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//---------------------------------------------------------------------------
//
// <copyright file="Vector3D.cs" company="Microsoft">
// Copyright (C) Microsoft Corporation. All rights reserved.
// </copyright>
//
//
// Description: 3D vector implementation.
//
// See spec at http://avalon/medialayer/Specifications/Avalon3D%20API%20Spec.mht
//
// History:
// 06/02/2003 : t-gregr - Created
//
//---------------------------------------------------------------------------
using MS.Internal;
using MS.Internal.Media3D;
using System;
using System.Windows;
using System.Windows.Media.Media3D;
namespace System.Windows.Media.Media3D
{
/// <summary>
/// Vector3D - 3D vector representation.
/// </summary>
public partial struct Vector3D
{
//------------------------------------------------------
//
// Constructors
//
//------------------------------------------------------
#region Constructors
/// <summary>
/// Constructor that sets vector's initial values.
/// </summary>
/// <param name="x">Value of the X coordinate of the new vector.</param>
/// <param name="y">Value of the Y coordinate of the new vector.</param>
/// <param name="z">Value of the Z coordinate of the new vector.</param>
public Vector3D(double x, double y, double z)
{
_x = x;
_y = y;
_z = z;
}
#endregion Constructors
//------------------------------------------------------
//
// Public Methods
//
//------------------------------------------------------
#region Public Methods
/// <summary>
/// Length of the vector.
/// </summary>
public double Length
{
get
{
return Math.Sqrt(_x * _x + _y * _y + _z * _z);
}
}
/// <summary>
/// Length of the vector squared.
/// </summary>
public double LengthSquared
{
get
{
return _x * _x + _y * _y + _z * _z;
}
}
/// <summary>
/// Updates the vector to maintain its direction, but to have a length
/// of 1. Equivalent to dividing the vector by its Length.
/// Returns NaN if length is zero.
/// </summary>
public void Normalize()
{
// Computation of length can overflow easily because it
// first computes squared length, so we first divide by
// the largest coefficient.
double m = Math.Abs(_x);
double absy = Math.Abs(_y);
double absz = Math.Abs(_z);
if (absy > m)
{
m = absy;
}
if (absz > m)
{
m = absz;
}
_x /= m;
_y /= m;
_z /= m;
double length = Math.Sqrt(_x * _x + _y * _y + _z * _z);
this /= length;
}
/// <summary>
/// Computes the angle between two vectors.
/// </summary>
/// <param name="vector1">First vector.</param>
/// <param name="vector2">Second vector.</param>
/// <returns>
/// Returns the angle required to rotate vector1 into vector2 in degrees.
/// This will return a value between [0, 180] degrees.
/// (Note that this is slightly different from the Vector member
/// function of the same name. Signed angles do not extend to 3D.)
/// </returns>
public static double AngleBetween(Vector3D vector1, Vector3D vector2)
{
vector1.Normalize();
vector2.Normalize();
double ratio = DotProduct(vector1, vector2);
// The "straight forward" method of acos(u.v) has large precision
// issues when the dot product is near +/-1. This is due to the
// steep slope of the acos function as we approach +/- 1. Slight
// precision errors in the dot product calculation cause large
// variation in the output value.
//
// | |
// \__ |
// ---___ |
// ---___ |
// ---_|_
// | ---___
// | ---___
// | ---__
// | \
// | |
// -|-------------------+-------------------|-
// -1 0 1
//
// acos(x)
//
// To avoid this we use an alternative method which finds the
// angle bisector by (u-v)/2:
//
// _>
// u _- \ (u-v)/2
// _- __-v
// _=__--
// .=----------->
// v
//
// Because u and v and unit vectors, (u-v)/2 forms a right angle
// with the angle bisector. The hypotenuse is 1, therefore
// 2*asin(|u-v|/2) gives us the angle between u and v.
//
// The largest possible value of |u-v| occurs with perpendicular
// vectors and is sqrt(2)/2 which is well away from extreme slope
// at +/-1.
//
// (See Windows OS Bug #1706299 for details)
double theta;
if (ratio < 0)
{
theta = Math.PI - 2.0 * Math.Asin((-vector1 - vector2).Length / 2.0);
}
else
{
theta = 2.0 * Math.Asin((vector1 - vector2).Length / 2.0);
}
return M3DUtil.RadiansToDegrees(theta);
}
/// <summary>
/// Operator -Vector (unary negation).
/// </summary>
/// <param name="vector">Vector being negated.</param>
/// <returns>Negation of the given vector.</returns>
public static Vector3D operator -(Vector3D vector)
{
return new Vector3D(-vector._x, -vector._y, -vector._z);
}
/// <summary>
/// Negates the values of X, Y, and Z on this Vector3D
/// </summary>
public void Negate()
{
_x = -_x;
_y = -_y;
_z = -_z;
}
/// <summary>
/// Vector addition.
/// </summary>
/// <param name="vector1">First vector being added.</param>
/// <param name="vector2">Second vector being added.</param>
/// <returns>Result of addition.</returns>
public static Vector3D operator +(Vector3D vector1, Vector3D vector2)
{
return new Vector3D(vector1._x + vector2._x,
vector1._y + vector2._y,
vector1._z + vector2._z);
}
/// <summary>
/// Vector addition.
/// </summary>
/// <param name="vector1">First vector being added.</param>
/// <param name="vector2">Second vector being added.</param>
/// <returns>Result of addition.</returns>
public static Vector3D Add(Vector3D vector1, Vector3D vector2)
{
return new Vector3D(vector1._x + vector2._x,
vector1._y + vector2._y,
vector1._z + vector2._z);
}
/// <summary>
/// Vector subtraction.
/// </summary>
/// <param name="vector1">Vector that is subtracted from.</param>
/// <param name="vector2">Vector being subtracted.</param>
/// <returns>Result of subtraction.</returns>
public static Vector3D operator -(Vector3D vector1, Vector3D vector2)
{
return new Vector3D(vector1._x - vector2._x,
vector1._y - vector2._y,
vector1._z - vector2._z);
}
/// <summary>
/// Vector subtraction.
/// </summary>
/// <param name="vector1">Vector that is subtracted from.</param>
/// <param name="vector2">Vector being subtracted.</param>
/// <returns>Result of subtraction.</returns>
public static Vector3D Subtract(Vector3D vector1, Vector3D vector2)
{
return new Vector3D(vector1._x - vector2._x,
vector1._y - vector2._y,
vector1._z - vector2._z);
}
/// <summary>
/// Vector3D + Point3D addition.
/// </summary>
/// <param name="vector">Vector by which we offset the point.</param>
/// <param name="point">Point being offset by the given vector.</param>
/// <returns>Result of addition.</returns>
public static Point3D operator +(Vector3D vector, Point3D point)
{
return new Point3D(vector._x + point._x,
vector._y + point._y,
vector._z + point._z);
}
/// <summary>
/// Vector3D + Point3D addition.
/// </summary>
/// <param name="vector">Vector by which we offset the point.</param>
/// <param name="point">Point being offset by the given vector.</param>
/// <returns>Result of addition.</returns>
public static Point3D Add(Vector3D vector, Point3D point)
{
return new Point3D(vector._x + point._x,
vector._y + point._y,
vector._z + point._z);
}
/// <summary>
/// Vector3D - Point3D subtraction.
/// </summary>
/// <param name="vector">Vector by which we offset the point.</param>
/// <param name="point">Point being offset by the given vector.</param>
/// <returns>Result of subtraction.</returns>
public static Point3D operator -(Vector3D vector, Point3D point)
{
return new Point3D(vector._x - point._x,
vector._y - point._y,
vector._z - point._z);
}
/// <summary>
/// Vector3D - Point3D subtraction.
/// </summary>
/// <param name="vector">Vector by which we offset the point.</param>
/// <param name="point">Point being offset by the given vector.</param>
/// <returns>Result of subtraction.</returns>
public static Point3D Subtract(Vector3D vector, Point3D point)
{
return new Point3D(vector._x - point._x,
vector._y - point._y,
vector._z - point._z);
}
/// <summary>
/// Scalar multiplication.
/// </summary>
/// <param name="vector">Vector being multiplied.</param>
/// <param name="scalar">Scalar value by which the vector is multiplied.</param>
/// <returns>Result of multiplication.</returns>
public static Vector3D operator *(Vector3D vector, double scalar)
{
return new Vector3D(vector._x * scalar,
vector._y * scalar,
vector._z * scalar);
}
/// <summary>
/// Scalar multiplication.
/// </summary>
/// <param name="vector">Vector being multiplied.</param>
/// <param name="scalar">Scalar value by which the vector is multiplied.</param>
/// <returns>Result of multiplication.</returns>
public static Vector3D Multiply(Vector3D vector, double scalar)
{
return new Vector3D(vector._x * scalar,
vector._y * scalar,
vector._z * scalar);
}
/// <summary>
/// Scalar multiplication.
/// </summary>
/// <param name="scalar">Scalar value by which the vector is multiplied</param>
/// <param name="vector">Vector being multiplied.</param>
/// <returns>Result of multiplication.</returns>
public static Vector3D operator *(double scalar, Vector3D vector)
{
return new Vector3D(vector._x * scalar,
vector._y * scalar,
vector._z * scalar);
}
/// <summary>
/// Scalar multiplication.
/// </summary>
/// <param name="scalar">Scalar value by which the vector is multiplied</param>
/// <param name="vector">Vector being multiplied.</param>
/// <returns>Result of multiplication.</returns>
public static Vector3D Multiply(double scalar, Vector3D vector)
{
return new Vector3D(vector._x * scalar,
vector._y * scalar,
vector._z * scalar);
}
/// <summary>
/// Scalar division.
/// </summary>
/// <param name="vector">Vector being divided.</param>
/// <param name="scalar">Scalar value by which we divide the vector.</param>
/// <returns>Result of division.</returns>
public static Vector3D operator /(Vector3D vector, double scalar)
{
return vector * (1.0 / scalar);
}
/// <summary>
/// Scalar division.
/// </summary>
/// <param name="vector">Vector being divided.</param>
/// <param name="scalar">Scalar value by which we divide the vector.</param>
/// <returns>Result of division.</returns>
public static Vector3D Divide(Vector3D vector, double scalar)
{
return vector * (1.0 / scalar);
}
/// <summary>
/// Vector3D * Matrix3D multiplication
/// </summary>
/// <param name="vector">Vector being tranformed.</param>
/// <param name="matrix">Transformation matrix applied to the vector.</param>
/// <returns>Result of multiplication.</returns>
public static Vector3D operator *(Vector3D vector, Matrix3D matrix)
{
return matrix.Transform(vector);
}
/// <summary>
/// Vector3D * Matrix3D multiplication
/// </summary>
/// <param name="vector">Vector being tranformed.</param>
/// <param name="matrix">Transformation matrix applied to the vector.</param>
/// <returns>Result of multiplication.</returns>
public static Vector3D Multiply(Vector3D vector, Matrix3D matrix)
{
return matrix.Transform(vector);
}
/// <summary>
/// Vector dot product.
/// </summary>
/// <param name="vector1">First vector.</param>
/// <param name="vector2">Second vector.</param>
/// <returns>Dot product of two vectors.</returns>
public static double DotProduct(Vector3D vector1, Vector3D vector2)
{
return DotProduct(ref vector1, ref vector2);
}
/// <summary>
/// Faster internal version of DotProduct that avoids copies
///
/// vector1 and vector2 to a passed by ref for perf and ARE NOT MODIFIED
/// </summary>
internal static double DotProduct(ref Vector3D vector1, ref Vector3D vector2)
{
return vector1._x * vector2._x +
vector1._y * vector2._y +
vector1._z * vector2._z;
}
/// <summary>
/// Vector cross product.
/// </summary>
/// <param name="vector1">First vector.</param>
/// <param name="vector2">Second vector.</param>
/// <returns>Cross product of two vectors.</returns>
public static Vector3D CrossProduct(Vector3D vector1, Vector3D vector2)
{
Vector3D result;
CrossProduct(ref vector1, ref vector2, out result);
return result;
}
/// <summary>
/// Faster internal version of CrossProduct that avoids copies
///
/// vector1 and vector2 to a passed by ref for perf and ARE NOT MODIFIED
/// </summary>
internal static void CrossProduct(ref Vector3D vector1, ref Vector3D vector2, out Vector3D result)
{
result._x = vector1._y * vector2._z - vector1._z * vector2._y;
result._y = vector1._z * vector2._x - vector1._x * vector2._z;
result._z = vector1._x * vector2._y - vector1._y * vector2._x;
}
/// <summary>
/// Vector3D to Point3D conversion.
/// </summary>
/// <param name="vector">Vector being converted.</param>
/// <returns>Point representing the given vector.</returns>
public static explicit operator Point3D(Vector3D vector)
{
return new Point3D(vector._x, vector._y, vector._z);
}
/// <summary>
/// Explicit conversion to Size3D. Note that since Size3D cannot contain negative values,
/// the resulting size will contains the absolute values of X, Y, and Z.
/// </summary>
/// <param name="vector">The vector to convert to a size.</param>
/// <returns>A size equal to this vector.</returns>
public static explicit operator Size3D(Vector3D vector)
{
return new Size3D(Math.Abs(vector._x), Math.Abs(vector._y), Math.Abs(vector._z));
}
#endregion Public Methods
}
}
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