <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>
/// <param name="result">When the method completes, contains the scaled vector.</param>
public static void Multiply(ref Float3 value, float scale, out Float3 result)
{
result = new Float3(value.X * scale, value.Y * scale, value.Z * 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 Float3 Multiply(Float3 value, float scale)
{
return new Float3(value.X * scale, value.Y * scale, value.Z * scale);
}
/// <summary>
/// Multiply a vector with another by performing component-wise multiplication.
/// </summary>
/// <param name="left">The first vector to multiply.</param>
/// <param name="right">The second vector to multiply.</param>
/// <param name="result">When the method completes, contains the multiplied vector.</param>
public static void Multiply(ref Float3 left, ref Float3 right, out Float3 result)
{
result = new Float3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
}
/// <summary>
/// Multiply a vector with another by performing component-wise multiplication.
/// </summary>
/// <param name="left">The first vector to Multiply.</param>
/// <param name="right">The second vector to multiply.</param>
/// <returns>The multiplied vector.</returns>
public static Float3 Multiply(Float3 left, Float3 right)
{
return new Float3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
}
/// <summary>
/// Divides 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 (per component).</param>
/// <param name="result">When the method completes, contains the divided vector.</param>
public static void Divide(ref Float3 value, ref Float3 scale, out Float3 result)
{
result = new Float3(value.X / scale.X, value.Y / scale.Y, value.Z / scale.Z);
}
/// <summary>
/// Divides 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 (per component).</param>
/// <returns>The divided vector.</returns>
public static Float3 Divide(Float3 value, Float3 scale)
{
return new Float3(value.X / scale.X, value.Y / scale.Y, value.Z / scale.Z);
}
/// <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>
/// <param name="result">When the method completes, contains the scaled vector.</param>
public static void Divide(ref Float3 value, float scale, out Float3 result)
{
result = new Float3(value.X / scale, value.Y / scale, value.Z / 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 Float3 Divide(Float3 value, float scale)
{
return new Float3(value.X / scale, value.Y / scale, value.Z / 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>
/// <param name="result">When the method completes, contains the scaled vector.</param>
public static void Divide(float scale, ref Float3 value, out Float3 result)
{
result = new Float3(scale / value.X, scale / value.Y, scale / value.Z);
}
/// <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 Float3 Divide(float scale, Float3 value)
{
return new Float3(scale / value.X, scale / value.Y, scale / value.Z);
}
/// <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 Float3 value, out Float3 result)
{
result = new Float3(-value.X, -value.Y, -value.Z);
}
/// <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 Float3 Negate(Float3 value)
{
return new Float3(-value.X, -value.Y, -value.Z);
}
/// <summary>
/// Returns a <see cref="Float3" /> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="Float3" /> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Float3" /> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Float3" /> containing the 3D 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 3D Cartesian coordinates of the specified point.</param>
public static void Barycentric(ref Float3 value1, ref Float3 value2, ref Float3 value3, float amount1, float amount2, out Float3 result)
{
result = new Float3(value1.X + amount1 * (value2.X - value1.X) + amount2 * (value3.X - value1.X),
value1.Y + amount1 * (value2.Y - value1.Y) + amount2 * (value3.Y - value1.Y),
value1.Z + amount1 * (value2.Z - value1.Z) + amount2 * (value3.Z - value1.Z));
}
/// <summary>
/// Returns a <see cref="Float3" /> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="Float3" /> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Float3" /> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Float3" /> containing the 3D 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="Float3" /> containing the 3D Cartesian coordinates of the specified point.</returns>
public static Float3 Barycentric(Float3 value1, Float3 value2, Float3 value3, float amount1, float amount2)
{
Barycentric(ref value1, ref value2, ref value3, amount1, amount2, out var 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 Float3 value, ref Float3 min, ref Float3 max, out Float3 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;
float z = value.Z;
z = z > max.Z ? max.Z : z;
z = z < min.Z ? min.Z : z;
result = new Float3(x, y, z);
}
/// <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 Float3 Clamp(Float3 value, Float3 min, Float3 max)
{
Clamp(ref value, ref min, ref max, out var result);
return result;
}
/// <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 he cross product of the two vectors.</param>
public static void Cross(ref Float3 left, ref Float3 right, out Float3 result)
{
result = new Float3(left.Y * right.Z - left.Z * right.Y,
left.Z * right.X - left.X * right.Z,
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 Float3 Cross(Float3 left, Float3 right)
{
Cross(ref left, ref right, out var result);
return result;
}
/// <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="Float3.DistanceSquared(ref Float3, ref Float3, out float)" /> may be preferred when only the relative distance is needed and speed is of the essence.</remarks>
public static void Distance(ref Float3 value1, ref Float3 value2, out float result)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
result = (float)Math.Sqrt(x * x + y * y + z * z);
}
/// <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="Float3.DistanceSquared(ref Float3, ref Float3, out float)" /> may be preferred when only the relative distance is needed and speed is of the essence.</remarks>
public static float Distance(ref Float3 value1, ref Float3 value2)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
return (float)Math.Sqrt(x * x + y * y + z * z);
}
/// <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="Float3.DistanceSquared(Float3, Float3)" /> may be preferred when only the relative distance is needed and speed is of the essence.</remarks>
public static float Distance(Float3 value1, Float3 value2)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
return (float)Math.Sqrt(x * x + y * y + z * z);
}
/// <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 Float3 value1, ref Float3 value2, out float result)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
result = x * x + y * y + z * z;
}
/// <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 Float3 value1, ref Float3 value2)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
return x * x + y * y + z * z;
}
/// <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(Float3 value1, Float3 value2)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
return x * x + y * y + z * z;
}
/// <summary>
/// Calculates the distance between two vectors on the XY plane (ignoring Z).
/// </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 in the XY plane.</param>
public static void DistanceXY(ref Float3 value1, ref Float3 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 squared distance between two vectors on the XY plane (ignoring Z).
/// </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 in the XY plane.</param>
public static void DistanceXYSquared(ref Float3 value1, ref Float3 value2, out float result)
{
float x = value1.X - value2.X;
float y = value1.Y - value2.Y;
result = x * x + y * y;
}
/// <summary>
/// Calculates the distance between two vectors on the XZ plane (ignoring Y).
/// </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 in the XY plane.</param>
public static void DistanceXZ(ref Float3 value1, ref Float3 value2, out float result)
{
float x = value1.X - value2.X;
float z = value1.Z - value2.Z;
result = (float)Math.Sqrt(x * x + z * z);
}
/// <summary>
/// Calculates the squared distance between two vectors on the XZ plane (ignoring Y).
/// </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 in the XY plane.</param>
public static void DistanceXZSquared(ref Float3 value1, ref Float3 value2, out float result)
{
float x = value1.X - value2.X;
float z = value1.Z - value2.Z;
result = x * x + z * z;
}
/// <summary>
/// Calculates the distance between two vectors on the YZ plane (ignoring X).
/// </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 in the YZ plane.</param>
public static void DistanceYZ(ref Float3 value1, ref Float3 value2, out float result)
{
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
result = (float)Math.Sqrt(y * y + z * z);
}
/// <summary>
/// Calculates the squared distance between two vectors on the YZ plane (ignoring X).
/// </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 in the YZ plane.</param>
public static void DistanceYZSquared(ref Float3 value1, ref Float3 value2, out float result)
{
float y = value1.Y - value2.Y;
float z = value1.Z - value2.Z;
result = y * y + z * z;
}
/// <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(Float3 left, Float3 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 Float3 left, ref Float3 right, float epsilon = Mathf.Epsilon)
{
return Mathf.WithinEpsilon(left.X, right.X, epsilon) && Mathf.WithinEpsilon(left.Y, right.Y, epsilon) && Mathf.WithinEpsilon(left.Z, right.Z, 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 Float3 left, ref Float3 right, out float result)
{
result = left.X * right.X + left.Y * right.Y + left.Z * right.Z;
}
/// <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 Float3 left, ref Float3 right)
{
return left.X * right.X + left.Y * right.Y + left.Z * right.Z;
}
/// <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(Float3 left, Float3 right)
{
return left.X * right.X + left.Y * right.Y + left.Z * right.Z;
}
/// <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 Float3 value, out Float3 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 Float3 Normalize(Float3 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 Float3 ClampLength(Float3 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 Float3 ClampLength(Float3 vector, float min, float max)
{
ClampLength(vector, min, max, out Float3 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 vector.</param>
public static void ClampLength(Float3 vector, float min, float max, out Float3 result)
{
result.X = vector.X;
result.Y = vector.Y;
result.Z = vector.Z;
float lenSq = result.LengthSquared;
if (lenSq > max * max)
{
float scaleFactor = max / (float)Math.Sqrt(lenSq);
result.X *= scaleFactor;
result.Y *= scaleFactor;
result.Z *= scaleFactor;
}
if (lenSq < min * min)
{
float scaleFactor = min / (float)Math.Sqrt(lenSq);
result.X *= scaleFactor;
result.Y *= scaleFactor;
result.Z *= scaleFactor;
}
}
/// <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 Float3 start, ref Float3 end, float amount, out Float3 result)
{
result.X = Mathf.Lerp(start.X, end.X, amount);
result.Y = Mathf.Lerp(start.Y, end.Y, amount);
result.Z = Mathf.Lerp(start.Z, end.Z, 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 Float3 Lerp(Float3 start, Float3 end, float amount)
{
Lerp(ref start, ref end, amount, out var 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 Float3 start, ref Float3 end, float amount, out Float3 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 Float3 SmoothStep(Float3 start, Float3 end, float amount)
{
SmoothStep(ref start, ref end, amount, out var 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 Float3 value1, ref Float3 tangent1, ref Float3 value2, ref Float3 tangent2, float amount, out Float3 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;
result.Z = value1.Z * part1 + value2.Z * part2 + tangent1.Z * part3 + tangent2.Z * 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 Float3 Hermite(Float3 value1, Float3 tangent1, Float3 value2, Float3 tangent2, float amount)
{
Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out var result);
return result;
}
/// <summary>
/// Performs a Catmull-Rom interpolation using the specified positions.
/// </summary>
/// <param name="value1">The first position in the interpolation.</param>
/// <param name="value2">The second position in the interpolation.</param>
/// <param name="value3">The third position in the interpolation.</param>
/// <param name="value4">The fourth position in the interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <param name="result">When the method completes, contains the result of the Catmull-Rom interpolation.</param>
public static void CatmullRom(ref Float3 value1, ref Float3 value2, ref Float3 value3, ref Float3 value4, float amount, out Float3 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);
result.Z = 0.5f * (2.0f * value2.Z + (-value1.Z + value3.Z) * amount +
(2.0f * value1.Z - 5.0f * value2.Z + 4.0f * value3.Z - value4.Z) * squared +
(-value1.Z + 3.0f * value2.Z - 3.0f * value3.Z + value4.Z) * 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 Float3 CatmullRom(Float3 value1, Float3 value2, Float3 value3, Float3 value4, float amount)
{
CatmullRom(ref value1, ref value2, ref value3, ref value4, amount, out var 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 Float3 left, ref Float3 right, out Float3 result)
{
result.X = left.X > right.X ? left.X : right.X;
result.Y = left.Y > right.Y ? left.Y : right.Y;
result.Z = left.Z > right.Z ? left.Z : right.Z;
}
/// <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 Float3 Max(Float3 left, Float3 right)
{
Max(ref left, ref right, out var 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 Float3 left, ref Float3 right, out Float3 result)
{
result.X = left.X < right.X ? left.X : right.X;
result.Y = left.Y < right.Y ? left.Y : right.Y;
result.Z = left.Z < right.Z ? left.Z : right.Z;
}
/// <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 Float3 Min(Float3 left, Float3 right)
{
Min(ref left, ref right, out var 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 Float3 Abs(Float3 v)
{
return new Float3(Math.Abs(v.X), Math.Abs(v.Y), Math.Abs(v.Z));
}
/// <summary>
/// Projects a vector onto another vector.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="onNormal">The projection normal vector.</param>
/// <returns>The projected vector.</returns>
public static Float3 Project(Float3 vector, Float3 onNormal)
{
float sqrMag = Dot(onNormal, onNormal);
if (sqrMag < Mathf.Epsilon)
return Zero;
return onNormal * Dot(vector, onNormal) / sqrMag;
}
/// <summary>
/// Projects a vector onto a plane defined by a normal orthogonal to the plane.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="planeNormal">The plane normal vector.</param>
/// <returns>The projected vector.</returns>
public static Float3 ProjectOnPlane(Float3 vector, Float3 planeNormal)
{
return vector - Project(vector, planeNormal);
}
/// <summary>
/// Calculates the angle (in degrees) between <paramref name="from"/> and <paramref name="to"/>. This is always the smallest value.
/// </summary>
/// <param name="from">The first vector.</param>
/// <param name="to">The second vector.</param>
/// <returns>The angle (in degrees).</returns>
public static float Angle(Float3 from, Float3 to)
{
float dot = Mathf.Clamp(Dot(from.Normalized, to.Normalized), -1.0f, 1.0f);
if (Mathf.Abs(dot) > (1.0f - Mathf.Epsilon))
return dot > 0.0f ? 0.0f : 180.0f;
return (float)Math.Acos(dot) * Mathf.RadiansToDegrees;
}
/// <summary>
/// Projects a 3D vector from object space into screen space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <param name="result">When the method completes, contains the vector in screen space.</param>
public static void Project(ref Float3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Float3 result)
{
TransformCoordinate(ref vector, ref worldViewProjection, out var v);
result = new Float3((1.0f + v.X) * 0.5f * width + x, (1.0f - v.Y) * 0.5f * height + y, v.Z * (maxZ - minZ) + minZ);
}
/// <summary>
/// Projects a 3D vector from object space into screen space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <returns>The vector in screen space.</returns>
public static Float3 Project(Float3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)
{
Project(ref vector, x, y, width, height, minZ, maxZ, ref worldViewProjection, out var result);
return result;
}
/// <summary>
/// Projects a 3D vector from screen space into object space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <param name="result">When the method completes, contains the vector in object space.</param>
public static void Unproject(ref Float3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Float3 result)
{
Matrix.Invert(ref worldViewProjection, out var matrix);
var v = new Float3
{
X = (vector.X - x) / width * 2.0f - 1.0f,
Y = -((vector.Y - y) / height * 2.0f - 1.0f),
Z = (vector.Z - minZ) / (maxZ - minZ)
};
TransformCoordinate(ref v, ref matrix, out result);
}
/// <summary>
/// Projects a 3D vector from screen space into object space.
/// </summary>
/// <param name="vector">The vector to project.</param>
/// <param name="x">The X position of the viewport.</param>
/// <param name="y">The Y position of the viewport.</param>
/// <param name="width">The width of the viewport.</param>
/// <param name="height">The height of the viewport.</param>
/// <param name="minZ">The minimum depth of the viewport.</param>
/// <param name="maxZ">The maximum depth of the viewport.</param>
/// <param name="worldViewProjection">The combined world-view-projection matrix.</param>
/// <returns>The vector in object space.</returns>
public static Float3 Unproject(Float3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)
{
Unproject(ref vector, x, y, width, height, minZ, maxZ, ref worldViewProjection, out var result);
return result;
}
/// <summary>
/// Returns the reflection of a vector off a surface that has the specified normal.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="normal">Normal of the surface.</param>
/// <param name="result">When the method completes, contains the reflected vector.</param>
/// <remarks>Reflect only gives the direction of a reflection off a surface, it does not determine whether the original vector was close enough to the surface to hit it.</remarks>
public static void Reflect(ref Float3 vector, ref Float3 normal, out Float3 result)
{
float dot = vector.X * normal.X + vector.Y * normal.Y + vector.Z * normal.Z;
result.X = vector.X - 2.0f * dot * normal.X;
result.Y = vector.Y - 2.0f * dot * normal.Y;
result.Z = vector.Z - 2.0f * dot * normal.Z;
}
/// <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 Float3 Reflect(Float3 vector, Float3 normal)
{
Reflect(ref vector, ref normal, out var result);
return result;
}
/// <summary>
/// Transforms a 3D 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="Float3" />.</param>
public static void Transform(ref Float3 vector, ref Quaternion rotation, out Float3 result)
{
float x = rotation.X + rotation.X;
float y = rotation.Y + rotation.Y;
float z = rotation.Z + rotation.Z;
float wx = rotation.W * x;
float wy = rotation.W * y;
float wz = rotation.W * z;
float xx = rotation.X * x;
float xy = rotation.X * y;
float xz = rotation.X * z;
float yy = rotation.Y * y;
float yz = rotation.Y * z;
float zz = rotation.Z * z;
result = new Float3(vector.X * (1.0f - yy - zz) + vector.Y * (xy - wz) + vector.Z * (xz + wy),
vector.X * (xy + wz) + vector.Y * (1.0f - xx - zz) + vector.Z * (yz - wx),
vector.X * (xz - wy) + vector.Y * (yz + wx) + vector.Z * (1.0f - xx - yy));
}
/// <summary>
/// Transforms a 3D 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="Float3" />.</returns>
public static Float3 Transform(Float3 vector, Quaternion rotation)
{
Transform(ref vector, ref rotation, out var result);
return result;
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Matrix3x3"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="Matrix3x3"/>.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="Float3"/>.</param>
public static void Transform(ref Float3 vector, ref Matrix3x3 transform, out Float3 result)
{
result = new Float3((vector.X * transform.M11) + (vector.Y * transform.M21) + (vector.Z * transform.M31),
(vector.X * transform.M12) + (vector.Y * transform.M22) + (vector.Z * transform.M32),
(vector.X * transform.M13) + (vector.Y * transform.M23) + (vector.Z * transform.M33));
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="Matrix3x3"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="Matrix3x3"/>.</param>
/// <returns>The transformed <see cref="Float3"/>.</returns>
public static Float3 Transform(Float3 vector, Matrix3x3 transform)
{
Transform(ref vector, ref transform, out var result);
return result;
}
/// <summary>
/// Transforms a 3D 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="Float3" />.</param>
public static void Transform(ref Float3 vector, ref Matrix transform, out Float3 result)
{
result = new Float3(vector.X * transform.M11 + vector.Y * transform.M21 + vector.Z * transform.M31 + transform.M41,
vector.X * transform.M12 + vector.Y * transform.M22 + vector.Z * transform.M32 + transform.M42,
vector.X * transform.M13 + vector.Y * transform.M23 + vector.Z * transform.M33 + transform.M43);
}
/// <summary>
/// Transforms a 3D 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 Float3 vector, ref Matrix transform, out Float4 result)
{
result = new Float4(vector.X * transform.M11 + vector.Y * transform.M21 + vector.Z * transform.M31 + transform.M41,
vector.X * transform.M12 + vector.Y * transform.M22 + vector.Z * transform.M32 + transform.M42,
vector.X * transform.M13 + vector.Y * transform.M23 + vector.Z * transform.M33 + transform.M43,
vector.X * transform.M14 + vector.Y * transform.M24 + vector.Z * transform.M34 + transform.M44);
}
/// <summary>
/// Transforms a 3D 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="Float3" />.</returns>
public static Float3 Transform(Float3 vector, Matrix transform)
{
Transform(ref vector, ref transform, out Float3 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 Float3 coordinate, ref Matrix transform, out Float3 result)
{
var vector = new Float4
{
X = coordinate.X * transform.M11 + coordinate.Y * transform.M21 + coordinate.Z * transform.M31 + transform.M41,
Y = coordinate.X * transform.M12 + coordinate.Y * transform.M22 + coordinate.Z * transform.M32 + transform.M42,
Z = coordinate.X * transform.M13 + coordinate.Y * transform.M23 + coordinate.Z * transform.M33 + transform.M43,
W = 1f / (coordinate.X * transform.M14 + coordinate.Y * transform.M24 + coordinate.Z * transform.M34 + transform.M44)
};
result = new Float3(vector.X * vector.W, vector.Y * vector.W, vector.Z * 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 Float3 TransformCoordinate(Float3 coordinate, Matrix transform)
{
TransformCoordinate(ref coordinate, ref transform, out var 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 Float3 normal, ref Matrix transform, out Float3 result)
{
result = new Float3(normal.X * transform.M11 + normal.Y * transform.M21 + normal.Z * transform.M31,
normal.X * transform.M12 + normal.Y * transform.M22 + normal.Z * transform.M32,
normal.X * transform.M13 + normal.Y * transform.M23 + normal.Z * transform.M33);
}
/// <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 Float3 TransformNormal(Float3 normal, Matrix transform)
{
TransformNormal(ref normal, ref transform, out var result);
return result;
}
/// <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 Float3 operator +(Float3 left, Float3 right)
{
return new Float3(left.X + right.X, left.Y + right.Y, left.Z + right.Z);
}
/// <summary>
/// Multiplies a vector with another by performing component-wise multiplication equivalent to <see cref="Multiply(ref Float3,ref Float3,out Float3)" />.
/// </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 Float3 operator *(Float3 left, Float3 right)
{
return new Float3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
}
/// <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 Float3 operator +(Float3 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 Float3 operator -(Float3 left, Float3 right)
{
return new Float3(left.X - right.X, left.Y - right.Y, left.Z - right.Z);
}
/// <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 Float3 operator -(Float3 value)
{
return new Float3(-value.X, -value.Y, -value.Z);
}
/// <summary>
/// Transforms a vector by the given rotation.
/// </summary>
/// <param name="vector">The vector to transform.</param>
/// <param name="rotation">The quaternion.</param>
/// <returns>The scaled vector.</returns>
public static Float3 operator *(Float3 vector, Quaternion rotation)
{
Transform(ref vector, ref rotation, out var result);
return result;
}
/// <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 Float3 operator *(float scale, Float3 value)
{
return new Float3(value.X * scale, value.Y * scale, value.Z * 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 Float3 operator *(Float3 value, float scale)
{
return new Float3(value.X * scale, value.Y * scale, value.Z * 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 Float3 operator /(Float3 value, float scale)
{
return new Float3(value.X / scale, value.Y / scale, value.Z / 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 Float3 operator /(float scale, Float3 value)
{
return new Float3(scale / value.X, scale / value.Y, scale / value.Z);
}
/// <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 Float3 operator *(double scale, Float3 value)
{
var s = (float)scale;
return new Float3(value.X * s, value.Y * s, value.Z * 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 Float3 operator *(Float3 value, double scale)
{
var s = (float)scale;
return new Float3(value.X * s, value.Y * s, value.Z * 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 Float3 operator /(Float3 value, double scale)
{
var s = (float)scale;
return new Float3(value.X / s, value.Y / s, value.Z / 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 Float3 operator /(double scale, Float3 value)
{
var s = (float)scale;
return new Float3(s / value.X, s / value.Y, s / value.Z);
}
/// <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 Float3 operator /(Float3 value, Float3 scale)
{
return new Float3(value.X / scale.X, value.Y / scale.Y, value.Z / scale.Z);
}
/// <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 Float3 operator %(Float3 value, float scale)
{
return new Float3(value.X % scale, value.Y % scale, value.Z % 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 Float3 operator %(float value, Float3 scale)
{
return new Float3(value % scale.X, value % scale.Y, value % scale.Z);
}
/// <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 Float3 operator %(Float3 value, Float3 scale)
{
return new Float3(value.X % scale.X, value.Y % scale.Y, value.Z % scale.Z);
}
/// <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 Float3 operator +(Float3 value, float scalar)
{
return new Float3(value.X + scalar, value.Y + scalar, value.Z + 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 Float3 operator +(float scalar, Float3 value)
{
return new Float3(scalar + value.X, scalar + value.Y, scalar + value.Z);
}
/// <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 added scalar from each element.</returns>
public static Float3 operator -(Float3 value, float scalar)
{
return new Float3(value.X - scalar, value.Y - scalar, value.Z - 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 Float3 operator -(float scalar, Float3 value)
{
return new Float3(scalar - value.X, scalar - value.Y, scalar - value.Z);
}
/// <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 ==(Float3 left, Float3 right)
{
return Mathf.NearEqual(left.X, right.X) && Mathf.NearEqual(left.Y, right.Y) && Mathf.NearEqual(left.Z, right.Z);
}
/// <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 !=(Float3 left, Float3 right)
{
return !Mathf.NearEqual(left.X, right.X) || !Mathf.NearEqual(left.Y, right.Y) || !Mathf.NearEqual(left.Z, right.Z);
}
/// <summary>
/// Performs an explicit conversion from <see cref="Float3" /> to <see cref="Vector3" />.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static implicit operator Vector3(Float3 value)
{
return new Vector3(value.X, value.Y, value.Z);
}
/// <summary>
/// Performs an implicit conversion from <see cref="Float3" /> to <see cref="Double3" />.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static implicit operator Double3(Float3 value)
{
return new Double3(value.X, value.Y, value.Z);
}
/// <summary>
/// Performs an explicit conversion from <see cref="Float3" /> to <see cref="Float2" />.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static explicit operator Float2(Float3 value)
{
return new Float2(value.X, value.Y);
}
/// <summary>
/// Performs an explicit conversion from <see cref="Float3" /> to <see cref="Float4" />.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static explicit operator Float4(Float3 value)
{
return new Float4(value, 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, _formatString, X, Y, Z);
}
/// <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), Z.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, Z);
}
/// <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, "X:{0} Y:{1} Z:{2}", X.ToString(format, formatProvider), Y.ToString(format, formatProvider), Z.ToString(format, formatProvider));
}
/// <summary>
/// Returns a hash code for this instance.
/// </summary>
public override int GetHashCode()
{
unchecked
{
int hashCode = X.GetHashCode();
hashCode = (hashCode * 397) ^ Y.GetHashCode();
hashCode = (hashCode * 397) ^ Z.GetHashCode();
return hashCode;
}
}
/// <summary>
/// Determines whether the specified <see cref="Float3" /> is equal to this instance.
/// </summary>
/// <param name="other">The <see cref="Float3" /> to compare with this instance.</param>
/// <returns><c>true</c> if the specified <see cref="Float3" /> is equal to this instance; otherwise, <c>false</c>.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public bool Equals(ref Float3 other)
{
return Mathf.NearEqual(other.X, X) && Mathf.NearEqual(other.Y, Y) && Mathf.NearEqual(other.Z, Z);
}
/// <summary>
/// Determines whether the specified <see cref="Float3" /> is equal to this instance.
/// </summary>
/// <param name="other">The <see cref="Float3" /> to compare with this instance.</param>
/// <returns><c>true</c> if the specified <see cref="Float3" /> is equal to this instance; otherwise, <c>false</c>.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public bool Equals(Float3 other)
{
return Mathf.NearEqual(other.X, X) && Mathf.NearEqual(other.Y, Y) && Mathf.NearEqual(other.Z, Z);
}
/// <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 Float3 other && Mathf.NearEqual(other.X, X) && Mathf.NearEqual(other.Y, Y) && Mathf.NearEqual(other.Z, Z);
}
}
}
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