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sharplib/math/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.ComponentModel;
using System.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Serialization;
namespace math
{
/// <summary>
/// Represents a three dimensional mathematical vector.
/// </summary>
[DataContract( Name = "float3" )]
[DataStyle( DataStyle.Compact )]
[StructLayout( LayoutKind.Sequential, Pack = 4 )]
public struct Vec3 : IEquatable<Vec3>, IFormattable
{
/// <summary>
/// The size of the <see cref="math.Vec3"/> type, in bytes.
/// </summary>
public static readonly int SizeInBytes = lib.Util.SizeOf<Vec3>();
/// <summary>
/// A <see cref="math.Vec3"/> with all of its components set to zero.
/// </summary>
public static readonly Vec3 Zero = new Vec3();
/// <summary>
/// The X unit <see cref="math.Vec3"/> (1, 0, 0).
/// </summary>
public static readonly Vec3 UnitX = new Vec3( 1.0f, 0.0f, 0.0f );
/// <summary>
/// The Y unit <see cref="math.Vec3"/> (0, 1, 0).
/// </summary>
public static readonly Vec3 UnitY = new Vec3( 0.0f, 1.0f, 0.0f );
/// <summary>
/// The Z unit <see cref="math.Vec3"/> (0, 0, 1).
/// </summary>
public static readonly Vec3 UnitZ = new Vec3( 0.0f, 0.0f, 1.0f );
/// <summary>
/// A <see cref="math.Vec3"/> with all of its components set to one.
/// </summary>
public static readonly Vec3 One = new Vec3( 1.0f, 1.0f, 1.0f );
/// <summary>
/// The X component of the vector.
/// </summary>
[DataMember( Order = 0 )]
public float X;
/// <summary>
/// The Y component of the vector.
/// </summary>
[DataMember( Order = 1 )]
public float Y;
/// <summary>
/// The Z component of the vector.
/// </summary>
[DataMember( Order = 2 )]
public float Z;
/// <summary>
/// Initializes a new instance of the <see cref="math.Vec3"/> struct.
/// </summary>
/// <param name="value">The value that will be assigned to all components.</param>
public Vec3( float value )
{
X = value;
Y = value;
Z = value;
}
/// <summary>
/// Initializes a new instance of the <see cref="math.Vec3"/> 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 Vec3( float x, float y, float z )
{
X = x;
Y = y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="math.Vec3"/> 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 Vec3( Vec2 value, float z )
{
X = value.X;
Y = value.Y;
Z = z;
}
/// <summary>
/// Initializes a new instance of the <see cref="math.Vec3"/> 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 Vec3( 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="math.Vec3.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="math.Vec3.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 Vec3 left, ref Vec3 right, out Vec3 result )
{
result = new Vec3( 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 Vec3 Add( Vec3 left, Vec3 right )
{
return new Vec3( 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 Vec3 left, ref Vec3 right, out Vec3 result )
{
result = new Vec3( 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 Vec3 Subtract( Vec3 left, Vec3 right )
{
return new Vec3( 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 Vec3 value, float scale, out Vec3 result )
{
result = new Vec3( 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 Vec3 Multiply( Vec3 value, float scale )
{
return new Vec3( 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 Vec3 left, ref Vec3 right, out Vec3 result )
{
result = new Vec3( 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 Vec3 Modulate( Vec3 left, Vec3 right )
{
return new Vec3( 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 Vec3 value, float scale, out Vec3 result )
{
result = new Vec3( 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 Vec3 Divide( Vec3 value, float scale )
{
return new Vec3( 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 Vec3 left, ref Vec3 right, out Vec3 result )
{
result = new Vec3( 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 Vec3 Demodulate( Vec3 left, Vec3 right )
{
return new Vec3( 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 Vec3 value, out Vec3 result )
{
result = new Vec3( -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 Vec3 Negate( Vec3 value )
{
return new Vec3( -value.X, -value.Y, -value.Z );
}
/// <summary>
/// Returns a <see cref="math.Vec3"/> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="math.Vec3"/> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="math.Vec3"/> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="math.Vec3"/> 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 Vec3 value1, ref Vec3 value2, ref Vec3 value3, float amount1, float amount2, out Vec3 result )
{
result = new Vec3(
( 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="math.Vec3"/> containing the 3D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 3D triangle.
/// </summary>
/// <param name="value1">A <see cref="math.Vec3"/> containing the 3D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="math.Vec3"/> containing the 3D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="math.Vec3"/> 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="math.Vec3"/> containing the 3D Cartesian coordinates of the specified point.</returns>
public static Vec3 Barycentric( Vec3 value1, Vec3 value2, Vec3 value3, float amount1, float amount2 )
{
Vec3 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 Vec3 value, ref Vec3 min, ref Vec3 max, out Vec3 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 Vec3( 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 Vec3 Clamp( Vec3 value, Vec3 min, Vec3 max )
{
Vec3 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 Vec3 left, ref Vec3 right, out Vec3 result )
{
result = new Vec3(
( 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 Vec3 Cross( Vec3 left, Vec3 right )
{
Vec3 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="math.Vec3.DistanceSquared(ref Vec3, ref Vec3, out float)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static void Distance( ref Vec3 value1, ref Vec3 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="math.Vec3.DistanceSquared(Vec3, Vec3)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static float Distance( Vec3 value1, Vec3 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 Vec3 value1, ref Vec3 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( Vec3 value1, Vec3 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 Vec3 left, ref Vec3 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( Vec3 left, Vec3 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 Vec3 value, out Vec3 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 Vec3 Normalize( Vec3 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 Vec3 start, ref Vec3 end, float amount, out Vec3 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 Vec3 Lerp( Vec3 start, Vec3 end, float amount )
{
Vec3 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 Vec3 start, ref Vec3 end, float amount, out Vec3 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 Vec3 SmoothStep( Vec3 start, Vec3 end, float amount )
{
Vec3 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 Vec3 value1, ref Vec3 tangent1, ref Vec3 value2, ref Vec3 tangent2, float amount, out Vec3 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 Vec3 Hermite( Vec3 value1, Vec3 tangent1, Vec3 value2, Vec3 tangent2, float amount )
{
Vec3 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 Vec3 value1, ref Vec3 value2, ref Vec3 value3, ref Vec3 value4, float amount, out Vec3 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 Vec3 CatmullRom( Vec3 value1, Vec3 value2, Vec3 value3, Vec3 value4, float amount )
{
Vec3 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 Vec3 left, ref Vec3 right, out Vec3 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 Vec3 Max( Vec3 left, Vec3 right )
{
Vec3 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 Vec3 left, ref Vec3 right, out Vec3 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 Vec3 Min( Vec3 left, Vec3 right )
{
Vec3 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 Vec3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Vec3 result )
{
Vec3 v;
TransformCoordinate( ref vector, ref worldViewProjection, out v );
result = new Vec3( ( ( 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 Vec3 Project( Vec3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection )
{
Vec3 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 Vec3 vector, float x, float y, float width, float height, float minZ, float maxZ, ref Matrix worldViewProjection, out Vec3 result )
{
Vec3 v = new Vec3();
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 Vec3 Unproject( Vec3 vector, float x, float y, float width, float height, float minZ, float maxZ, Matrix worldViewProjection )
{
Vec3 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 Vec3 vector, ref Vec3 normal, out Vec3 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 Vec3 Reflect( Vec3 vector, Vec3 normal )
{
Vec3 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( Vec3[] destination, params Vec3[] 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 )
{
Vec3 newvector = source[i];
for( int r = 0; r < i; ++r )
{
newvector -= ( Vec3.Dot( destination[r], newvector ) / Vec3.Dot( destination[r], destination[r] ) ) * destination[r];
}
destination[i] = newvector;
}
}
/// <summary>
/// Orthonormalizes a list of vectors.
/// </summary>
/// <param name="destination">The list of orthonormalized vectors.</param>
/// <param name="source">The list of vectors to orthonormalize.</param>
/// <remarks>
/// <para>Orthonormalization is the process of making all vectors orthogonal to each
/// other and making all vectors of unit length. This means that any given vector will
/// be orthogonal to any other given vector in the list.</para>
/// <para>Because this method uses the modified Gram-Schmidt process, the resulting vectors
/// tend to be numerically unstable. The numeric stability decreases according to the vectors
/// position in the list so that the first vector is the most stable and the last vector is the
/// least stable.</para>
/// </remarks>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Orthonormalize( Vec3[] destination, params Vec3[] source )
{
//Uses the modified Gram-Schmidt process.
//Because we are making unit vectors, we can optimize the math for orthogonalization
//and simplify the projection operation to remove the division.
//q1 = m1 / |m1|
//q2 = (m2 - (q1 ⋅ m2) * q1) / |m2 - (q1 ⋅ m2) * q1|
//q3 = (m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2) / |m3 - (q1 ⋅ m3) * q1 - (q2 ⋅ m3) * q2|
//q4 = (m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3) / |m4 - (q1 ⋅ m4) * q1 - (q2 ⋅ m4) * q2 - (q3 ⋅ m4) * q3|
//q5 = ...
if( source == null )
throw new ArgumentNullException( "_source" );
if( destination == null )
throw new ArgumentNullException( "destination" );
if( destination.Length < source.Length )
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
for( int i = 0; i < source.Length; ++i )
{
Vec3 newvector = source[i];
for( int r = 0; r < i; ++r )
{
newvector -= Vec3.Dot( destination[r], newvector ) * destination[r];
}
newvector.Normalize();
destination[i] = newvector;
}
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="math.Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="math.Quaternion"/> rotation to apply.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="math.Vec4"/>.</param>
public static void Transform( ref Vec3 vector, ref Quaternion rotation, out Vec3 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 Vec3(
( ( 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="math.Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="math.Quaternion"/> rotation to apply.</param>
/// <returns>The transformed <see cref="math.Vec4"/>.</returns>
public static Vec3 Transform( Vec3 vector, Quaternion rotation )
{
Vec3 result;
Transform( ref vector, ref rotation, out result );
return result;
}
/// <summary>
/// Transforms an array of vectors by the given <see cref="math.Quaternion"/> rotation.
/// </summary>
/// <param name="source">The array of vectors to transform.</param>
/// <param name="rotation">The <see cref="math.Quaternion"/> rotation to apply.</param>
/// <param name="destination">The array for which the transformed vectors are stored.
/// This array may be the same array as <paramref name="source"/>.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Transform( Vec3[] source, ref Quaternion rotation, Vec3[] destination )
{
if( source == null )
throw new ArgumentNullException( "_source" );
if( destination == null )
throw new ArgumentNullException( "destination" );
if( destination.Length < source.Length )
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
float x = rotation.X + rotation.X;
float y = rotation.Y + rotation.Y;
float z = rotation.Z + rotation.Z;
float 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;
float num1 = ( ( 1.0f - yy ) - zz );
float num2 = ( xy - wz );
float num3 = ( xz + wy );
float num4 = ( xy + wz );
float num5 = ( ( 1.0f - xx ) - zz );
float num6 = ( yz - wx );
float num7 = ( xz - wy );
float num8 = ( yz + wx );
float num9 = ( ( 1.0f - xx ) - yy );
for( int i = 0; i < source.Length; ++i )
{
destination[i] = new Vec3(
( ( source[i].X * num1 ) + ( source[i].Y * num2 ) ) + ( source[i].Z * num3 ),
( ( source[i].X * num4 ) + ( source[i].Y * num5 ) ) + ( source[i].Z * num6 ),
( ( source[i].X * num7 ) + ( source[i].Y * num8 ) ) + ( source[i].Z * num9 ) );
}
}
/// <summary>
/// Transforms a 3D vector by the given <see cref="math.Matrix"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="math.Vec4"/>.</param>
public static void Transform( ref Vec3 vector, ref Matrix transform, out Vec4 result )
{
result = new Vec4(
( 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="math.Matrix"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="math.Vec3"/>.</param>
public static void Transform( ref Vec3 vector, ref Matrix transform, out Vec3 result )
{
result = new Vec3(
( 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="math.Matrix"/>.
/// </summary>
/// <param name="vector">The source vector.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <returns>The transformed <see cref="math.Vec4"/>.</returns>
public static Vec4 Transform( Vec3 vector, Matrix transform )
{
Vec4 result;
Transform( ref vector, ref transform, out result );
return result;
}
/// <summary>
/// Transforms an array of 3D vectors by the given <see cref="math.Matrix"/>.
/// </summary>
/// <param name="source">The array of vectors to transform.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <param name="destination">The array for which the transformed vectors are stored.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
public static void Transform( Vec3[] source, ref Matrix transform, Vec4[] destination )
{
if( source == null )
throw new ArgumentNullException( "_source" );
if( destination == null )
throw new ArgumentNullException( "destination" );
if( destination.Length < source.Length )
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
for( int i = 0; i < source.Length; ++i )
{
Transform( ref source[i], ref transform, out destination[i] );
}
}
/// <summary>
/// Performs a coordinate transformation using the given <see cref="math.Matrix"/>.
/// </summary>
/// <param name="coordinate">The coordinate vector to transform.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed coordinates.</param>
/// <remarks>
/// A coordinate transform performs the transformation with the assumption that the w component
/// is one. The four dimensional vector obtained from the transformation operation has each
/// component in the vector divided by the w component. This forces the wcomponent to be one and
/// therefore makes the vector homogeneous. The homogeneous vector is often prefered when working
/// with coordinates as the w component can safely be ignored.
/// </remarks>
public static void TransformCoordinate( ref Vec3 coordinate, ref Matrix transform, out Vec3 result )
{
var invW = 1f / ( ( coordinate.X * transform.M14 ) + ( coordinate.Y * transform.M24 ) + ( coordinate.Z * transform.M34 ) + transform.M44 );
result = new Vec3(
( ( coordinate.X * transform.M11 ) + ( coordinate.Y * transform.M21 ) + ( coordinate.Z * transform.M31 ) + transform.M41 ) * invW,
( ( coordinate.X * transform.M12 ) + ( coordinate.Y * transform.M22 ) + ( coordinate.Z * transform.M32 ) + transform.M42 ) * invW,
( ( coordinate.X * transform.M13 ) + ( coordinate.Y * transform.M23 ) + ( coordinate.Z * transform.M33 ) + transform.M43 ) * invW );
}
/// <summary>
/// Performs a coordinate transformation using the given <see cref="math.Matrix"/>.
/// </summary>
/// <param name="coordinate">The coordinate vector to transform.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <returns>The transformed coordinates.</returns>
/// <remarks>
/// A coordinate transform performs the transformation with the assumption that the w component
/// is one. The four dimensional vector obtained from the transformation operation has each
/// component in the vector divided by the w component. This forces the wcomponent to be one and
/// therefore makes the vector homogeneous. The homogeneous vector is often prefered when working
/// with coordinates as the w component can safely be ignored.
/// </remarks>
public static Vec3 TransformCoordinate( Vec3 coordinate, Matrix transform )
{
Vec3 result;
TransformCoordinate( ref coordinate, ref transform, out result );
return result;
}
/// <summary>
/// Performs a coordinate transformation on an array of vectors using the given <see cref="math.Matrix"/>.
/// </summary>
/// <param name="source">The array of coordinate vectors to trasnform.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <param name="destination">The array for which the transformed vectors are stored.
/// This array may be the same array as <paramref name="source"/>.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
/// <remarks>
/// A coordinate transform performs the transformation with the assumption that the w component
/// is one. The four dimensional vector obtained from the transformation operation has each
/// component in the vector divided by the w component. This forces the wcomponent to be one and
/// therefore makes the vector homogeneous. The homogeneous vector is often prefered when working
/// with coordinates as the w component can safely be ignored.
/// </remarks>
public static void TransformCoordinate( Vec3[] source, ref Matrix transform, Vec3[] destination )
{
if( source == null )
throw new ArgumentNullException( "_source" );
if( destination == null )
throw new ArgumentNullException( "destination" );
if( destination.Length < source.Length )
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
for( int i = 0; i < source.Length; ++i )
{
TransformCoordinate( ref source[i], ref transform, out destination[i] );
}
}
/// <summary>
/// Performs a normal transformation using the given <see cref="math.Matrix"/>.
/// </summary>
/// <param name="normal">The normal vector to transform.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed normal.</param>
/// <remarks>
/// A normal transform performs the transformation with the assumption that the w component
/// is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The
/// end result is a vector that is not translated, but all other transformation properties
/// apply. This is often prefered for normal vectors as normals purely represent direction
/// rather than location because normal vectors should not be translated.
/// </remarks>
public static void TransformNormal( ref Vec3 normal, ref Matrix transform, out Vec3 result )
{
result = new Vec3(
( 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="math.Matrix"/>.
/// </summary>
/// <param name="normal">The normal vector to transform.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <returns>The transformed normal.</returns>
/// <remarks>
/// A normal transform performs the transformation with the assumption that the w component
/// is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The
/// end result is a vector that is not translated, but all other transformation properties
/// apply. This is often prefered for normal vectors as normals purely represent direction
/// rather than location because normal vectors should not be translated.
/// </remarks>
public static Vec3 TransformNormal( Vec3 normal, Matrix transform )
{
Vec3 result;
TransformNormal( ref normal, ref transform, out result );
return result;
}
/// <summary>
/// Performs a normal transformation on an array of vectors using the given <see cref="math.Matrix"/>.
/// </summary>
/// <param name="source">The array of normal vectors to transform.</param>
/// <param name="transform">The transformation <see cref="math.Matrix"/>.</param>
/// <param name="destination">The array for which the transformed vectors are stored.
/// This array may be the same array as <paramref name="source"/>.</param>
/// <exception cref="ArgumentNullException">Thrown when <paramref name="source"/> or <paramref name="destination"/> is <c>null</c>.</exception>
/// <exception cref="ArgumentOutOfRangeException">Thrown when <paramref name="destination"/> is shorter in length than <paramref name="source"/>.</exception>
/// <remarks>
/// A normal transform performs the transformation with the assumption that the w component
/// is zero. This causes the fourth row and fourth collumn of the matrix to be unused. The
/// end result is a vector that is not translated, but all other transformation properties
/// apply. This is often prefered for normal vectors as normals purely represent direction
/// rather than location because normal vectors should not be translated.
/// </remarks>
public static void TransformNormal( Vec3[] source, ref Matrix transform, Vec3[] destination )
{
if( source == null )
throw new ArgumentNullException( "_source" );
if( destination == null )
throw new ArgumentNullException( "destination" );
if( destination.Length < source.Length )
throw new ArgumentOutOfRangeException( "destination", "The destination array must be of same length or larger length than the _source array." );
for( int i = 0; i < source.Length; ++i )
{
TransformNormal( ref source[i], ref transform, out destination[i] );
}
}
/// <summary>
/// Calculate the yaw/pitch/roll rotation equivalent to the provided quaterion.
/// </summary>
/// <param name="quaternion">The input rotation as quaternion</param>
/// <returns>The equivation yaw/pitch/roll rotation</returns>
public static Vec3 RotationYawPitchRoll( Quaternion quaternion )
{
Vec3 yawPitchRoll;
Quaternion.RotationYawPitchRoll( ref quaternion, out yawPitchRoll.X, out yawPitchRoll.Y, out yawPitchRoll.Z );
return yawPitchRoll;
}
/// <summary>
/// Calculate the yaw/pitch/roll rotation equivalent to the provided quaterion.
/// </summary>
/// <param name="quaternion">The input rotation as quaternion</param>
/// <param name="yawPitchRoll">The equivation yaw/pitch/roll rotation</param>
public static void RotationYawPitchRoll( ref Quaternion quaternion, out Vec3 yawPitchRoll )
{
Quaternion.RotationYawPitchRoll( ref quaternion, out yawPitchRoll.X, out yawPitchRoll.Y, out yawPitchRoll.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 Vec3 operator +( Vec3 left, Vec3 right )
{
return new Vec3( 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 (unchange).</param>
/// <returns>The asserted (unchanged) vector.</returns>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator +( Vec3 value )
{
return value;
}
/// <summary>
/// Subtracts two vectors.
/// </summary>
/// <param name="left">The first vector to subtract.</param>
/// <param name="right">The second vector to subtract.</param>
/// <returns>The difference of the two vectors.</returns>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator -( Vec3 left, Vec3 right )
{
return new Vec3( 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>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator -( Vec3 value )
{
return new Vec3( -value.X, -value.Y, -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>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator *( float scale, Vec3 value )
{
return new Vec3( 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 Vec3 operator *( Vec3 value, float scale )
{
return new Vec3( 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 multiply.</param>
/// <param name="right">The second vector to multiply.</param>
/// <returns>The multiplication of the two vectors.</returns>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator *( Vec3 left, Vec3 right )
{
return new Vec3( left.X * right.X, left.Y * right.Y, left.Z * right.Z );
}
/// <summary>
/// Adds a vector with 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 vector offset.</returns>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator +( Vec3 value, float scale )
{
return new Vec3( value.X + scale, value.Y + scale, value.Z + scale );
}
/// <summary>
/// Substracts 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 vector offset.</returns>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator -( Vec3 value, float scale )
{
return new Vec3( value.X - scale, value.Y - scale, value.Z - scale );
}
/// <summary>
/// Divides a numerator by a vector.
/// </summary>
/// <param name="numerator">The numerator.</param>
/// <param name="value">The value.</param>
/// <returns>The scaled vector.</returns>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator /( float numerator, Vec3 value )
{
return new Vec3( numerator / value.X, numerator / value.Y, numerator / 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>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator /( Vec3 value, float scale )
{
return new Vec3( value.X / scale, value.Y / scale, value.Z / scale );
}
/// <summary>
/// Divides a vector by the given vector, component-wise.
/// </summary>
/// <param name="value">The vector to scale.</param>
/// <param name="by">The by.</param>
/// <returns>The scaled vector.</returns>
[MethodImpl( MethodImplOptions.AggressiveInlining )]
public static Vec3 operator /( Vec3 value, Vec3 by )
{
return new Vec3( value.X / by.X, value.Y / by.Y, value.Z / by.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>
public static bool operator ==( Vec3 left, Vec3 right )
{
return left.Equals( right );
}
/// <summary>
/// Tests for inequality between two objects.
/// </summary>
/// <param name="left">The first value to compare.</param>
/// <param name="right">The second value to compare.</param>
/// <returns><c>true</c> if <paramref name="left"/> has a different value than <paramref name="right"/>; otherwise, <c>false</c>.</returns>
public static bool operator !=( Vec3 left, Vec3 right )
{
return !left.Equals( right );
}
/// <summary>
/// Performs an explicit conversion from <see cref="math.Vec3"/> to <see cref="math.Vec2"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static explicit operator Vec2( Vec3 value )
{
return new Vec2( value.X, value.Y );
}
/// <summary>
/// Performs an explicit conversion from <see cref="math.Vec3"/> to <see cref="math.Vec4"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static explicit operator Vec4( Vec3 value )
{
return new Vec4( value, 0.0f );
}
/// <summary>
/// Tests whether one 3D vector is near another 3D 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 3D, <c>false</c> otherwise</returns>
public static bool NearEqual( Vec3 left, Vec3 right, Vec3 epsilon )
{
return NearEqual( ref left, ref right, ref epsilon );
}
/// <summary>
/// Tests whether one 3D vector is near another 3D 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 3D, <c>false</c> otherwise</returns>
public static bool NearEqual( ref Vec3 left, ref Vec3 right, ref Vec3 epsilon )
{
return MathUtil.WithinEpsilon( left.X, right.X, epsilon.X ) &&
MathUtil.WithinEpsilon( left.Y, right.Y, epsilon.Y ) &&
MathUtil.WithinEpsilon( left.Z, right.Z, epsilon.Z );
}
/// <summary>
/// Returns a <see cref="string"/> that represents this instance.
/// </summary>
/// <returns>
/// A <see cref="string"/> that represents this instance.
/// </returns>
public override string ToString()
{
return string.Format( CultureInfo.CurrentCulture, "X:{0} Y:{1} Z:{2}", X, Y, Z );
}
/// <summary>
/// Returns a <see cref="string"/> that represents this instance.
/// </summary>
/// <param name="format">The format.</param>
/// <returns>
/// A <see cref="string"/> that represents this instance.
/// </returns>
public string ToString( string format )
{
if( format == null )
return ToString();
return string.Format( CultureInfo.CurrentCulture, "X:{0} Y:{1} Z:{2}", X.ToString( format, CultureInfo.CurrentCulture ),
Y.ToString( format, CultureInfo.CurrentCulture ), Z.ToString( format, CultureInfo.CurrentCulture ) );
}
/// <summary>
/// Returns a <see cref="string"/> that represents this instance.
/// </summary>
/// <param name="formatProvider">The format provider.</param>
/// <returns>
/// A <see cref="string"/> that represents this instance.
/// </returns>
public string ToString( IFormatProvider formatProvider )
{
return string.Format( formatProvider, "X:{0} Y:{1} Z:{2}", X, Y, Z );
}
/// <summary>
/// Returns a <see cref="string"/> that represents this instance.
/// </summary>
/// <param name="format">The format.</param>
/// <param name="formatProvider">The format provider.</param>
/// <returns>
/// A <see cref="string"/> that represents this instance.
/// </returns>
public string ToString( string format, IFormatProvider formatProvider )
{
if( format == null )
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>
/// <returns>
/// A hash code for this instance, suitable for use in hashing algorithms and data structures like a hash table.
/// </returns>
public override int GetHashCode()
{
return X.GetHashCode() + Y.GetHashCode() + Z.GetHashCode();
}
/// <summary>
/// Determines whether the specified <see cref="math.Vec3"/> is equal to this instance.
/// </summary>
/// <param name="other">The <see cref="math.Vec3"/> to compare with this instance.</param>
/// <returns>
/// <c>true</c> if the specified <see cref="math.Vec3"/> is equal to this instance; otherwise, <c>false</c>.
/// </returns>
public bool Equals( Vec3 other )
{
return ( (float)Math.Abs( other.X - X ) < MathUtil.ZeroTolerance &&
(float)Math.Abs( other.Y - Y ) < MathUtil.ZeroTolerance &&
(float)Math.Abs( other.Z - Z ) < MathUtil.ZeroTolerance );
}
/// <summary>
/// Determines whether the specified <see cref="object"/> is equal to this instance.
/// </summary>
/// <param name="value">The <see cref="object"/> to compare with this instance.</param>
/// <returns>
/// <c>true</c> if the specified <see cref="object"/> is equal to this instance; otherwise, <c>false</c>.
/// </returns>
public override bool Equals( object value )
{
if( value == null )
return false;
if( value.GetType() != GetType() )
return false;
return Equals( (Vec3)value );
}
#if WPFInterop
/// <summary>
/// Performs an implicit conversion from <see cref="math.Vector3"/> to <see cref="System.Windows.Media.Media3D.Vector3D"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static implicit operator System.Windows.Media.Media3D.Vector3D(Vector3 value)
{
return new System.Windows.Media.Media3D.Vector3D(value.X, value.Y, value.Z);
}
/// <summary>
/// Performs an explicit conversion from <see cref="System.Windows.Media.Media3D.Vector3D"/> to <see cref="math.Vector3"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static explicit operator Vector3(System.Windows.Media.Media3D.Vector3D value)
{
return new Vector3((float)value.X, (float)value.Y, (float)value.Z);
}
#endif
#if XnaInterop
/// <summary>
/// Performs an implicit conversion from <see cref="math.Vector3"/> to <see cref="Microsoft.Xna.Framework.Vector3"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static implicit operator Microsoft.Xna.Framework.Vector3(Vector3 value)
{
return new Microsoft.Xna.Framework.Vector3(value.X, value.Y, value.Z);
}
/// <summary>
/// Performs an implicit conversion from <see cref="Microsoft.Xna.Framework.Vector3"/> to <see cref="math.Vector3"/>.
/// </summary>
/// <param name="value">The value.</param>
/// <returns>The result of the conversion.</returns>
public static implicit operator Vector3(Microsoft.Xna.Framework.Vector3 value)
{
return new Vector3(value.X, value.Y, value.Z);
}
#endif
}
}
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