Vector3D.cs source code in C# .NET

                        Code:
                         / 4.0 / 4.0 / untmp / DEVDIV_TFS / Dev10 / Releases / RTMRel / wpf / src / Core / CSharp / System / Windows / Media3D / Vector3D.cs / 1305600 / Vector3D.cs
                        
                        
                            //---------------------------------------------------------------------------- 
//
// 
//    Copyright (C) Microsoft Corporation.  All rights reserved.
//  
//
// 
// 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 
{
    ///  
    /// Vector3D - 3D vector representation. 
    /// 
    public partial struct Vector3D 
    {
        //-----------------------------------------------------
        //
        //  Constructors 
        //
        //----------------------------------------------------- 
 
        #region Constructors
 
        /// 
        /// Constructor that sets vector's initial values.
        /// 
        /// Value of the X coordinate of the new vector. 
        /// Value of the Y coordinate of the new vector.
        /// Value of the Z coordinate of the new vector. 
        public Vector3D(double x, double y, double z) 
        {
            _x = x; 
            _y = y;
            _z = z;
        }
 
        #endregion Constructors
 
 
        //------------------------------------------------------
        // 
        //  Public Methods
        //
        //-----------------------------------------------------
 
        #region Public Methods
 
        ///  
        /// Length of the vector.
        ///  
        public double Length
        {
            get
            { 
                return Math.Sqrt(_x * _x + _y * _y + _z * _z);
            } 
        } 

        ///  
        /// Length of the vector squared.
        /// 
        public double LengthSquared
        { 
            get
            { 
                return _x * _x + _y * _y + _z * _z; 
            }
        } 

        /// 
        /// 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.
        ///  
        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;
        }
 
        /// 
        /// Computes the angle between two vectors. 
        ///  
        /// First vector.
        /// Second vector. 
        /// 
        /// 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.)
        ///  
        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);
        } 

        ///  
        /// Operator -Vector (unary negation). 
        /// 
        /// Vector being negated. 
        /// Negation of the given vector.
        public static Vector3D operator -(Vector3D vector)
        {
            return new Vector3D(-vector._x, -vector._y, -vector._z); 
        }
 
        ///  
        /// Negates the values of X, Y, and Z on this Vector3D
        ///  
        public void Negate()
        {
            _x = -_x;
            _y = -_y; 
            _z = -_z;
        } 
 
        /// 
        /// Vector addition. 
        /// 
        /// First vector being added.
        /// Second vector being added.
        /// Result of addition. 
        public static Vector3D operator +(Vector3D vector1, Vector3D vector2)
        { 
            return new Vector3D(vector1._x + vector2._x, 
                                vector1._y + vector2._y,
                                vector1._z + vector2._z); 
        }

        /// 
        /// Vector addition. 
        /// 
        /// First vector being added. 
        /// Second vector being added. 
        /// Result of addition.
        public static Vector3D Add(Vector3D vector1, Vector3D vector2) 
        {
            return new Vector3D(vector1._x + vector2._x,
                                vector1._y + vector2._y,
                                vector1._z + vector2._z); 
        }
 
        ///  
        /// Vector subtraction.
        ///  
        /// Vector that is subtracted from.
        /// Vector being subtracted.
        /// Result of subtraction.
        public static Vector3D operator -(Vector3D vector1, Vector3D vector2) 
        {
            return new Vector3D(vector1._x - vector2._x, 
                                vector1._y - vector2._y, 
                                vector1._z - vector2._z);
        } 

        /// 
        /// Vector subtraction.
        ///  
        /// Vector that is subtracted from.
        /// Vector being subtracted. 
        /// Result of subtraction. 
        public static Vector3D Subtract(Vector3D vector1, Vector3D vector2)
        { 
            return new Vector3D(vector1._x - vector2._x,
                                vector1._y - vector2._y,
                                vector1._z - vector2._z);
        } 

        ///  
        /// Vector3D + Point3D addition. 
        /// 
        /// Vector by which we offset the point. 
        /// Point being offset by the given vector.
        /// Result of addition.
        public static Point3D operator +(Vector3D vector, Point3D point)
        { 
            return new Point3D(vector._x + point._x,
                               vector._y + point._y, 
                               vector._z + point._z); 
        }
 
        /// 
        /// Vector3D + Point3D addition.
        /// 
        /// Vector by which we offset the point. 
        /// Point being offset by the given vector.
        /// Result of addition. 
        public static Point3D Add(Vector3D vector, Point3D point) 
        {
            return new Point3D(vector._x + point._x, 
                               vector._y + point._y,
                               vector._z + point._z);
        }
 
        /// 
        /// Vector3D - Point3D subtraction. 
        ///  
        /// Vector by which we offset the point.
        /// Point being offset by the given vector. 
        /// Result of subtraction.
        public static Point3D operator -(Vector3D vector, Point3D point)
        {
            return new Point3D(vector._x - point._x, 
                               vector._y - point._y,
                               vector._z - point._z); 
        } 

        ///  
        /// Vector3D - Point3D subtraction.
        /// 
        /// Vector by which we offset the point.
        /// Point being offset by the given vector. 
        /// Result of subtraction.
        public static Point3D Subtract(Vector3D vector, Point3D point) 
        { 
            return new Point3D(vector._x - point._x,
                               vector._y - point._y, 
                               vector._z - point._z);
        }

        ///  
        /// Scalar multiplication.
        ///  
        /// Vector being multiplied. 
        /// Scalar value by which the vector is multiplied.
        /// Result of multiplication. 
        public static Vector3D operator *(Vector3D vector, double scalar)
        {
            return new Vector3D(vector._x * scalar,
                                vector._y * scalar, 
                                vector._z * scalar);
        } 
 
        /// 
        /// Scalar multiplication. 
        /// 
        /// Vector being multiplied.
        /// Scalar value by which the vector is multiplied.
        /// Result of multiplication. 
        public static Vector3D Multiply(Vector3D vector, double scalar)
        { 
            return new Vector3D(vector._x * scalar, 
                                vector._y * scalar,
                                vector._z * scalar); 
        }

        /// 
        /// Scalar multiplication. 
        /// 
        /// Scalar value by which the vector is multiplied 
        /// Vector being multiplied. 
        /// Result of multiplication.
        public static Vector3D operator *(double scalar, Vector3D vector) 
        {
            return new Vector3D(vector._x * scalar,
                                vector._y * scalar,
                                vector._z * scalar); 
        }
 
        ///  
        /// Scalar multiplication.
        ///  
        /// Scalar value by which the vector is multiplied
        /// Vector being multiplied.
        /// Result of multiplication.
        public static Vector3D Multiply(double scalar, Vector3D vector) 
        {
            return new Vector3D(vector._x * scalar, 
                                vector._y * scalar, 
                                vector._z * scalar);
        } 

        /// 
        /// Scalar division.
        ///  
        /// Vector being divided.
        /// Scalar value by which we divide the vector. 
        /// Result of division. 
        public static Vector3D operator /(Vector3D vector, double scalar)
        { 
            return vector * (1.0 / scalar);
        }

        ///  
        /// Scalar division.
        ///  
        /// Vector being divided. 
        /// Scalar value by which we divide the vector.
        /// Result of division. 
        public static Vector3D Divide(Vector3D vector, double scalar)
        {
            return vector * (1.0 / scalar);
        } 

        ///  
        /// Vector3D * Matrix3D multiplication 
        /// 
        /// Vector being tranformed. 
        /// Transformation matrix applied to the vector.
        /// Result of multiplication.
        public static Vector3D operator *(Vector3D vector, Matrix3D matrix)
        { 
            return matrix.Transform(vector);
        } 
 
        /// 
        /// Vector3D * Matrix3D multiplication 
        /// 
        /// Vector being tranformed.
        /// Transformation matrix applied to the vector.
        /// Result of multiplication. 
        public static Vector3D Multiply(Vector3D vector, Matrix3D matrix)
        { 
            return matrix.Transform(vector); 
        }
 
        /// 
        /// Vector dot product.
        /// 
        /// First vector. 
        /// Second vector.
        /// Dot product of two vectors. 
        public static double DotProduct(Vector3D vector1, Vector3D vector2) 
        {
            return DotProduct(ref vector1, ref vector2); 
        }

        /// 
        /// Faster internal version of DotProduct that avoids copies 
        ///
        /// vector1 and vector2 to a passed by ref for perf and ARE NOT MODIFIED 
        ///  
        internal static double DotProduct(ref Vector3D vector1, ref Vector3D vector2)
        { 
            return vector1._x * vector2._x +
                   vector1._y * vector2._y +
                   vector1._z * vector2._z;
        } 

        ///  
        /// Vector cross product. 
        /// 
        /// First vector. 
        /// Second vector.
        /// Cross product of two vectors.
        public static Vector3D CrossProduct(Vector3D vector1, Vector3D vector2)
        { 
            Vector3D result;
            CrossProduct(ref vector1, ref vector2, out result); 
            return result; 
        }
 
        /// 
        /// Faster internal version of CrossProduct that avoids copies
        ///
        /// vector1 and vector2 to a passed by ref for perf and ARE NOT MODIFIED 
        /// 
        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;
        }

        ///  
        /// Vector3D to Point3D conversion.
        ///  
        /// Vector being converted. 
        /// Point representing the given vector.
        public static explicit operator Point3D(Vector3D vector) 
        {
            return new Point3D(vector._x, vector._y, vector._z);
        }
 
        /// 
        /// 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. 
        /// 
        /// The vector to convert to a size. 
        /// A size equal to this vector.
        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 
    }
} 

// File provided for Reference Use Only by Microsoft Corporation (c) 2007.
// Copyright (c) Microsoft Corporation. All rights reserved.
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