public override int Add(QuaternionD value)
 {
     lock (this._root) return this._collection.Add(value);
 }
 public override void CopyTo(QuaternionD[] array)
 {
     lock (this._root) this._collection.CopyTo(array);
 }
 /// <overloads>
 /// Copies the <see cref="QuaternionDArrayList"/> or a portion of it to a one-dimensional array.
 /// </overloads>
 /// <summary>
 /// Copies the entire <see cref="QuaternionDArrayList"/> to a one-dimensional <see cref="Array"/>
 /// of <see cref="QuaternionD"/> elements, starting at the beginning of the target array.
 /// </summary>
 /// <param name="array">The one-dimensional <see cref="Array"/> that is the destination of the
 /// <see cref="QuaternionD"/> elements copied from the <see cref="QuaternionDArrayList"/>.
 /// The <b>Array</b> must have zero-based indexing.</param>
 /// <exception cref="ArgumentNullException">
 /// <paramref name="array"/> is a null reference.</exception>
 /// <exception cref="ArgumentException">
 /// The number of elements in the source <see cref="QuaternionDArrayList"/> is greater
 /// than the available space in the destination <paramref name="array"/>.</exception>
 /// <remarks>Please refer to <see cref="ArrayList.CopyTo"/> for details.</remarks>
 public virtual void CopyTo(QuaternionD[] array)
 {
     CheckTargetArray(array, 0);
     Array.Copy(this._array, array, this._count);
 }
 public override void AddRange(QuaternionD[] array)
 {
     throw new NotSupportedException(
         "Read-only collections cannot be modified.");
 }
 public override void Remove(QuaternionD value)
 {
     this._collection.Remove(value);
 }
        /// <summary>
        /// Adds a <see cref="QuaternionD"/> to the end of the <see cref="QuaternionDArrayList"/>.
        /// </summary>
        /// <param name="value">The <see cref="QuaternionD"/> object
        /// to be added to the end of the <see cref="QuaternionDArrayList"/>.
        /// </param>
        /// <returns>The <see cref="QuaternionDArrayList"/> index at which the
        /// <paramref name="value"/> has been added.</returns>
        /// <exception cref="NotSupportedException">
        /// <para>The <see cref="QuaternionDArrayList"/> is read-only.</para>
        /// <para>-or-</para>
        /// <para>The <b>QuaternionDArrayList</b> has a fixed size.</para>
        /// <para>-or-</para>
        /// <para>The <b>QuaternionDArrayList</b> already contains the specified
        /// <paramref name="value"/>, and the <b>QuaternionDArrayList</b>
        /// ensures that all elements are unique.</para></exception>
        /// <remarks>Please refer to <see cref="ArrayList.Add"/> for details.</remarks>
        public virtual int Add(QuaternionD value)
        {
            if (this._count == this._array.Length)
                EnsureCapacity(this._count + 1);

            ++this._version;
            this._array[this._count] = value;
            return this._count++;
        }
Ejemplo n.º 7
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 /// <summary>
 /// Multiplies a quaternion by a scalar.
 /// </summary>
 /// <param name="q">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="s">A scalar.</param>
 /// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
 public static QuaternionD operator*(QuaternionD q, double s)
 {
     return(QuaternionD.Multiply(q, s));
 }
 public override void CopyTo(QuaternionD[] array)
 {
     this._collection.CopyTo(array);
 }
Ejemplo n.º 9
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 /// <summary>
 /// Subtracts a quaternion from a quaternion.
 /// </summary>
 /// <param name="a">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="b">A <see cref="QuaternionD"/> instance.</param>
 /// <returns>A new <see cref="QuaternionD"/> instance containing the difference.</returns>
 public static QuaternionD operator-(QuaternionD a, QuaternionD b)
 {
     return(QuaternionD.Subtract(a, b));
 }
Ejemplo n.º 10
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 /// <summary>
 /// Multiplies quaternion <paramref name="a"/> by quaternion <paramref name="b"/>.
 /// </summary>
 /// <param name="a">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="b">A <see cref="QuaternionD"/> instance.</param>
 /// <returns>A new <see cref="QuaternionD"/> containing the result.</returns>
 public static QuaternionD operator*(QuaternionD a, QuaternionD b)
 {
     return(QuaternionD.Multiply(a, b));
 }
Ejemplo n.º 11
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 /// <summary>
 /// Adds two quaternions.
 /// </summary>
 /// <param name="a">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="b">A <see cref="QuaternionD"/> instance.</param>
 /// <returns>A new <see cref="QuaternionD"/> instance containing the sum.</returns>
 public static QuaternionD operator+(QuaternionD a, QuaternionD b)
 {
     return(QuaternionD.Add(a, b));
 }
Ejemplo n.º 12
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 /// <summary>
 /// Calculates the dot product of two quaternions.
 /// </summary>
 /// <param name="a">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="b">A <see cref="QuaternionD"/> instance.</param>
 /// <returns>The dot product value.</returns>
 public static double Dot(QuaternionD a, QuaternionD b)
 {
     return(a.W * b.W + a.X * b.X + a.Y * b.Y + a.Z * b.Z);
 }
Ejemplo n.º 13
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 /// <summary>
 /// Subtracts a quaternion from a quaternion.
 /// </summary>
 /// <param name="a">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="b">A <see cref="QuaternionD"/> instance.</param>
 /// <returns>A new <see cref="QuaternionD"/> instance containing the difference.</returns>
 public static QuaternionD Subtract(QuaternionD a, QuaternionD b)
 {
     return(new QuaternionD(a.W - b.W, a.X - b.X, a.Y - b.Y, a.Z - b.Z));
 }
 public override void Remove(QuaternionD value)
 {
     lock (this._root) this._collection.Remove(value);
 }
Ejemplo n.º 15
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 /// <summary>
 /// Divides a quaternion by a scalar.
 /// </summary>
 /// <param name="q">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="s">A scalar.</param>
 /// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
 public static QuaternionD operator/(QuaternionD q, double s)
 {
     return(QuaternionD.Divide(q, s));
 }
            public override void AddRange(QuaternionD[] array)
            {
                foreach (QuaternionD value in array)
                    CheckUnique(value);

                this._collection.AddRange(array);
            }
Ejemplo n.º 17
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 /// <summary>
 /// Divides a scalar by a quaternion.
 /// </summary>
 /// <param name="q">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="s">A scalar.</param>
 /// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
 public static QuaternionD operator/(double s, QuaternionD q)
 {
     return(QuaternionD.Multiply(q, 1 / s));
 }
 public override int IndexOf(QuaternionD value)
 {
     return this._collection.IndexOf(value);
 }
Ejemplo n.º 19
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        public void Identity_IsIdentity()
        {
            var expected = new QuaternionD(0, 0, 0, 1);

            Assert.Equal(expected, QuaternionD.Identity);
        }
 private void CheckUnique(int index, QuaternionD value)
 {
     int existing = IndexOf(value);
     if (existing >= 0 && existing != index)
         throw new NotSupportedException(
             "Unique collections cannot contain duplicate elements.");
 }
Ejemplo n.º 21
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        public void Sub_Static(QuaternionD left, QuaternionD right, QuaternionD expected)
        {
            var actual = QuaternionD.Sub(left, right);

            Assert.Equal(expected, actual);
        }
 /// <summary>
 /// Searches the entire sorted <see cref="QuaternionDArrayList"/> for an
 /// <see cref="QuaternionD"/> element using the default comparer
 /// and returns the zero-based index of the element.
 /// </summary>
 /// <param name="value">The <see cref="QuaternionD"/> object
 /// to locate in the <see cref="QuaternionDArrayList"/>.
 /// </param>
 /// <returns>The zero-based index of <paramref name="value"/> in the sorted
 /// <see cref="QuaternionDArrayList"/>, if <paramref name="value"/> is found;
 /// otherwise, a negative number, which is the bitwise complement of the index
 /// of the next element that is larger than <paramref name="value"/> or, if there
 /// is no larger element, the bitwise complement of <see cref="Count"/>.</returns>
 /// <exception cref="InvalidOperationException">
 /// Neither <paramref name="value"/> nor the elements of the <see cref="QuaternionDArrayList"/>
 /// implement the <see cref="IComparable"/> interface.</exception>
 /// <remarks>Please refer to <see cref="ArrayList.BinarySearch"/> for details.</remarks>
 public virtual int BinarySearch(QuaternionD value)
 {
     return Array.BinarySearch(this._array, 0, this._count, value);
 }
Ejemplo n.º 23
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        public void Multiply_TwoQuaternions_Static(QuaternionD left, QuaternionD right, QuaternionD expected)
        {
            var actual = QuaternionD.Multiply(left, right);

            Assert.Equal(expected, actual);
        }
Ejemplo n.º 24
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 /// <summary>
 /// Adds two quaternions.
 /// </summary>
 /// <param name="a">A <see cref="QuaternionD"/> instance.</param>
 /// <param name="b">A <see cref="QuaternionD"/> instance.</param>
 /// <returns>A new <see cref="QuaternionD"/> instance containing the sum.</returns>
 public static QuaternionD Add(QuaternionD a, QuaternionD b)
 {
     return(new QuaternionD(a.W + b.W, a.X + b.X, a.Y + b.Y, a.Z + b.Z));
 }
Ejemplo n.º 25
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        public void Multiply_QuaternionScalar_Staic(QuaternionD quat, double scale, QuaternionD expected)
        {
            var actual = QuaternionD.Multiply(quat, scale);

            Assert.Equal(expected, actual);
        }
 public override void Remove(QuaternionD value)
 {
     throw new NotSupportedException(
         "Read-only collections cannot be modified.");
 }
Ejemplo n.º 27
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        public void Transform_double4(double4 vec, QuaternionD quat, double4 expected)
        {
            var actual = QuaternionD.Transform(vec, quat);

            Assert.Equal(expected, actual);
        }
 public override void AddRange(QuaternionD[] array)
 {
     lock (this._root) this._collection.AddRange(array);
 }
Ejemplo n.º 29
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        public void Sub_Operator(QuaternionD left, QuaternionD right, QuaternionD expected)
        {
            var actual = left - right;

            Assert.Equal(expected, actual);
        }
 public override void Insert(int index, QuaternionD value)
 {
     lock (this._root) this._collection.Insert(index, value);
 }
Ejemplo n.º 31
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        public void Multiply_TwoQuaternions_Operator(QuaternionD left, QuaternionD right, QuaternionD expected)
        {
            var actual = left * right;

            Assert.Equal(expected, actual);
        }
 public override int Add(QuaternionD value)
 {
     CheckUnique(value);
     return this._collection.Add(value);
 }
Ejemplo n.º 33
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        public void Multiply_QuaternionScalar_Operator(QuaternionD quat, double scale, QuaternionD expected)
        {
            var actual = quat * scale;

            Assert.Equal(expected, actual);
        }
 public override int BinarySearch(QuaternionD value)
 {
     return this._collection.BinarySearch(value);
 }
Ejemplo n.º 35
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        public void Multiply_ScalarQuaternion_Operator(QuaternionD quat, double scale, QuaternionD expected)
        {
            var actual = scale * quat;

            Assert.Equal(expected, actual);
        }
 public override void CopyTo(QuaternionD[] array, int arrayIndex)
 {
     this._collection.CopyTo(array, arrayIndex);
 }
Ejemplo n.º 37
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        /// <summary>
        /// Calculates the exponent of a quaternion.
        /// </summary>
        /// <param name="a">A <see cref="QuaternionD"/> instance.</param>
        /// <returns>The quaternion's exponent.</returns>
        public QuaternionD Exp(QuaternionD a)
        {
            QuaternionD result = new QuaternionD(0,0,0,0);

            double angle = System.Math.Sqrt(a.X*a.X + a.Y*a.Y + a.Z*a.Z);
            double sin = System.Math.Sin(angle);

            if (MathFunctions.Abs(sin) > 0)
            {
                double coeff = angle / sin;
                result.X = coeff * a.X;
                result.Y = coeff * a.Y;
                result.Z = coeff * a.Z;
            }
            else
            {
                result.X = a.X;
                result.Y = a.Y;
                result.Z = a.Z;
            }

            return result;
        }
 public override void Insert(int index, QuaternionD value)
 {
     CheckUnique(value);
     this._collection.Insert(index, value);
 }
 /// <summary>
 /// Builds a rotation matrix from a quaternion.
 /// </summary>
 /// <param name="q">A <see cref="QuaternionF"/> instance.</param>
 /// <returns>A <see cref="Matrix4D"/> representing the rotation.</returns>
 public static Matrix4D RotationQuaternion(QuaternionD q)
 {
     // TODO: Implement this.
     throw new NotImplementedException();
 }
 private void CheckUnique(QuaternionD value)
 {
     if (IndexOf(value) >= 0)
         throw new NotSupportedException(
             "Unique collections cannot contain duplicate elements.");
 }
 /// <summary>
 /// Returns the zero-based index of the first occurrence of the specified
 /// <see cref="QuaternionD"/> in the <see cref="QuaternionDArrayList"/>.
 /// </summary>
 /// <param name="value">The <see cref="QuaternionD"/> object
 /// to locate in the <see cref="QuaternionDArrayList"/>.
 /// </param>
 /// <returns>
 /// The zero-based index of the first occurrence of <paramref name="value"/>
 /// in the <see cref="QuaternionDArrayList"/>, if found; otherwise, -1.
 /// </returns>
 /// <remarks>Please refer to <see cref="ArrayList.IndexOf"/> for details.</remarks>
 public virtual int IndexOf(QuaternionD value)
 {
     return Array.IndexOf(this._array, value, 0, this._count);
 }
        /// <summary>
        /// Initializes a new instance of the <see cref="QuaternionDArrayList"/> class
        /// that contains elements copied from the specified <see cref="QuaternionD"/>
        /// array and that has the same initial capacity as the number of elements copied.
        /// </summary>
        /// <param name="array">An <see cref="Array"/> of <see cref="QuaternionD"/>
        /// elements that are copied to the new collection.</param>
        /// <exception cref="ArgumentNullException">
        /// <paramref name="array"/> is a null reference.</exception>
        /// <remarks>Please refer to <see cref="ArrayList(ICollection)"/> for details.</remarks>
        public QuaternionDArrayList(QuaternionD[] array)
        {
            if (array == null)
                throw new ArgumentNullException("array");

            this._array = new QuaternionD[array.Length];
            AddRange(array);
        }
        /// <summary>
        /// Inserts a <see cref="QuaternionD"/> element into the
        /// <see cref="QuaternionDArrayList"/> at the specified index.
        /// </summary>
        /// <param name="index">The zero-based index at which <paramref name="value"/>
        /// should be inserted.</param>
        /// <param name="value">The <see cref="QuaternionD"/> object
        /// to insert into the <see cref="QuaternionDArrayList"/>.
        /// </param>
        /// <exception cref="ArgumentOutOfRangeException">
        /// <para><paramref name="index"/> is less than zero.</para>
        /// <para>-or-</para>
        /// <para><paramref name="index"/> is greater than <see cref="Count"/>.</para>
        /// </exception>
        /// <exception cref="NotSupportedException">
        /// <para>The <see cref="QuaternionDArrayList"/> is read-only.</para>
        /// <para>-or-</para>
        /// <para>The <b>QuaternionDArrayList</b> has a fixed size.</para>
        /// <para>-or-</para>
        /// <para>The <b>QuaternionDArrayList</b> already contains the specified
        /// <paramref name="value"/>, and the <b>QuaternionDArrayList</b>
        /// ensures that all elements are unique.</para></exception>
        /// <remarks>Please refer to <see cref="ArrayList.Insert"/> for details.</remarks>
        public virtual void Insert(int index, QuaternionD value)
        {
            if (index < 0)
                throw new ArgumentOutOfRangeException("index",
                    index, "Argument cannot be negative.");

            if (index > this._count)
                throw new ArgumentOutOfRangeException("index",
                    index, "Argument cannot exceed Count.");

            if (this._count == this._array.Length)
                EnsureCapacity(this._count + 1);

            ++this._version;
            if (index < this._count)
                Array.Copy(this._array, index,
                    this._array, index + 1, this._count - index);

            this._array[index] = value;
            ++this._count;
        }
        /// <summary>
        /// Adds the elements of a <see cref="QuaternionD"/> array
        /// to the end of the <see cref="QuaternionDArrayList"/>.
        /// </summary>
        /// <param name="array">An <see cref="Array"/> of <see cref="QuaternionD"/> elements
        /// that should be added to the end of the <see cref="QuaternionDArrayList"/>.</param>
        /// <exception cref="ArgumentNullException">
        /// <paramref name="array"/> is a null reference.</exception>
        /// <exception cref="NotSupportedException">
        /// <para>The <see cref="QuaternionDArrayList"/> is read-only.</para>
        /// <para>-or-</para>
        /// <para>The <b>QuaternionDArrayList</b> has a fixed size.</para>
        /// <para>-or-</para>
        /// <para>The <b>QuaternionDArrayList</b> already contains one or more elements
        /// in the specified <paramref name="array"/>, and the <b>QuaternionDArrayList</b>
        /// ensures that all elements are unique.</para></exception>
        /// <remarks>Please refer to <see cref="ArrayList.AddRange"/> for details.</remarks>
        public virtual void AddRange(QuaternionD[] array)
        {
            if (array == null)
                throw new ArgumentNullException("array");

            if (array.Length == 0) return;
            if (this._count + array.Length > this._array.Length)
                EnsureCapacity(this._count + array.Length);

            ++this._version;
            Array.Copy(array, 0, this._array, this._count, array.Length);
            this._count += array.Length;
        }
 /// <summary>
 /// Removes the first occurrence of the specified <see cref="QuaternionD"/>
 /// from the <see cref="QuaternionDArrayList"/>.
 /// </summary>
 /// <param name="value">The <see cref="QuaternionD"/> object
 /// to remove from the <see cref="QuaternionDArrayList"/>.
 /// </param>
 /// <exception cref="NotSupportedException">
 /// <para>The <see cref="QuaternionDArrayList"/> is read-only.</para>
 /// <para>-or-</para>
 /// <para>The <b>QuaternionDArrayList</b> has a fixed size.</para></exception>
 /// <remarks>Please refer to <see cref="ArrayList.Remove"/> for details.</remarks>
 public virtual void Remove(QuaternionD value)
 {
     int index = IndexOf(value);
     if (index >= 0) RemoveAt(index);
 }
 /// <summary>
 /// Determines whether the <see cref="QuaternionDArrayList"/>
 /// contains the specified <see cref="QuaternionD"/> element.
 /// </summary>
 /// <param name="value">The <see cref="QuaternionD"/> object
 /// to locate in the <see cref="QuaternionDArrayList"/>.
 /// </param>
 /// <returns><c>true</c> if <paramref name="value"/> is found in the
 /// <see cref="QuaternionDArrayList"/>; otherwise, <c>false</c>.</returns>
 /// <remarks>Please refer to <see cref="ArrayList.Contains"/> for details.</remarks>
 public bool Contains(QuaternionD value)
 {
     return (IndexOf(value) >= 0);
 }
 /// <summary>
 /// Copies the elements of the <see cref="QuaternionDArrayList"/> to a new
 /// <see cref="Array"/> of <see cref="QuaternionD"/> elements.
 /// </summary>
 /// <returns>A one-dimensional <see cref="Array"/> of <see cref="QuaternionD"/>
 /// elements containing copies of the elements of the <see cref="QuaternionDArrayList"/>.</returns>
 /// <remarks>Please refer to <see cref="ArrayList.ToArray"/> for details.</remarks>
 public virtual QuaternionD[] ToArray()
 {
     QuaternionD[] array = new QuaternionD[this._count];
     Array.Copy(this._array, array, this._count);
     return array;
 }
 /// <summary>
 /// Copies the entire <see cref="QuaternionDArrayList"/> to a one-dimensional <see cref="Array"/>
 /// of <see cref="QuaternionD"/> elements, starting at the specified index of the target array.
 /// </summary>
 /// <param name="array">The one-dimensional <see cref="Array"/> that is the destination of the
 /// <see cref="QuaternionD"/> elements copied from the <see cref="QuaternionDArrayList"/>.
 /// The <b>Array</b> must have zero-based indexing.</param>
 /// <param name="arrayIndex">The zero-based index in <paramref name="array"/>
 /// at which copying begins.</param>
 /// <exception cref="ArgumentNullException">
 /// <paramref name="array"/> is a null reference.</exception>
 /// <exception cref="ArgumentOutOfRangeException">
 /// <paramref name="arrayIndex"/> is less than zero.</exception>
 /// <exception cref="ArgumentException"><para>
 /// <paramref name="arrayIndex"/> is equal to or greater than the length of <paramref name="array"/>.
 /// </para><para>-or-</para><para>
 /// The number of elements in the source <see cref="QuaternionDArrayList"/> is greater than the
 /// available space from <paramref name="arrayIndex"/> to the end of the destination
 /// <paramref name="array"/>.</para></exception>
 /// <remarks>Please refer to <see cref="ArrayList.CopyTo"/> for details.</remarks>
 public virtual void CopyTo(QuaternionD[] array, int arrayIndex)
 {
     CheckTargetArray(array, arrayIndex);
     Array.Copy(this._array, 0, array, arrayIndex, this._count);
 }
Ejemplo n.º 49
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        /// <summary>
        ///     Diagonalizes a given covariance matrix with double precision.
        ///
        ///     <para>
        ///         Credits to: https://github.com/melax/sandbox
        ///         http://melax.github.io/diag.html
        ///         A must be a symmetric matrix.
        ///         returns quaternion q such that its corresponding matrix Q
        ///         can be used to Diagonalize A
        ///         Diagonal matrix D = transpose(Q) * A * (Q); thus A == Q * D * QT
        ///         The directions of Q (cols of Q) are the eigenvectors D's diagonal is the eigenvalues.
        ///         As per 'col' convention if float3x3 Q = qgetmatrix(q); then Q*v = q*v*conj(q).
        ///     </para>
        /// </summary>
        /// <param name="A">The covariance matrix</param>
        /// <returns></returns>
        public static EigenD Diagonalizer(double4x4 A)
        {
            const int maxsteps = 512; // certainly wont need that many.

            var q = new QuaternionD(0, 0, 0, 1);
            var D = double4x4.Identity;
            var Q = double4x4.Identity;

            for (var i = 0; i < maxsteps; i++)
            {
                // Q = float4x4.CreateRotation(q); // v*Q == q*v*conj(q)
                Q = q.ToRotMat();                                                                                                              // v*Q == q*v*conj(q)
                D = Q.Transpose() * A * Q;                                                                                                     // A = Q^T*D*Q
                var offDiagonal = new double3(D.M23, D.M13, D.M12);                                                                            // elements not on the diagonal
                var om          = new double3(System.Math.Abs(offDiagonal.x), System.Math.Abs(offDiagonal.y), System.Math.Abs(offDiagonal.z)); // mag of each offdiag elem
                var k           = (om.x > om.y && om.x > om.z) ? 0 : (om.y > om.z) ? 1 : 2;                                                    // index of largest element of offdiag
                var k1          = (k + 1) % 3;
                var k2          = (k + 2) % 3;

                if (offDiagonal[k].Equals(0.0f))
                {
                    break;                               // diagonal already
                }
                var theta = (D[k2, k2] - D[k1, k1]) / (2.0f * offDiagonal[k]);
                var sgn   = (theta > 0.0f) ? 1.0f : -1.0f;
                theta *= sgn;                                                                                 // make it positive
                var t = sgn / (theta + ((theta < 1.0e+6f) ? System.Math.Sqrt(theta * theta + 1.0f) : theta)); // sign(T)/(|T|+sqrt(T^2+1))
                var c = 1.0f / System.Math.Sqrt(t * t + 1.0f);                                                //  c= 1/(t^2+1) , t=s/c

                if (c.Equals(1.0f))
                {
                    break;                           // no room for improvement - reached machine precision.
                }
                var jr = new QuaternionD(0, 0, 0, 0) // jacobi rotation for this iteration.
                {
                    [k] = (sgn * System.Math.Sqrt((1.0f - c) / 2.0f))
                };

                // using 1/2 angle identity sin(a/2) = sqrt((1-cos(a))/2)
                jr[k] *= -1.0f; // note we want a final result semantic that takes D to A, not A to D
                jr.w   = System.Math.Sqrt(1.0f - (jr[k] * jr[k]));
                if (jr.w.Equals(1.0f))
                {
                    break;                    // reached limits of floating point precision
                }
                q *= jr;
                q.Normalize();
            }

            var vectorMat = Q;

            return(new EigenD
            {
                Values = new[]
                {
                    D.M11,
                    D.M22,
                    D.M33
                },
                Vectors = new double3[] { vectorMat.Row0.xyz, vectorMat.Row1.xyz, vectorMat.Row2.xyz }
            });
        }