/// <summary>
/// Creates a matrix that represents a spherical linear interpolation from one
/// matrix to another.
/// </summary>
/// <remarks>
/// <para>This is an implementation of interpolation without quaternions.</para>
/// <para>
/// Given two orthonormal 3x3 matrices this function calculates the shortest
/// possible interpolation-path between the two rotations. The interpolation curve
/// forms the shortest great arc on the rotation sphere (geodesic).
/// </para>
/// <para>Angular velocity of the interpolation is constant.</para>
/// <para>Possible stability problems:</para>
/// <para>
/// There are two singularities at angle = 0 and angle = <see cref="Math.PI"/> .
/// At 0 the interpolation-axis is arbitrary, which means any axis will produce
/// the same result because we have no rotation. (1,0,0) axis is used in this
/// case. At <see cref="Math.PI"/> the rotations point away from each other and
/// the interpolation-axis is unpredictable. In this case axis (1,0,0) is used as
/// well. If the angle is ~0 or ~PI, then a very small vector has to be normalized
/// and this can cause numerical instability.
/// </para>
/// </remarks>
/// <param name="m">First matrix.</param>
/// <param name="n">Second matrix.</param>
/// <param name="t">Interpolation parameter.</param>
public void SetSlerp(Matrix34 m, Matrix34 n, float t)
{
// calculate delta-rotation between m and n (=39 flops)
Matrix33 d = new Matrix33(), i = new Matrix33();
d.M00 = m.M00 * n.M00 + m.M10 * n.M10 + m.M20 * n.M20; d.M01 = m.M00 * n.M01 + m.M10 * n.M11 + m.M20 * n.M21; d.M02 = m.M00 * n.M02 + m.M10 * n.M12 + m.M20 * n.M22;
d.M10 = m.M01 * n.M00 + m.M11 * n.M10 + m.M21 * n.M20; d.M11 = m.M01 * n.M01 + m.M11 * n.M11 + m.M21 * n.M21; d.M12 = m.M01 * n.M02 + m.M11 * n.M12 + m.M21 * n.M22;
d.M20 = d.M01 * d.M12 - d.M02 * d.M11; d.M21 = d.M02 * d.M10 - d.M00 * d.M12; d.M22 = d.M00 * d.M11 - d.M01 * d.M10;
// extract angle and axis
double cosine = MathHelpers.Clamp((d.M00 + d.M11 + d.M22 - 1.0) * 0.5, -1.0, +1.0);
double angle = Math.Atan2(Math.Sqrt(1.0 - cosine * cosine), cosine);
var axis = new Vector3(d.M21 - d.M12, d.M02 - d.M20, d.M10 - d.M01);
double l = Math.Sqrt(axis | axis); if (l > 0.00001)
{
axis /= (float)l;
}
else
{
axis = new Vector3(1, 0, 0);
}
i.SetRotationAroundAxis((float)angle * t, axis); // angle interpolation and calculation of new delta-matrix (=26 flops)
// final concatenation (=39 flops)
this.M00 = m.M00 * i.M00 + m.M01 * i.M10 + m.M02 * i.M20; this.M01 = m.M00 * i.M01 + m.M01 * i.M11 + m.M02 * i.M21; this.M02 = m.M00 * i.M02 + m.M01 * i.M12 + m.M02 * i.M22;
this.M10 = m.M10 * i.M00 + m.M11 * i.M10 + m.M12 * i.M20; this.M11 = m.M10 * i.M01 + m.M11 * i.M11 + m.M12 * i.M21; this.M12 = m.M10 * i.M02 + m.M11 * i.M12 + m.M12 * i.M22;
this.M20 = this.M01 * this.M12 - this.M02 * this.M11; this.M21 = this.M02 * this.M10 - this.M00 * this.M12; this.M22 = this.M00 * this.M11 - this.M01 * this.M10;
this.M03 = m.M03 * (1 - t) + n.M03 * t;
this.M13 = m.M13 * (1 - t) + n.M13 * t;
this.M23 = m.M23 * (1 - t) + n.M23 * t;
}
/// <summary>
/// Creates a new matrix which columns are initialized with values supplied by
/// given vectors.
/// </summary>
/// <param name="vx">
/// <see cref="Vector3"/> object that provides values for the first column.
/// </param>
/// <param name="vy">
/// <see cref="Vector3"/> object that provides values for the second column.
/// </param>
/// <param name="vz">
/// <see cref="Vector3"/> object that provides values for the third column.
/// </param>
/// <param name="vw">
/// <see cref="Vector3"/> object that provides values for the fourth column.
/// </param>
/// <returns>
/// New matrix which columns are initialized with values supplied by given
/// vectors.
/// </returns>
public static Matrix34 CreateFromColumns(Vector3 vx, Vector3 vy, Vector3 vz, Vector3 vw)
{
var matrix = new Matrix34();
matrix.SetColumns(vx, vy, vz, vw);
return(matrix);
}
/// <summary>
/// Creates a matrix that represents transformations represented by given
/// arguments.
/// </summary>
/// <param name="s"><see cref="Vector3"/> object that represents scale.</param>
/// <param name="q">
/// <see cref="Quaternion"/> object that represents rotation.
/// </param>
/// <param name="t">
/// Optional <see cref="Vector3"/> object that represents translation.
/// </param>
/// <returns>
/// Matrix that represents transformations represented by given arguments.
/// </returns>
public static Matrix34 Create(Vector3 s, Quaternion q, Vector3 t = default(Vector3))
{
var matrix = new Matrix34();
matrix.Set(s, q, t);
return(matrix);
}
/// <summary>
/// Creates a rotation matrix around an arbitrary axis (Eulers Theorem).
/// </summary>
/// <param name="c"> Cosine of the angle of the rotation.</param>
/// <param name="s"> Sine of the angle of the rotation.</param>
/// <param name="axis">
/// <see cref="Vector3"/> object that represents axis of rotation.
/// </param>
/// <param name="t"> Optional translation vector.</param>
/// <returns>A new rotation matrix around an arbitrary axis.</returns>
public static Matrix34 CreateRotationAroundAxis(float c, float s, Vector3 axis, Vector3 t = default(Vector3))
{
var matrix = new Matrix34();
matrix.SetRotationAroundAxis(c, s, axis, t);
return(matrix);
}
/// <summary>
/// Creates a matrix that represents a spherical linear interpolation from one
/// matrix to another.
/// </summary>
/// <param name="m">First matrix.</param>
/// <param name="n">Second matrix.</param>
/// <param name="t">Interpolation parameter.</param>
/// <returns>
/// Matrix which transformations are interpolated between given matrices.
/// </returns>
public static Matrix34 CreateSlerp(Matrix34 m, Matrix34 n, float t)
{
var matrix = new Matrix34();
matrix.SetSlerp(m, n, t);
return(matrix);
}
/// <summary>
/// Creates a matrix that represents rotation represented by given Euler angles.
/// </summary>
/// <param name="rad">Angles of rotation.</param>
/// <param name="t"> Optional translation vector.</param>
/// <returns>
/// A new matrix that represents rotation represented by given Euler angles.
/// </returns>
public static Matrix34 CreateRotationWithEulerAngles(EulerAngles rad, Vector3 t = default(Vector3))
{
var matrix = new Matrix34();
matrix.SetRotationWithEulerAngles(rad, t);
return(matrix);
}
/// <summary>
/// Creates a matrix that represents a translation without any other
/// transformations.
/// </summary>
/// <param name="v">
/// <see cref="Vector3"/> object that represents translation.
/// </param>
/// <returns>
/// Matrix that represents a translation without any other transformations.
/// </returns>
public static Matrix34 CreatePureTranslation(Vector3 v)
{
var matrix = new Matrix34();
matrix.SetPureTranslation(v);
return(matrix);
}
/// <summary>
/// Creates a matrix that represents a rotation around Z axis.
/// </summary>
/// <param name="rad">Angle of rotation in radians.</param>
/// <param name="t"> Optional translation vector.</param>
/// <returns>A new matrix that represents a rotation around Z axis.</returns>
public static Matrix34 CreateRotationAroundZ(float rad, Vector3 t = default(Vector3))
{
var matrix = new Matrix34();
matrix.SetRotationAroundZ(rad, t);
return(matrix);
}
/// <summary>
/// Creates a rotation matrix around an arbitrary axis (Eulers Theorem).
/// </summary>
/// <param name="rot">
/// <see cref="Vector3"/> object which length represents an angle of rotation and
/// which direction represents an axis of rotation.
/// </param>
/// <param name="t"> Optional translation vector.</param>
/// <returns>A new rotation matrix.</returns>
public static Matrix34 CreateRotationAroundAxis(Vector3 rot, Vector3 t = default(Vector3))
{
var matrix = new Matrix34();
matrix.SetRotationAroundAxis(rot, t);
return(matrix);
}
/// <summary>
/// Creates a matrix that represents scaling.
/// </summary>
/// <param name="s"><see cref="Vector3"/> object that represents scale.</param>
/// <param name="t">
/// Optional <see cref="Vector3"/> object that represents translation.
/// </param>
/// <returns>Matrix that represents scaling.</returns>
public static Matrix34 CreateScale(Vector3 s, Vector3 t = default(Vector3))
{
var matrix = new Matrix34();
matrix.SetScale(s, t);
return(matrix);
}
/// <summary>
/// Sets the values of this matrix to one that represents a rotation around an
/// axis.
/// </summary>
/// <param name="c"> Cosine of the angle of the rotation.</param>
/// <param name="s"> Sine of the angle of the rotation.</param>
/// <param name="axis">
/// <see cref="Vector3"/> object that represents axis of rotation.
/// </param>
/// <param name="t"> Optional translation vector.</param>
public void SetRotationAroundAxis(float c, float s, Vector3 axis, Vector3 t = default(Vector3))
{
this = new Matrix34(Matrix33.CreateRotationAroundAxis(c, s, axis))
{
M03 = t.X,
M13 = t.Y,
M23 = t.Z
};
}
/// <summary>
/// Creates new instance of <see cref="Matrix44" /> class.
/// </summary>
/// <param name="m"> <see cref="Matrix34" /> to fill new matrix with. </param>
public Matrix44(ref Matrix34 m)
: this()
{
if (!m.IsValid)
{
throw new ArgumentException("Parameter must be a valid matrix.");
}
this.Row0.X = m.Row1.X; this.Row0.Y = m.Row1.Y; this.Row0.Z = m.Row1.Z; this.Row0.W = m.Row1.W;
this.Row1.X = m.Row2.X; this.Row1.Y = m.Row2.Y; this.Row1.Z = m.Row2.Z; this.Row1.W = m.Row2.W;
this.Row2.X = m.Row2.X; this.Row2.Y = m.Row2.Y; this.Row2.Z = m.Row2.Z; this.Row2.W = m.Row2.W;
this.Row3.X = 0; this.Row3.Y = 0; this.Row3.Z = 0; this.Row3.W = 1;
}
/// <summary>
/// Creates new instance of <see cref="Matrix33"/> struct.
/// </summary>
/// <param name="m">
/// <see cref="Matrix34"/> object from which first 3 columns will be copied.
/// </param>
/// <returns>New instance of <see cref="Matrix33"/> struct.</returns>
public Matrix33(Matrix34 m)
: this()
{
this.M00 = m.M00;
this.M01 = m.M01;
this.M02 = m.M02;
this.M10 = m.M10;
this.M11 = m.M11;
this.M12 = m.M12;
this.M20 = m.M20;
this.M21 = m.M21;
this.M22 = m.M22;
}
/// <summary>
/// Determines whether this matrix can be considered equal to another one within
/// bounds of given precision.
/// </summary>
/// <param name="m">Another matrix.</param>
/// <param name="e">
/// <see cref="Single"/> object that represents maximal difference between two
/// values that allows to consider them equal.
/// </param>
/// <returns>
/// True, if difference between values of each corresponding pair is less then
/// <paramref name="e"/> .
/// </returns>
public bool IsEquivalent(Matrix34 m, float e = 0.05f)
{
return
(
(Math.Abs(this.M00 - m.M00) <= e) &&
(Math.Abs(this.M01 - m.M01) <= e) &&
(Math.Abs(this.M02 - m.M02) <= e) &&
(Math.Abs(this.M03 - m.M03) <= e) &&
(Math.Abs(this.M10 - m.M10) <= e) &&
(Math.Abs(this.M11 - m.M11) <= e) &&
(Math.Abs(this.M12 - m.M12) <= e) &&
(Math.Abs(this.M13 - m.M13) <= e) &&
(Math.Abs(this.M20 - m.M20) <= e) &&
(Math.Abs(this.M21 - m.M21) <= e) &&
(Math.Abs(this.M22 - m.M22) <= e) &&
(Math.Abs(this.M23 - m.M23) <= e));
}
/// <summary>
/// </summary>
/// <param name="vx"> </param>
/// <param name="vy"> </param>
/// <param name="vz"> </param>
/// <param name="pos"></param>
public void SetFromVectors(Vector3 vx, Vector3 vy, Vector3 vz, Vector3 pos)
{
var m34 = new Matrix34
{
M00 = vx.X,
M01 = vy.X,
M02 = vz.X,
M03 = pos.X,
M10 = vx.Y,
M11 = vy.Y,
M12 = vz.Y,
M13 = pos.Y,
M20 = vx.Z,
M21 = vy.Z,
M22 = vz.Z,
M23 = pos.Z
};
this = new QuaternionTranslation(m34);
}
/// <summary>
/// Creates new instance of <see cref="Quaternion"/> struct.
/// </summary>
/// <param name="matrix">
/// 3x4 matrix that contains representation of rotation.
/// </param>
public Quaternion(Matrix34 matrix)
: this(new Matrix33(matrix))
{
}
/// <summary>
/// Creates new instance of type <see cref="QuaternionTranslation"/>.
/// </summary>
/// <param name="m">
/// <see cref="Matrix34"/> that represents both translation and orientation.
/// </param>
public QuaternionTranslation(Matrix34 m)
{
this.Q = new Quaternion(m);
this.T = m.Translation;
}
/// <summary>
/// Convert three Euler angles to 3x3 matrix (rotation order:XYZ)
/// </summary>
/// <param name="rad">Angles of rotation.</param>
/// <param name="t"> Optional translation vector.</param>
public void SetRotationWithEulerAngles(EulerAngles rad, Vector3 t = default(Vector3))
{
this = new Matrix34(Matrix33.CreateRotationFromAngles(rad));
this.SetTranslation(t);
}
/// <summary>
/// Sets the values of this matrix to one that represents a rotation around Z
/// axis.
/// </summary>
/// <param name="rad">Angle of rotation in radians.</param>
/// <param name="t"> Optional translation vector.</param>
public void SetRotationAroundZ(float rad, Vector3 t = default(Vector3))
{
this = new Matrix34(Matrix33.CreateRotationAroundZ(rad));
this.SetTranslation(t);
}
/// <summary>
/// Sets the values of this matrix to one that represents a rotation around an
/// axis.
/// </summary>
/// <param name="rot">
/// <see cref="Vector3"/> object which length represents an angle of rotation and
/// which direction represents an axis of rotation.
/// </param>
/// <param name="t"> Optional translation vector.</param>
public void SetRotationAroundAxis(Vector3 rot, Vector3 t = default(Vector3))
{
this = new Matrix34(Matrix33.CreateRotationAroundAxis(rot));
this.SetTranslation(t);
}
/// <summary>
/// Sets the value of the matrix to one that represents scaling.
/// </summary>
/// <param name="s"><see cref="Vector3"/> object that represents scale.</param>
/// <param name="t">
/// Optional <see cref="Vector3"/> object that represents translation.
/// </param>
public void SetScale(Vector3 s, Vector3 t = default(Vector3))
{
this = new Matrix34(Matrix33.CreateScale(s));
this.SetTranslation(t);
}
