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Double4.cs
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Double4.cs
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// Copyright (c) Stride contributors. (https://stride3d.net)
// Distributed under the MIT license. See the LICENSE.md file in the project root for more information.
using System;
using System.ComponentModel;
using System.Globalization;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
namespace Stride.Core.Mathematics
{
/// <summary>
/// Represents a four dimensional mathematical vector with double-precision floats.
/// </summary>
[DataContract("double4")]
[DataStyle(DataStyle.Compact)]
[StructLayout(LayoutKind.Sequential, Pack = 4)]
public struct Double4 : IEquatable<Double4>, IFormattable
{
/// <summary>
/// The size of the <see cref="Stride.Core.Mathematics.Double4"/> type, in bytes.
/// </summary>
public static readonly int SizeInBytes = Utilities.SizeOf<Double4>();
/// <summary>
/// A <see cref="Stride.Core.Mathematics.Double4"/> with all of its components set to zero.
/// </summary>
public static readonly Double4 Zero = new Double4();
/// <summary>
/// The X unit <see cref="Stride.Core.Mathematics.Double4"/> (1, 0, 0, 0).
/// </summary>
public static readonly Double4 UnitX = new Double4(1.0, 0.0, 0.0, 0.0);
/// <summary>
/// The Y unit <see cref="Stride.Core.Mathematics.Double4"/> (0, 1, 0, 0).
/// </summary>
public static readonly Double4 UnitY = new Double4(0.0, 1.0, 0.0, 0.0);
/// <summary>
/// The Z unit <see cref="Stride.Core.Mathematics.Double4"/> (0, 0, 1, 0).
/// </summary>
public static readonly Double4 UnitZ = new Double4(0.0, 0.0, 1.0, 0.0);
/// <summary>
/// The W unit <see cref="Stride.Core.Mathematics.Double4"/> (0, 0, 0, 1).
/// </summary>
public static readonly Double4 UnitW = new Double4(0.0, 0.0, 0.0, 1.0);
/// <summary>
/// A <see cref="Stride.Core.Mathematics.Double4"/> with all of its components set to one.
/// </summary>
public static readonly Double4 One = new Double4(1.0, 1.0, 1.0, 1.0);
/// <summary>
/// The X component of the vector.
/// </summary>
[DataMember(0)]
public double X;
/// <summary>
/// The Y component of the vector.
/// </summary>
[DataMember(1)]
public double Y;
/// <summary>
/// The Z component of the vector.
/// </summary>
[DataMember(2)]
public double Z;
/// <summary>
/// The W component of the vector.
/// </summary>
[DataMember(3)]
public double W;
/// <summary>
/// Initializes a new instance of the <see cref="Stride.Core.Mathematics.Double4"/> struct.
/// </summary>
/// <param name="value">The value that will be assigned to all components.</param>
public Double4(double value)
{
X = value;
Y = value;
Z = value;
W = value;
}
/// <summary>
/// Initializes a new instance of the <see cref="Stride.Core.Mathematics.Double4"/> 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>
/// <param name="w">Initial value for the W component of the vector.</param>
public Double4(double x, double y, double z, double w)
{
X = x;
Y = y;
Z = z;
W = w;
}
/// <summary>
/// Initializes a new instance of the <see cref="Stride.Core.Mathematics.Double4"/> struct.
/// </summary>
/// <param name="value">A vector containing the values with which to initialize the X, Y, and Z components.</param>
/// <param name="w">Initial value for the W component of the vector.</param>
public Double4(Double3 value, double w)
{
X = value.X;
Y = value.Y;
Z = value.Z;
W = w;
}
/// <summary>
/// Initializes a new instance of the <see cref="Stride.Core.Mathematics.Double4"/> 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>
/// <param name="w">Initial value for the W component of the vector.</param>
public Double4(Double2 value, double z, double w)
{
X = value.X;
Y = value.Y;
Z = z;
W = w;
}
/// <summary>
/// Initializes a new instance of the <see cref="Stride.Core.Mathematics.Double4"/> struct.
/// </summary>
/// <param name="values">The values to assign to the X, Y, Z, and W components of the vector. This must be an array with four 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 four elements.</exception>
public Double4(double[] values)
{
if (values == null)
throw new ArgumentNullException("values");
if (values.Length != 4)
throw new ArgumentOutOfRangeException("values", "There must be four and only four input values for Double4.");
X = values[0];
Y = values[1];
Z = values[2];
W = values[3];
}
/// <summary>
/// Initializes a new instance of the <see cref="Stride.Core.Mathematics.Double4"/> struct.
/// </summary>
/// <param name="v">The Vector4 to construct the Double4 from.</param>
public Double4(Vector4 v)
{
X = v.X;
Y = v.Y;
Z = v.Z;
W = v.W;
}
/// <summary>
/// Gets a value indicting whether this instance is normalized.
/// </summary>
public bool IsNormalized
{
get { return Math.Abs((X * X) + (Y * Y) + (Z * Z) + (W * W) - 1f) < MathUtil.ZeroTolerance; }
}
/// <summary>
/// Gets or sets the component at the specified index.
/// </summary>
/// <value>The value of the X, Y, Z, or W 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, 2 for the Z component, and 3 for the W 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, 3].</exception>
public double this[int index]
{
get
{
switch (index)
{
case 0: return X;
case 1: return Y;
case 2: return Z;
case 3: return W;
}
throw new ArgumentOutOfRangeException("index", "Indices for Double4 run from 0 to 3, inclusive.");
}
set
{
switch (index)
{
case 0: X = value; break;
case 1: Y = value; break;
case 2: Z = value; break;
case 3: W = value; break;
default: throw new ArgumentOutOfRangeException("index", "Indices for Double4 run from 0 to 3, inclusive.");
}
}
}
/// <summary>
/// Calculates the length of the vector.
/// </summary>
/// <returns>The length of the vector.</returns>
/// <remarks>
/// <see cref="Stride.Core.Mathematics.Double4.LengthSquared"/> may be preferred when only the relative length is needed
/// and speed is of the essence.
/// </remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public double Length()
{
return (double)Math.Sqrt((X * X) + (Y * Y) + (Z * Z) + (W * W));
}
/// <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="Stride.Core.Mathematics.Double4.Length"/> when only a relative length is needed
/// and speed is of the essence.
/// </remarks>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public double LengthSquared()
{
return (X * X) + (Y * Y) + (Z * Z) + (W * W);
}
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
[MethodImpl(MethodImplOptions.AggressiveInlining)]
public void Normalize()
{
double length = Length();
if (length > MathUtil.ZeroTolerance)
{
double inverse = 1.0 / length;
X *= inverse;
Y *= inverse;
Z *= inverse;
W *= inverse;
}
}
/// <summary>
/// Raises the exponent for each components.
/// </summary>
/// <param name="exponent">The exponent.</param>
public void Pow(double exponent)
{
X = (double)Math.Pow(X, exponent);
Y = (double)Math.Pow(Y, exponent);
Z = (double)Math.Pow(Z, exponent);
W = (double)Math.Pow(W, exponent);
}
/// <summary>
/// Creates an array containing the elements of the vector.
/// </summary>
/// <returns>A four-element array containing the components of the vector.</returns>
public double[] ToArray()
{
return new double[] { X, Y, Z, W };
}
/// <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 Double4 left, ref Double4 right, out Double4 result)
{
result = new Double4(left.X + right.X, left.Y + right.Y, left.Z + right.Z, left.W + right.W);
}
/// <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 Double4 Add(Double4 left, Double4 right)
{
return new Double4(left.X + right.X, left.Y + right.Y, left.Z + right.Z, left.W + right.W);
}
/// <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 Double4 left, ref Double4 right, out Double4 result)
{
result = new Double4(left.X - right.X, left.Y - right.Y, left.Z - right.Z, left.W - right.W);
}
/// <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 Double4 Subtract(Double4 left, Double4 right)
{
return new Double4(left.X - right.X, left.Y - right.Y, left.Z - right.Z, left.W - right.W);
}
/// <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 Double4 value, double scale, out Double4 result)
{
result = new Double4(value.X * scale, value.Y * scale, value.Z * scale, value.W * 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 Double4 Multiply(Double4 value, double scale)
{
return new Double4(value.X * scale, value.Y * scale, value.Z * scale, value.W * 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 Double4 left, ref Double4 right, out Double4 result)
{
result = new Double4(left.X * right.X, left.Y * right.Y, left.Z * right.Z, left.W * right.W);
}
/// <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 Double4 Modulate(Double4 left, Double4 right)
{
return new Double4(left.X * right.X, left.Y * right.Y, left.Z * right.Z, left.W * right.W);
}
/// <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 Double4 value, double scale, out Double4 result)
{
result = new Double4(value.X / scale, value.Y / scale, value.Z / scale, value.W / 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 Double4 Divide(Double4 value, double scale)
{
return new Double4(value.X / scale, value.Y / scale, value.Z / scale, value.W / 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 Double4 left, ref Double4 right, out Double4 result)
{
result = new Double4(left.X / right.X, left.Y / right.Y, left.Z / right.Z, left.W / right.W);
}
/// <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 Double4 Demodulate(Double4 left, Double4 right)
{
return new Double4(left.X / right.X, left.Y / right.Y, left.Z / right.Z, left.W / right.W);
}
/// <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 Double4 value, out Double4 result)
{
result = new Double4(-value.X, -value.Y, -value.Z, -value.W);
}
/// <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 Double4 Negate(Double4 value)
{
return new Double4(-value.X, -value.Y, -value.Z, -value.W);
}
/// <summary>
/// Returns a <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 4D triangle.
/// </summary>
/// <param name="value1">A <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D 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 4D Cartesian coordinates of the specified point.</param>
public static void Barycentric(ref Double4 value1, ref Double4 value2, ref Double4 value3, double amount1, double amount2, out Double4 result)
{
result = new Double4((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)),
(value1.W + (amount1 * (value2.W - value1.W))) + (amount2 * (value3.W - value1.W)));
}
/// <summary>
/// Returns a <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D Cartesian coordinates of a point specified in Barycentric coordinates relative to a 4D triangle.
/// </summary>
/// <param name="value1">A <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D Cartesian coordinates of vertex 1 of the triangle.</param>
/// <param name="value2">A <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D Cartesian coordinates of vertex 2 of the triangle.</param>
/// <param name="value3">A <see cref="Stride.Core.Mathematics.Double4"/> containing the 4D 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="Stride.Core.Mathematics.Double4"/> containing the 4D Cartesian coordinates of the specified point.</returns>
public static Double4 Barycentric(Double4 value1, Double4 value2, Double4 value3, double amount1, double amount2)
{
Double4 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 Double4 value, ref Double4 min, ref Double4 max, out Double4 result)
{
double x = value.X;
x = (x > max.X) ? max.X : x;
x = (x < min.X) ? min.X : x;
double y = value.Y;
y = (y > max.Y) ? max.Y : y;
y = (y < min.Y) ? min.Y : y;
double z = value.Z;
z = (z > max.Z) ? max.Z : z;
z = (z < min.Z) ? min.Z : z;
double w = value.W;
w = (w > max.W) ? max.W : w;
w = (w < min.W) ? min.W : w;
result = new Double4(x, y, z, w);
}
/// <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 Double4 Clamp(Double4 value, Double4 min, Double4 max)
{
Double4 result;
Clamp(ref value, ref min, ref max, 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="Stride.Core.Mathematics.Double4.DistanceSquared(ref Double4, ref Double4, out double)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static void Distance(ref Double4 value1, ref Double4 value2, out double result)
{
double x = value1.X - value2.X;
double y = value1.Y - value2.Y;
double z = value1.Z - value2.Z;
double w = value1.W - value2.W;
result = (double)Math.Sqrt((x * x) + (y * y) + (z * z) + (w * w));
}
/// <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="Stride.Core.Mathematics.Double4.DistanceSquared(Double4, Double4)"/> may be preferred when only the relative distance is needed
/// and speed is of the essence.
/// </remarks>
public static double Distance(Double4 value1, Double4 value2)
{
double x = value1.X - value2.X;
double y = value1.Y - value2.Y;
double z = value1.Z - value2.Z;
double w = value1.W - value2.W;
return (double)Math.Sqrt((x * x) + (y * y) + (z * z) + (w * w));
}
/// <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 Double4 value1, ref Double4 value2, out double result)
{
double x = value1.X - value2.X;
double y = value1.Y - value2.Y;
double z = value1.Z - value2.Z;
double w = value1.W - value2.W;
result = (x * x) + (y * y) + (z * z) + (w * w);
}
/// <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 double DistanceSquared(Double4 value1, Double4 value2)
{
double x = value1.X - value2.X;
double y = value1.Y - value2.Y;
double z = value1.Z - value2.Z;
double w = value1.W - value2.W;
return (x * x) + (y * y) + (z * z) + (w * w);
}
/// <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 Double4 left, ref Double4 right, out double result)
{
result = (left.X * right.X) + (left.Y * right.Y) + (left.Z * right.Z) + (left.W * right.W);
}
/// <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 double Dot(Double4 left, Double4 right)
{
return (left.X * right.X) + (left.Y * right.Y) + (left.Z * right.Z) + (left.W * right.W);
}
/// <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 Double4 value, out Double4 result)
{
Double4 temp = value;
result = temp;
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 Double4 Normalize(Double4 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 Double4 start, ref Double4 end, double amount, out Double4 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);
result.W = start.W + ((end.W - start.W) * 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 Double4 Lerp(Double4 start, Double4 end, double amount)
{
Double4 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 Double4 start, ref Double4 end, double amount, out Double4 result)
{
amount = (amount > 1.0) ? 1.0 : ((amount < 0.0) ? 0.0 : 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);
result.W = start.W + ((end.W - start.W) * 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 Double4 SmoothStep(Double4 start, Double4 end, double amount)
{
Double4 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 Double4 value1, ref Double4 tangent1, ref Double4 value2, ref Double4 tangent2, double amount, out Double4 result)
{
double squared = amount * amount;
double cubed = amount * squared;
double part1 = ((2.0f * cubed) - (3.0f * squared)) + 1.0;
double part2 = (-2.0f * cubed) + (3.0f * squared);
double part3 = (cubed - (2.0f * squared)) + amount;
double part4 = cubed - squared;
result = new Double4((((value1.X * part1) + (value2.X * part2)) + (tangent1.X * part3)) + (tangent2.X * part4),
(((value1.Y * part1) + (value2.Y * part2)) + (tangent1.Y * part3)) + (tangent2.Y * part4),
(((value1.Z * part1) + (value2.Z * part2)) + (tangent1.Z * part3)) + (tangent2.Z * part4),
(((value1.W * part1) + (value2.W * part2)) + (tangent1.W * part3)) + (tangent2.W * 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 Double4 Hermite(Double4 value1, Double4 tangent1, Double4 value2, Double4 tangent2, double amount)
{
Double4 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 Double4 value1, ref Double4 value2, ref Double4 value3, ref Double4 value4, double amount, out Double4 result)
{
double squared = amount * amount;
double 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));
result.W = 0.5f * ((((2.0f * value2.W) + ((-value1.W + value3.W) * amount)) + (((((2.0f * value1.W) - (5.0f * value2.W)) + (4.0f * value3.W)) - value4.W) * squared)) + ((((-value1.W + (3.0f * value2.W)) - (3.0f * value3.W)) + value4.W) * 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 Double4 CatmullRom(Double4 value1, Double4 value2, Double4 value3, Double4 value4, double amount)
{
Double4 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 Double4 left, ref Double4 right, out Double4 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;
result.W = (left.W > right.W) ? left.W : right.W;
}
/// <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 Double4 Max(Double4 left, Double4 right)
{
Double4 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 Double4 left, ref Double4 right, out Double4 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;
result.W = (left.W < right.W) ? left.W : right.W;
}
/// <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 Double4 Min(Double4 left, Double4 right)
{
Double4 result;
Min(ref left, ref right, 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(Double4[] destination, params Double4[] 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)
{
Double4 newvector = source[i];
for (int r = 0; r < i; ++r)
{
newvector -= (Double4.Dot(destination[r], newvector) / Double4.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(Double4[] destination, params Double4[] 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)
{
Double4 newvector = source[i];
for (int r = 0; r < i; ++r)
{
newvector -= Double4.Dot(destination[r], newvector) * destination[r];
}
newvector.Normalize();
destination[i] = newvector;
}
}
/// <summary>
/// Transforms a 4D vector by the given <see cref="Stride.Core.Mathematics.Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="Stride.Core.Mathematics.Quaternion"/> rotation to apply.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="Stride.Core.Mathematics.Double4"/>.</param>
public static void Transform(ref Double4 vector, ref Quaternion rotation, out Double4 result)
{
double x = rotation.X + rotation.X;
double y = rotation.Y + rotation.Y;
double z = rotation.Z + rotation.Z;
double wx = rotation.W * x;
double wy = rotation.W * y;
double wz = rotation.W * z;
double xx = rotation.X * x;
double xy = rotation.X * y;
double xz = rotation.X * z;
double yy = rotation.Y * y;
double yz = rotation.Y * z;
double zz = rotation.Z * z;
result = new Double4(
((vector.X * ((1.0 - yy) - zz)) + (vector.Y * (xy - wz))) + (vector.Z * (xz + wy)),
((vector.X * (xy + wz)) + (vector.Y * ((1.0 - xx) - zz))) + (vector.Z * (yz - wx)),
((vector.X * (xz - wy)) + (vector.Y * (yz + wx))) + (vector.Z * ((1.0 - xx) - yy)),
vector.W);
}
/// <summary>
/// Transforms a 4D vector by the given <see cref="Stride.Core.Mathematics.Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="Stride.Core.Mathematics.Quaternion"/> rotation to apply.</param>
/// <returns>The transformed <see cref="Stride.Core.Mathematics.Double4"/>.</returns>
public static Double4 Transform(Double4 vector, Quaternion rotation)
{
Double4 result;
Transform(ref vector, ref rotation, out result);
return result;
}
/// <summary>
/// Transforms an array of vectors by the given <see cref="Stride.Core.Mathematics.Quaternion"/> rotation.
/// </summary>
/// <param name="source">The array of vectors to transform.</param>
/// <param name="rotation">The <see cref="Stride.Core.Mathematics.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(Double4[] source, ref Quaternion rotation, Double4[] destination)
{
if (source == null)
throw new ArgumentNullException("source");