/// <summary>
/// Creates a 3D Z-rotation matrix.
/// </summary>
/// <remarks>For a right-handed 3D system (like WPF), a positive angle value results in a counter-clockwise rotation around the axis. For a left-handed 3D system, a positive angle value results in a clockwise rotation around the axis.</remarks>
/// <param name="angle">Angle value in degree.</param>
/// <param name="handedness">The handedness of the coordinate system (optional). Under WPF, the defaut value is Right-handed.</param>
/// <returns>A Matrix3D object.</returns>
public static Matrix3D GetZRotationMatrix(double angle, Handedness3D handedness = Handedness3D.RightHanded)
{
//var m = new Matrix3D();
//m.Rotate(new Quaternion(new Vector3D(0, 0, 1), angle));
//return m;
// var radianAngle = GeometryHelper.DegreeToRadian(angle);
double radianAngle = 0.0;
if (handedness == Handedness3D.LeftHanded)
{
radianAngle = (2 * Math.PI) - GeometryHelper.DegreeToRadian(angle);
}
else
{
radianAngle = GeometryHelper.DegreeToRadian(angle);
}
return(new Matrix3D
{
M11 = Math.Cos(radianAngle), M21 = -Math.Sin(radianAngle),
M12 = Math.Sin(radianAngle), M22 = Math.Cos(radianAngle)
});
}
/// <summary>
/// Creates a 3D Y-rotation matrix.
/// </summary>
/// <remarks>For a left-handed 3D system (the default in Silverlight projections), a positive angle value results in a clockwise rotation around the axis. For a right-handed 3D system, a positive angle value results in a counter-clockwise rotation around the axis.</remarks>
/// <param name="angle">Angle value in degree.</param>
/// <param name="handedness">The handedness of the coordinate system (optional). Under Silverlight, the defaut value is Left-handed.</param>
/// <returns>A Matrix3D object.</returns>
public static Matrix3D GetYRotationMatrix(double angle, Handedness3D handedness = Handedness3D.LeftHanded)
{
//var m = new Matrix3D();
//m.Rotate(new Quaternion(new Vector3D(0, 1, 0), angle));
//return m;
double radianAngle = 0.0;
// angle inverted in respect to the relative orientation of Z to X
if (handedness == Handedness3D.LeftHanded)
{
radianAngle = GeometryHelper.DegreeToRadian(angle);
}
else
{
radianAngle = (2 * Math.PI) - GeometryHelper.DegreeToRadian(angle);
}
return(new Matrix3D
{
M11 = Math.Cos(radianAngle), M31 = -Math.Sin(radianAngle),
M13 = Math.Sin(radianAngle), M33 = Math.Cos(radianAngle)
});
}
/// <summary>
/// Rounds a vertex of a triangle.
/// </summary>
/// <param name="pA">First point.</param>
/// <param name="pB">Second point. Vertex to round</param>
/// <param name="pC">Third point.</param>
/// <param name="roundingRate">Vertex rounding rate. The value must be comprized between 0.0 and 0.5.</param>
/// <returns></returns>
public static Point3DCollection RoundCorner(Point3D pA, Point3D pB, Point3D pC, double roundingRate)
{
if (!((pA.Z == pB.Z) && (pB.Z == pC.Z))
)
{
throw new ArgumentOutOfRangeException("pA");
}
if ((roundingRate < 0.0) ||
(roundingRate > 0.5)
)
{
throw new ArgumentOutOfRangeException("roundingRate");
}
Point3DCollection points = new Point3DCollection();
int roundingDefinition = (int)(roundingRate * 40.0);
Vector3D v1 = new Vector3D();
v1 = pA - pB;
v1.X = Math.Round(v1.X, 3);
v1.Y = Math.Round(v1.Y, 3);
v1.Z = Math.Round(v1.Z, 3);
Point3D p1 = Point3D.Add(pB, Vector3D.Multiply(v1, roundingRate));
Vector3D v2 = new Vector3D();
v2 = pC - pB;
v2.X = Math.Round(v2.X, 3);
v2.Y = Math.Round(v2.Y, 3);
v2.Z = Math.Round(v2.Z, 3);
Point3D p2 = Point3D.Add(pB, Vector3D.Multiply(v2, roundingRate));
// v1 is the normal vector for the linear curve
// v1.X*x + v1.Y*y + c1 = 0;
// p1 is owned by this curve so
double c1 = -(v1.X * p1.X) - (v1.Y * p1.Y);
// same for v2 and p2
double c2 = -(v2.X * p2.X) - (v2.Y * p2.Y);
// center for the arc that owns p1 and p2
Point3D center = new Point3D();
if (v1.Y == 0.0)
{
if (v1.X == 0.0)
{
throw new InvalidOperationException();
}
center.X = -c1 / v1.X;
if (v2.Y == 0.0)
{
throw new InvalidOperationException();
}
else
{
center.Y = (-c2 - v2.X * center.X) / v2.Y;
}
}
else
{
if (v2.Y == 0.0)
{
if (v2.X == 0.0)
{
throw new InvalidOperationException();
}
center.X = -c2 / v2.X;
}
else
{
center.X = (c1 / v1.Y - c2 / v2.Y) / (v2.X / v2.Y - v1.X / v1.Y);
}
center.Y = (-c1 - v1.X * center.X) / v1.Y;
}
center.Z = pB.Z;
// angle of the arc between p1 and p2
// 360 - 180 - Vector3D.AngleBetween(v1, v2)
double angleArc = GeometryHelper.DegreeToRadian(180 - Vector3D.AngleBetween(v1, v2));
// angle of each part
double angleStep = angleArc / roundingDefinition;
Vector3D vRadius = p1 - center;
double angleBaseDeg = Vector3D.AngleBetween(new Vector3D(1, 0, 0), vRadius);
// necessar adjustment because of Vector3D.AngleBetween() - see documentation
if (p1.Y < 0.0)
{
angleBaseDeg = 360 - angleBaseDeg;
}
double angleBase = GeometryHelper.DegreeToRadian(angleBaseDeg);
points.Add(p1);
// points of the arc
for (int j = 1; j <= roundingDefinition - 1; j++)
{
double angle = angleBase + (angleStep * j);
Point3D p = new Point3D();
p.X = center.X + Math.Cos(angle) * vRadius.Length;
p.Y = center.Y + Math.Sin(angle) * vRadius.Length;
p.Z = pB.Z;
points.Add(p);
}
points.Add(p2);
return(points);
}
