/// <summary>
/// Create a transform by origin, X, Y, and Z axes. Axes are automatically unitized — to create non-uniform transforms, use Transform.Scale.
/// </summary>
/// <param name="origin">The origin of the transform.</param>
/// <param name="xAxis">The X axis of the transform.</param>
/// <param name="yAxis">The Y axis of the transform.</param>
/// <param name="zAxis">The Z axis of the transform.</param>
public Transform(Vector3 origin,
Vector3 xAxis,
Vector3 yAxis,
Vector3 zAxis)
{
this.Matrix = new Matrix(xAxis.Unitized(), yAxis.Unitized(), zAxis.Unitized(), origin);
}
/// <summary>
/// Create a transform by origin and X and Z axes.
/// </summary>
/// <param name="origin">The origin of the transform.</param>
/// <param name="xAxis">The X axis of the transform.</param>
/// <param name="zAxis">The Z axis of the transform.</param>
/// <param name="rotation">An optional rotation in degrees around the transform's z axis.</param>
public Transform(Vector3 origin, Vector3 xAxis, Vector3 zAxis, double rotation = 0.0)
{
var x = xAxis.Unitized();
var z = zAxis.Unitized();
var y = z.Cross(x).Unitized();
this.Matrix = new Matrix(x, y, z, Vector3.Origin);
ApplyRotationAndTranslation(rotation, z, origin);
}
/// <summary>
/// Compute the 2D convex hull of a set of 3D points in a plane.
/// </summary>
/// <param name="points">A collection of points</param>
/// <param name="planeNormal">The normal direction of the plane in which to compute the hull.</param>
/// <returns>A polygon representing the convex hull, projected along the normal vector to the average depth of the provided points.</returns>
public static Polygon FromPointsInPlane(IEnumerable <Vector3> points, Vector3 planeNormal)
{
if (planeNormal.Length().ApproximatelyEquals(0))
{
throw new ArgumentException("The current normal vector cannot be of length 0");
}
if (planeNormal.Unitized() == Vector3.ZAxis ||
planeNormal.Unitized().Negate() == Vector3.ZAxis)
{
return(FromPoints(points));
}
else
{
var center3D = points.Average();
var toOrientation = new Transform(center3D, planeNormal);
var fromOrientation = toOrientation.Inverted();
var tPoints = points.Select(p => fromOrientation.OfPoint(p)).Select(p => new Vector3(p.X, p.Y));
var twoDHull = FromPoints(tPoints);
return(twoDHull.TransformedPolygon(toOrientation));
}
}
/// <summary>
/// The normal of this polygon, according to Newell's Method.
/// </summary>
/// <returns>The unitized sum of the cross products of each pair of edges.</returns>
public override Vector3 Normal()
{
var normal = new Vector3();
for (int i = 0; i < Vertices.Count; i++)
{
var p0 = Vertices[i];
var p1 = Vertices[(i + 1) % Vertices.Count];
normal.X += (p0.Y - p1.Y) * (p0.Z + p1.Z);
normal.Y += (p0.Z - p1.Z) * (p0.X + p1.X);
normal.Z += (p0.X - p1.X) * (p0.Y + p1.Y);
}
return(normal.Unitized());
}
/// <summary>
/// Calculate the normal of the plane containing a set of points.
/// </summary>
/// <param name="points">The points in the plane.</param>
/// <returns>The normal of the plane containing the points.</returns>
internal static Vector3 NormalFromPlanarWoundPoints(this IList <Vector3> points)
{
var normal = new Vector3();
for (int i = 0; i < points.Count; i++)
{
var p0 = points[i];
var p1 = points[(i + 1) % points.Count];
normal.X += (p0.Y - p1.Y) * (p0.Z + p1.Z);
normal.Y += (p0.Z - p1.Z) * (p0.X + p1.X);
normal.Z += (p0.X - p1.X) * (p0.Y + p1.Y);
}
return(normal.Unitized());
}
/// <summary>
/// The normal of this polyline, according to Newell's Method.
/// </summary>
/// <returns>The unitized sum of the cross products of each pair of edges.</returns>
public virtual Vector3 Normal()
{
// This is a slight variation on Newell that does not
// close the loop, as we do for polygons. For polylines,
// closing the loop often results in self-intersection
// which returns a zero length vector.
var normal = new Vector3();
for (int i = 0; i < Vertices.Count - 1; i++)
{
var p0 = Vertices[i];
var p1 = Vertices[i + 1];
normal.X += (p0.Y - p1.Y) * (p0.Z + p1.Z);
normal.Y += (p0.Z - p1.Z) * (p0.X + p1.X);
normal.Z += (p0.X - p1.X) * (p0.Y + p1.Y);
}
return(normal.Unitized());
}
/// <summary>
/// Construct a line of length from a start along direction.
/// </summary>
/// <param name="start"></param>
/// <param name="direction"></param>
/// <param name="length"></param>
public Line(Vector3 start, Vector3 direction, double length)
{
this.Start = start;
this.End = start + direction.Unitized() * length;
}