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Vector3.cs
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Vector3.cs
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// Copyright (c) Xenko contributors (https://xenko.com) and Silicon Studio Corp. (https://www.siliconstudio.co.jp)
// Distributed under the MIT license. See the LICENSE.md file in the project root for more information.
//
// -----------------------------------------------------------------------------
// 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.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
namespace Xenko.Core.Mathematics
{
/// <summary>
/// Represents a three dimensional mathematical vector.
/// </summary>
[DataContract("float3")]
[DataStyle(DataStyle.Compact)]
[StructLayout(LayoutKind.Sequential, Pack = 4)]
public struct Vector3 : IEquatable<Vector3>, IFormattable
{
/// <summary>
/// The size of the <see cref="Xenko.Core.Mathematics.Vector3"/> type, in bytes.
/// </summary>
public static readonly int SizeInBytes = Utilities.SizeOf<Vector3>();
/// <summary>
/// A <see cref="Xenko.Core.Mathematics.Vector3"/> with all of its components set to zero.
/// </summary>
public static readonly Vector3 Zero = new Vector3();
/// <summary>
/// The X unit <see cref="Xenko.Core.Mathematics.Vector3"/> (1, 0, 0).
/// </summary>
public static readonly Vector3 UnitX = new Vector3(1.0f, 0.0f, 0.0f);
/// <summary>
/// The Y unit <see cref="Xenko.Core.Mathematics.Vector3"/> (0, 1, 0).
/// </summary>
public static readonly Vector3 UnitY = new Vector3(0.0f, 1.0f, 0.0f);
/// <summary>
/// The Z unit <see cref="Xenko.Core.Mathematics.Vector3"/> (0, 0, 1).
/// </summary>
public static readonly Vector3 UnitZ = new Vector3(0.0f, 0.0f, 1.0f);
/// <summary>
/// A <see cref="Xenko.Core.Mathematics.Vector3"/> with all of its components set to one.
/// </summary>
public static readonly Vector3 One = new Vector3(1.0f, 1.0f, 1.0f);
/// <summary>
/// The X component of the vector.
/// </summary>
[DataMember(0)]
public float X;
/// <summary>
/// The Y component of the vector.
/// </summary>
[DataMember(1)]
public float Y;
/// <summary>
/// The Z component of the vector.
/// </summary>
[DataMember(2)]
public float Z;
/// <summary>
/// Initializes a new instance of the <see cref="Xenko.Core.Mathematics.Vector3"/> struct.
/// </summary>
/// <param name="value">The value that will be assigned to all components.</param>
public Vector3(float value)
{
X = value;
Y = value;
Z = value;
}
/// <summary>
/// Initializes a new instance of the <see cref="Xenko.Core.Mathematics.Vector3"/> 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 Vector3(float x, float y, float z)
{
X = x;
Y = y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Xenko.Core.Mathematics.Vector3"/> 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 Vector3(Vector2 value, float z)
{
X = value.X;
Y = value.Y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="Xenko.Core.Mathematics.Vector3"/> 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 Vector3(float[] values)
{
if (values == null)
throw new ArgumentNullException("values");
if (values.Length != 3)
throw new ArgumentOutOfRangeException("values", "There must be three and only three input values for Vector3.");
X = values[0];
Y = values[1];
Z = values[2];
}
/// <summary>
/// Gets a value indicting whether this instance is normalized.
/// </summary>
public bool IsNormalized
{
get { return Math.Abs((X * X) + (Y * Y) + (Z * Z) - 1f) < MathUtil.ZeroTolerance; }
}
/// <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("index", "Indices for Vector3 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("index", "Indices for Vector3 run from 0 to 2, inclusive.");
}
}
}
/// <summary>
/// Calculates the length of the vector.
/// </summary>
/// <returns>The length of the vector.</returns>
/// <remarks>
/// <see cref="Xenko.Core.Mathematics.Vector3.LengthSquared"/> may be preferred when only the relative length is needed
/// and speed is of the essence.
/// </remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public float Length()
{
return (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="Xenko.Core.Mathematics.Vector3.Length"/> when only a relative length is needed
/// and speed is of the essence.
/// </remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public float LengthSquared()
{
return (X * X) + (Y * Y) + (Z * Z);
}
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Normalize()
{
float length = Length();
if (length > MathUtil.ZeroTolerance)
{
float inv = 1.0f / length;
X *= inv;
Y *= inv;
Z *= inv;
}
}
/// <summary>
/// Raises the exponent for each components.
/// </summary>
/// <param name="exponent">The exponent.</param>
public void Pow(float exponent)
{
X = (float)Math.Pow(X, exponent);
Y = (float)Math.Pow(Y, exponent);
Z = (float)Math.Pow(Z, exponent);
}
/// <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 float[] { 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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Add(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Add(Vector3 left, Vector3 right)
{
return new Vector3(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>
/// <param name="result">When the method completes, contains the difference of the two vectors.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Subtract(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Subtract(Vector3 left, Vector3 right)
{
return new Vector3(left.X - right.X, left.Y - right.Y, left.Z - 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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Multiply(ref Vector3 value, float scale, out Vector3 result)
{
result = new Vector3(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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Multiply(Vector3 value, float scale)
{
return new Vector3(value.X * scale, value.Y * scale, value.Z * scale);
}
/// <summary>
/// Modulates a vector with another by performing component-wise multiplication.
/// </summary>
/// <param name="left">The first vector to modulate.</param>
/// <param name="right">The second vector to modulate.</param>
/// <param name="result">When the method completes, contains the modulated vector.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Modulate(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(left.X * right.X, left.Y * right.Y, left.Z * right.Z);
}
/// <summary>
/// Modulates a vector with another by performing component-wise multiplication.
/// </summary>
/// <param name="left">The first vector to modulate.</param>
/// <param name="right">The second vector to modulate.</param>
/// <returns>The modulated vector.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Modulate(Vector3 left, Vector3 right)
{
return new Vector3(left.X * right.X, left.Y * right.Y, left.Z * 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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Divide(ref Vector3 value, float scale, out Vector3 result)
{
result = new Vector3(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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Divide(Vector3 value, float scale)
{
return new Vector3(value.X / scale, value.Y / scale, value.Z / scale);
}
/// <summary>
/// Demodulates a vector with another by performing component-wise division.
/// </summary>
/// <param name="left">The first vector to demodulate.</param>
/// <param name="right">The second vector to demodulate.</param>
/// <param name="result">When the method completes, contains the demodulated vector.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Demodulate(ref Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(left.X / right.X, left.Y / right.Y, left.Z / right.Z);
}
/// <summary>
/// Demodulates a vector with another by performing component-wise division.
/// </summary>
/// <param name="left">The first vector to demodulate.</param>
/// <param name="right">The second vector to demodulate.</param>
/// <returns>The demodulated vector.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Demodulate(Vector3 left, Vector3 right)
{
return new Vector3(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>
/// <param name="result">When the method completes, contains a vector facing in the opposite direction.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Negate(ref Vector3 value, out Vector3 result)
{
result = new Vector3(-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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Negate(Vector3 value)
{
return new Vector3(-value.X, -value.Y, -value.Z);
}
/// <summary>
/// Returns a <see cref="Xenko.Core.Mathematics.Vector3"/> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="Xenko.Core.Mathematics.Vector3"/> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Xenko.Core.Mathematics.Vector3"/> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Xenko.Core.Mathematics.Vector3"/> 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 Vector3 value1, ref Vector3 value2, ref Vector3 value3, float amount1, float amount2, out Vector3 result)
{
result = new Vector3(
(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="Xenko.Core.Mathematics.Vector3"/> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="Xenko.Core.Mathematics.Vector3"/> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Xenko.Core.Mathematics.Vector3"/> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Xenko.Core.Mathematics.Vector3"/> 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="Xenko.Core.Mathematics.Vector3"/> containing the 3D Cartesian coordinates of the specified point.</returns>
public static Vector3 Barycentric(Vector3 value1, Vector3 value2, Vector3 value3, float amount1, float amount2)
{
Vector3 result;
Barycentric(ref value1, ref value2, ref value3, amount1, amount2, out 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 Vector3 value, ref Vector3 min, ref Vector3 max, out Vector3 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 Vector3(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 Vector3 Clamp(Vector3 value, Vector3 min, Vector3 max)
{
Vector3 result;
Clamp(ref value, ref min, ref max, out 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 Vector3 left, ref Vector3 right, out Vector3 result)
{
result = new Vector3(
(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 Vector3 Cross(Vector3 left, Vector3 right)
{
Vector3 result;
Cross(ref left, ref right, out 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="Xenko.Core.Mathematics.Vector3.DistanceSquared(ref Vector3, ref Vector3, out float)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static void Distance(ref Vector3 value1, ref Vector3 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="Xenko.Core.Mathematics.Vector3.DistanceSquared(Vector3, Vector3)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static float Distance(Vector3 value1, Vector3 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>
/// <remarks>Distance squared is the value before taking the square root.
/// Distance squared can often be used in place of distance if relative comparisons are being made.
/// For example, consider three points A, B, and C. To determine whether B or C is further from A,
/// compare the distance between A and B to the distance between A and C. Calculating the two distances
/// involves two square roots, which are computationally expensive. However, using distance squared
/// provides the same information and avoids calculating two square roots.
/// </remarks>
public static void DistanceSquared(ref Vector3 value1, ref Vector3 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>
/// <remarks>Distance squared is the value before taking the square root.
/// Distance squared can often be used in place of distance if relative comparisons are being made.
/// For example, consider three points A, B, and C. To determine whether B or C is further from A,
/// compare the distance between A and B to the distance between A and C. Calculating the two distances
/// involves two square roots, which are computationally expensive. However, using distance squared
/// provides the same information and avoids calculating two square roots.
/// </remarks>
public static float DistanceSquared(Vector3 value1, Vector3 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 dot product of two vectors.
/// </summary>
/// <param name="left">First source vector.</param>
/// <param name="right">Second source vector.</param>
/// <param name="result">When the method completes, contains the dot product of the two vectors.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Dot(ref Vector3 left, ref Vector3 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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static float Dot(Vector3 left, Vector3 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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Normalize(ref Vector3 value, out Vector3 result)
{
result = value;
result.Normalize();
}
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
/// <param name="value">The vector to normalize.</param>
/// <returns>The normalized vector.</returns>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Normalize(Vector3 value)
{
value.Normalize();
return value;
}
/// <summary>
/// Performs a linear interpolation between two vectors.
/// </summary>
/// <param name="start">Start vector.</param>
/// <param name="end">End vector.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <param name="result">When the method completes, contains the linear interpolation of the two vectors.</param>
/// <remarks>
/// This method performs the linear interpolation based on the following formula.
/// <code>start + (end - start) * amount</code>
/// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
/// </remarks>
public static void Lerp(ref Vector3 start, ref Vector3 end, float amount, out Vector3 result)
{
result.X = start.X + ((end.X - start.X) * amount);
result.Y = start.Y + ((end.Y - start.Y) * amount);
result.Z = start.Z + ((end.Z - start.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>
/// This method performs the linear interpolation based on the following formula.
/// <code>start + (end - start) * amount</code>
/// Passing <paramref name="amount"/> a value of 0 will cause <paramref name="start"/> to be returned; a value of 1 will cause <paramref name="end"/> to be returned.
/// </remarks>
public static Vector3 Lerp(Vector3 start, Vector3 end, float amount)
{
Vector3 result;
Lerp(ref start, ref end, amount, out result);
return result;
}
/// <summary>
/// Performs a cubic interpolation between two vectors.
/// </summary>
/// <param name="start">Start vector.</param>
/// <param name="end">End vector.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <param name="result">When the method completes, contains the cubic interpolation of the two vectors.</param>
public static void SmoothStep(ref Vector3 start, ref Vector3 end, float amount, out Vector3 result)
{
amount = (amount > 1.0f) ? 1.0f : ((amount < 0.0f) ? 0.0f : amount);
amount = (amount * amount) * (3.0f - (2.0f * amount));
result.X = start.X + ((end.X - start.X) * amount);
result.Y = start.Y + ((end.Y - start.Y) * amount);
result.Z = start.Z + ((end.Z - start.Z) * amount);
}
/// <summary>
/// Performs a cubic interpolation between two vectors.
/// </summary>
/// <param name="start">Start vector.</param>
/// <param name="end">End vector.</param>
/// <param name="amount">Value between 0 and 1 indicating the weight of <paramref name="end"/>.</param>
/// <returns>The cubic interpolation of the two vectors.</returns>
public static Vector3 SmoothStep(Vector3 start, Vector3 end, float amount)
{
Vector3 result;
SmoothStep(ref start, ref end, amount, out result);
return result;
}
/// <summary>
/// Performs a Hermite spline interpolation.
/// </summary>
/// <param name="value1">First source position vector.</param>
/// <param name="tangent1">First source tangent vector.</param>
/// <param name="value2">Second source position vector.</param>
/// <param name="tangent2">Second source tangent vector.</param>
/// <param name="amount">Weighting factor.</param>
/// <param name="result">When the method completes, contains the result of the Hermite spline interpolation.</param>
public static void Hermite(ref Vector3 value1, ref Vector3 tangent1, ref Vector3 value2, ref Vector3 tangent2, float amount, out Vector3 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 Vector3 Hermite(Vector3 value1, Vector3 tangent1, Vector3 value2, Vector3 tangent2, float amount)
{
Vector3 result;
Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
return result;
}
/// <summary>
/// Performs a Catmull-Rom interpolation using the specified positions.
/// </summary>
/// <param name="value1">The first position in the interpolation.</param>
/// <param name="value2">The second position in the interpolation.</param>
/// <param name="value3">The third position in the interpolation.</param>
/// <param name="value4">The fourth position in the interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <param name="result">When the method completes, contains the result of the Catmull-Rom interpolation.</param>
public static void CatmullRom(ref Vector3 value1, ref Vector3 value2, ref Vector3 value3, ref Vector3 value4, float amount, out Vector3 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 Vector3 CatmullRom(Vector3 value1, Vector3 value2, Vector3 value3, Vector3 value4, float amount)
{
Vector3 result;
CatmullRom(ref value1, ref value2, ref value3, ref value4, amount, out result);
return result;
}
/// <summary>
/// Returns a vector containing the smallest components of the specified vectors.
/// </summary>
/// <param name="left">The first source vector.</param>
/// <param name="right">The second source vector.</param>
/// <param name="result">When the method completes, contains an new vector composed of the largest components of the source vectors.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Max(ref Vector3 left, ref Vector3 right, out Vector3 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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Max(Vector3 left, Vector3 right)
{
Vector3 result;
Max(ref left, ref right, out result);
return result;
}
/// <summary>
/// Returns a vector containing the smallest components of the specified vectors.
/// </summary>
/// <param name="left">The first source vector.</param>
/// <param name="right">The second source vector.</param>
/// <param name="result">When the method completes, contains an new vector composed of the smallest components of the source vectors.</param>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static void Min(ref Vector3 left, ref Vector3 right, out Vector3 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>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public static Vector3 Min(Vector3 left, Vector3 right)
{
Vector3 result;
Min(ref left, ref right, out result);
return result;
}
/// <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 Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Vector3 result)
{
Vector3 v;
TransformCoordinate(ref vector, ref worldViewProjection, out v);
result = new Vector3(((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 Vector3 Project(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)
{
Vector3 result;
Project(ref vector, x, y, width, height, minZ, maxZ, ref worldViewProjection, out 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 Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Vector3 result)
{
Vector3 v = new Vector3();
Matrix matrix;
Matrix.Invert(ref worldViewProjection, out matrix);
v.X = (((vector.X - x) / width) * 2.0f) - 1.0f;
v.Y = -((((vector.Y - y) / height) * 2.0f) - 1.0f);
v.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 Vector3 Unproject(Vector3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection)
{
Vector3 result;
Unproject(ref vector, x, y, width, height, minZ, maxZ, ref worldViewProjection, out result);
return result;
}
/// <summary>
/// Returns the reflection of a vector off a surface that has the specified normal.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="normal">Normal of the surface.</param>
/// <param name="result">When the method completes, contains the reflected vector.</param>
/// <remarks>Reflect only gives the direction of a reflection off a surface, it does not determine
/// whether the original vector was close enough to the surface to hit it.</remarks>
public static void Reflect(ref Vector3 vector, ref Vector3 normal, out Vector3 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 Vector3 Reflect(Vector3 vector, Vector3 normal)
{
Vector3 result;
Reflect(ref vector, ref normal, out result);
return result;
}
/// <summary>
/// Orthogonalizes a list of vectors.
/// </summary>
/// <param name="destination">The list of orthogonalized vectors.</param>
/// <param name="source">The list of vectors to orthogonalize.</param>
/// <remarks>
/// <para>Orthogonalization is the process of making all vectors orthogonal to each other. This
/// means that any given vector in the list will be orthogonal to any other given vector in the
/// list.</para>
/// <para>Because this method uses the modified Gram-Schmidt process, the resulting vectors
/// tend to be numerically unstable. The numeric stability decreases according to the vectors
/// position in the list so that the first vector is the most stable and the last vector is the
/// least stable.</para>
/// </remarks>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Orthogonalize(Vector3[] destination, params Vector3[] source)
{
//Uses the modified Gram-Schmidt process.
//q1 = m1
//q2 = m2 - ((q1 ⋅ m2) / (q1 ⋅ q1)) * q1
//q3 = m3 - ((q1 ⋅ m3) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m3) / (q2 ⋅ q2)) * q2
//q4 = m4 - ((q1 ⋅ m4) / (q1 ⋅ q1)) * q1 - ((q2 ⋅ m4) / (q2 ⋅ q2)) * q2 - ((q3 ⋅ m4) / (q3 ⋅ q3)) * q3
//q5 = ...
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
for (int i = 0; i < source.Length; ++i)
{