/// <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 Vector4D value1, ref Vector4D tangent1, ref Vector4D value2, ref Vector4D tangent2, double amount, out Vector4D result)
{
double squared = amount * amount;
double cubed = amount * squared;
double part1 = ((2.0 * cubed) - (3.0 * squared)) + 1.0;
double part2 = (-2.0 * cubed) + (3.0 * squared);
double part3 = (cubed - (2.0 * squared)) + amount;
double part4 = cubed - squared;
result = new Vector4D((((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 coordinate transformation using the given <see cref="SharpDX.Matrix"/>.
/// </summary>
/// <param name="coordinate">The coordinate vector to transform.</param>
/// <param name="transform">The transformation <see cref="SharpDX.Matrix"/>.</param>
/// <param name="result">When the method completes, contains the transformed coordinates.</param>
/// <remarks>
/// A coordinate transform performs the transformation with the assumption that the w component
/// is one. The four dimensional vector obtained from the transformation operation has each
/// component in the vector divided by the w component. This forces the w component to be one and
/// therefore makes the vector homogeneous. The homogeneous vector is often preferred when working
/// with coordinates as the w component can safely be ignored.
/// </remarks>
public static void TransformCoordinate(ref Vector3D coordinate, ref MatrixD transform, out Vector3D result)
{
Vector4D vector = new Vector4D();
vector.X = (coordinate.X * transform.M11) + (coordinate.Y * transform.M21) + (coordinate.Z * transform.M31) + transform.M41;
vector.Y = (coordinate.X * transform.M12) + (coordinate.Y * transform.M22) + (coordinate.Z * transform.M32) + transform.M42;
vector.Z = (coordinate.X * transform.M13) + (coordinate.Y * transform.M23) + (coordinate.Z * transform.M33) + transform.M43;
vector.W = 1f / ((coordinate.X * transform.M14) + (coordinate.Y * transform.M24) + (coordinate.Z * transform.M34) + transform.M44);
result = new Vector3D(vector.X * vector.W, vector.Y * vector.W, vector.Z * vector.W);
}
/// <summary>
/// Creates a MatrixD that flattens geometry into a shadow.
/// </summary>
/// <param name="light">The light direction. If the W component is 0, the light is directional light; if the
/// W component is 1, the light is a point light.</param>
/// <param name="plane">The plane onto which to project the geometry as a shadow. This parameter is assumed to be normalized.</param>
/// <param name="result">When the method completes, contains the shadow MatrixD.</param>
public static void Shadow(ref Vector4D light, ref Plane plane, out MatrixD result)
{
double dot = (plane.Normal.X * light.X) + (plane.Normal.Y * light.Y) + (plane.Normal.Z * light.Z) + (plane.D * light.W);
double x = -plane.Normal.X;
double y = -plane.Normal.Y;
double z = -plane.Normal.Z;
double d = -plane.D;
result.M11 = (x * light.X) + dot;
result.M21 = y * light.X;
result.M31 = z * light.X;
result.M41 = d * light.X;
result.M12 = x * light.Y;
result.M22 = (y * light.Y) + dot;
result.M32 = z * light.Y;
result.M42 = d * light.Y;
result.M13 = x * light.Z;
result.M23 = y * light.Z;
result.M33 = (z * light.Z) + dot;
result.M43 = d * light.Z;
result.M14 = x * light.W;
result.M24 = y * light.W;
result.M34 = z * light.W;
result.M44 = (d * light.W) + dot;
}
/// <summary>
/// Transforms a 4D vector by the given <see cref="SharpDX.Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="SharpDX.Quaternion"/> rotation to apply.</param>
/// <returns>The transformed <see cref="SharpDX.Vector4D"/>.</returns>
public static Vector4D Transform(Vector4D vector, Quaternion rotation)
{
Vector4D result;
Transform(ref vector, ref rotation, out result);
return result;
}
public static void Transform(ref Vector3D vector, ref MatrixD transform, out Vector4D result)
{
result = new Vector4D(
(vector.X * transform.M11) + (vector.Y * transform.M21) + (vector.Z * transform.M31) + transform.M41,
(vector.X * transform.M12) + (vector.Y * transform.M22) + (vector.Z * transform.M32) + transform.M42,
(vector.X * transform.M13) + (vector.Y * transform.M23) + (vector.Z * transform.M33) + transform.M43,
(vector.X * transform.M14) + (vector.Y * transform.M24) + (vector.Z * transform.M34) + transform.M44);
}
/// <summary>
/// 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 Vector4D SmoothStep(Vector4D start, Vector4D end, double amount)
{
Vector4D result;
SmoothStep(ref start, ref end, amount, out result);
return result;
}
/// <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>
public static Vector4D Subtract(Vector4D left, Vector4D right)
{
return new Vector4D(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>
/// <param name="result">When the method completes, contains the modulated vector.</param>
public static void Modulate(ref Vector4D left, ref Vector4D right, out Vector4D result)
{
result = new Vector4D(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>
public static Vector4D Modulate(Vector4D left, Vector4D right)
{
return new Vector4D(left.X * right.X, left.Y * right.Y, left.Z * right.Z, 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>
/// <param name="result">When the method completes, contains an new vector composed of the smallest components of the source vectors.</param>
public static void Min(ref Vector4D left, ref Vector4D right, out Vector4D 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>
public static Vector4D Min(Vector4D left, Vector4D right)
{
Vector4D result;
Min(ref left, ref right, out result);
return result;
}
/// <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>
/// <param name="result">When the method completes, contains an new vector composed of the largest components of the source vectors.</param>
public static void Max(ref Vector4D left, ref Vector4D right, out Vector4D 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>
/// 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 Vector4D start, ref Vector4D end, double amount, out Vector4D 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 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 Vector4D Hermite(Vector4D value1, Vector4D tangent1, Vector4D value2, Vector4D tangent2, double amount)
{
Vector4D result;
Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
return result;
}
/// <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(Vector4D[] destination, params Vector4D[] 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)
{
Vector4D newvector = source[i];
for (int r = 0; r < i; ++r)
{
newvector -= Vector4D.Dot(destination[r], newvector) * destination[r];
}
newvector.Normalize();
destination[i] = newvector;
}
}
/// <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>
public static void Multiply(ref Vector4D value, double scale, out Vector4D result)
{
result = new Vector4D(value.X * scale, value.Y * scale, value.Z * scale, value.W * scale);
}
/// <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 Vector4D start, ref Vector4D end, double amount, out Vector4D result)
{
amount = (amount > 1.0) ? 1.0 : ((amount < 0.0) ? 0.0 : amount);
amount = (amount * amount) * (3.0 - (2.0 * 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>
/// 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>
public static Vector4D Multiply(Vector4D value, double scale)
{
return new Vector4D(value.X * scale, value.Y * scale, value.Z * scale, value.W * scale);
}
/// <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>
public static void Subtract(ref Vector4D left, ref Vector4D right, out Vector4D result)
{
result = new Vector4D(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>
public static void Negate(ref Vector4D value, out Vector4D result)
{
result = new Vector4D(-value.X, -value.Y, -value.Z, -value.W);
}
/// <summary>
/// Transforms a 4D vector by the given <see cref="SharpDX.Quaternion"/> rotation.
/// </summary>
/// <param name="vector">The vector to rotate.</param>
/// <param name="rotation">The <see cref="SharpDX.Quaternion"/> rotation to apply.</param>
/// <param name="result">When the method completes, contains the transformed <see cref="SharpDX.Vector4D"/>.</param>
public static void Transform(ref Vector4D vector, ref Quaternion rotation, out Vector4D 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 Vector4D(
((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>
/// 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>
public static Vector4D Negate(Vector4D value)
{
return new Vector4D(-value.X, -value.Y, -value.Z, -value.W);
}
/// <summary>
/// Transforms an array of vectors by the given <see cref="SharpDX.Quaternion"/> rotation.
/// </summary>
/// <param name="source">The array of vectors to transform.</param>
/// <param name="rotation">The <see cref="SharpDX.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(Vector4D[] source, ref Quaternion rotation, Vector4D[] destination)
{
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
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;
double num1 = ((1.0 - yy) - zz);
double num2 = (xy - wz);
double num3 = (xz + wy);
double num4 = (xy + wz);
double num5 = ((1.0 - xx) - zz);
double num6 = (yz - wx);
double num7 = (xz - wy);
double num8 = (yz + wx);
double num9 = ((1.0 - xx) - yy);
for (int i = 0; i < source.Length; ++i)
{
destination[i] = new Vector4D(
((source[i].X * num1) + (source[i].Y * num2)) + (source[i].Z * num3),
((source[i].X * num4) + (source[i].Y * num5)) + (source[i].Z * num6),
((source[i].X * num7) + (source[i].Y * num8)) + (source[i].Z * num9),
source[i].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>
public static void Normalize(ref Vector4D value, out Vector4D result)
{
Vector4D temp = value;
result = temp;
result.Normalize();
}
public static void Transform(Vector3D[] source, ref MatrixD transform, Vector4D[] destination)
{
if (source == null)
throw new ArgumentNullException("source");
if (destination == null)
throw new ArgumentNullException("destination");
if (destination.Length < source.Length)
throw new ArgumentOutOfRangeException("destination", "The destination array must be of same length or larger length than the source array.");
for (int i = 0; i < source.Length; ++i)
{
Transform(ref source[i], ref transform, out destination[i]);
}
}
/// <summary>
/// Converts the vector into a unit vector.
/// </summary>
/// <param name="value">The vector to normalize.</param>
/// <returns>The normalized vector.</returns>
public static Vector4D Normalize(Vector4D value)
{
value.Normalize();
return value;
}
/// <summary>
/// Brings the MatrixD into reduced row echelon form using elementary row operations.
/// </summary>
/// <param name="value">The MatrixD to put into reduced row echelon form.</param>
/// <param name="augment">The fifth column of the MatrixD.</param>
/// <param name="result">When the method completes, contains the resultant MatrixD after the operation.</param>
/// <param name="augmentResult">When the method completes, contains the resultant fifth column of the MatrixD.</param>
/// <remarks>
/// <para>The fifth column is often called the augmented part of the MatrixD. This is because the fifth
/// column is really just an extension of the MatrixD so that there is a place to put all of the
/// non-zero components after the operation is complete.</para>
/// <para>Often times the resultant MatrixD will the identity MatrixD or a MatrixD similar to the identity
/// MatrixD. Sometimes, however, that is not possible and numbers other than zero and one may appear.</para>
/// <para>This method can be used to solve systems of linear equations. Upon completion of this method,
/// the <paramref name="augmentResult"/> will contain the solution for the system. It is up to the user
/// to analyze both the input and the result to determine if a solution really exists.</para>
/// </remarks>
public static void ReducedRowEchelonForm(ref MatrixD value, ref Vector4D augment, out MatrixD result, out Vector4D augmentResult)
{
//Source: http://rosettacode.org
//Reference: http://rosettacode.org/wiki/Reduced_row_echelon_form
double[,] MatrixD = new double[4, 5];
MatrixD[0, 0] = value[0, 0];
MatrixD[0, 1] = value[0, 1];
MatrixD[0, 2] = value[0, 2];
MatrixD[0, 3] = value[0, 3];
MatrixD[0, 4] = augment[0];
MatrixD[1, 0] = value[1, 0];
MatrixD[1, 1] = value[1, 1];
MatrixD[1, 2] = value[1, 2];
MatrixD[1, 3] = value[1, 3];
MatrixD[1, 4] = augment[1];
MatrixD[2, 0] = value[2, 0];
MatrixD[2, 1] = value[2, 1];
MatrixD[2, 2] = value[2, 2];
MatrixD[2, 3] = value[2, 3];
MatrixD[2, 4] = augment[2];
MatrixD[3, 0] = value[3, 0];
MatrixD[3, 1] = value[3, 1];
MatrixD[3, 2] = value[3, 2];
MatrixD[3, 3] = value[3, 3];
MatrixD[3, 4] = augment[3];
int lead = 0;
int rowcount = 4;
int columncount = 5;
for (int r = 0; r < rowcount; r++)
{
if (columncount <= lead)
break;
int i = r;
while (MatrixD[i, lead] == 0)
{
i++;
if (i == rowcount)
{
i = r;
lead++;
if (columncount == lead)
break;
}
}
for (int j = 0; j < columncount; j++)
{
double temp = MatrixD[r, j];
MatrixD[r, j] = MatrixD[i, j];
MatrixD[i, j] = temp;
}
double div = MatrixD[r, lead];
for (int j = 0; j < columncount; j++)
{
MatrixD[r, j] /= div;
}
for (int j = 0; j < rowcount; j++)
{
if (j != r)
{
double sub = MatrixD[j, lead];
for (int k = 0; k < columncount; k++) MatrixD[j, k] -= (sub * MatrixD[r, k]);
}
}
lead++;
}
result.M11 = MatrixD[0, 0];
result.M12 = MatrixD[0, 1];
result.M13 = MatrixD[0, 2];
result.M14 = MatrixD[0, 3];
result.M21 = MatrixD[1, 0];
result.M22 = MatrixD[1, 1];
result.M23 = MatrixD[1, 2];
result.M24 = MatrixD[1, 3];
result.M31 = MatrixD[2, 0];
result.M32 = MatrixD[2, 1];
result.M33 = MatrixD[2, 2];
result.M34 = MatrixD[2, 3];
result.M41 = MatrixD[3, 0];
result.M42 = MatrixD[3, 1];
result.M43 = MatrixD[3, 2];
result.M44 = MatrixD[3, 3];
augmentResult.X = MatrixD[0, 4];
augmentResult.Y = MatrixD[1, 4];
augmentResult.Z = MatrixD[2, 4];
augmentResult.W = MatrixD[3, 4];
}
/// <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(Vector4D[] destination, params Vector4D[] 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)
{
Vector4D newvector = source[i];
for (int r = 0; r < i; ++r)
{
newvector -= (Vector4D.Dot(destination[r], newvector) / Vector4D.Dot(destination[r], destination[r])) * destination[r];
}
destination[i] = newvector;
}
}
/// <summary>
/// Creates a MatrixD that flattens geometry into a shadow.
/// </summary>
/// <param name="light">The light direction. If the W component is 0, the light is directional light; if the
/// W component is 1, the light is a point light.</param>
/// <param name="plane">The plane onto which to project the geometry as a shadow. This parameter is assumed to be normalized.</param>
/// <returns>The shadow MatrixD.</returns>
public static MatrixD Shadow(Vector4D light, Plane plane)
{
MatrixD result;
Shadow(ref light, ref plane, out result);
return result;
}
/// <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>
public static double Dot(Vector4D left, Vector4D right)
{
return (left.X * right.X) + (left.Y * right.Y) + (left.Z * right.Z) + (left.W * right.W);
}