public bool Normalize()
{
bool normalized = true;
CircularLinkedList <UV> points = GetPoints();
CircularLinkedListNode <UV> node = points.Head;
do
{
UV p0 = node.Previous.Value;
UV p1 = node.Value;
UV p2 = node.Next.Value;
double angle = VectorManipulator.CalculatesAngle(p0, p1, p2);
if (AlmostEqual(angle, Math.PI, 0.01) || AlmostEqual(angle, 0, 0.01))
{
points.Remove(p1);
normalized = false;
}
node = node.Next;
} while (node != points.Head);
curveArray = CreateCurveArrayFromPoints(points);
if (!normalized)
{
Normalize();
}
return(normalized);
}
public List <CurveArray> DividePolygonInHalf(XYZ divisionDirection, out Line cutLine)
{
Normalize();
CircularLinkedList <UV> points = GetPoints();
List <CircularLinkedListNode <UV> > newPoints = new List <CircularLinkedListNode <UV> >();
UV centroid = CalculatePolygonCentroid(points);
cutLine = Line.CreateUnbound(VectorManipulator.TransformUVinXYZ(centroid), divisionDirection);
foreach (Curve curve in curveArray)
{
SetComparisonResult result = cutLine.Intersect(curve, out IntersectionResultArray resultArray);
if (result == SetComparisonResult.Overlap)
{
UV newPoint = VectorManipulator.ProjectInPlaneXY(resultArray.get_Item(0).XYZPoint);
XYZ p0 = curve.GetEndPoint(0);
XYZ p1 = curve.GetEndPoint(1);
newPoints.Add(AddPointBetween(points, VectorManipulator.ProjectInPlaneXY(p0), VectorManipulator.ProjectInPlaneXY(p1), newPoint));
}
}
CircularLinkedList <UV> newPolygon0 = CreatePolygonBetweenVertices(newPoints[0], newPoints[1]);
CircularLinkedList <UV> newPolygon1 = CreatePolygonBetweenVertices(newPoints[1], newPoints[0]);
List <CurveArray> dividedCurveArrays = new List <CurveArray>
{
CreateCurveArrayFromPoints(newPolygon0),
CreateCurveArrayFromPoints(newPolygon1)
};
cutLine = Line.CreateBound(VectorManipulator.TransformUVinXYZ(newPoints[0].Value), VectorManipulator.TransformUVinXYZ(newPoints[1].Value));
return(dividedCurveArrays);
}
/// <summary>
/// Get all notches in a list of ordered points that represent the vertices of
/// a polygon. A notch is a point that the reflex angle in internal.
/// </summary>
/// <param name="points">
/// The poitns in the LinkedList must be ordered in clockwise order.
/// </param>
/// <returns>
/// Returns a List with the notches.
/// </returns>
private List <UV> GetNotches(CircularLinkedList <UV> points)
{
List <UV> notches = new List <UV>();
if (points.Count < 5)
{
return(notches);
}
CircularLinkedListNode <UV> node = points.Head;
do
{
UV p0 = node.Value;
UV p1 = node.Next.Value;
UV p2 = node.Next.Next.Value;
double angle = VectorManipulator.CalculatesAngle(p0, p1, p2);
if (angle > Math.PI)
{
notches.Add(p1);
}
node = node.Next;
} while (node != points.Head);
return(notches);
}
/// <summary>
/// Add a new vertice in order in the list of vertices of the polygon given the IntersectionResultArray.
/// </summary>
/// <param name="points"></param>
/// <param name="resultArray"></param>
/// <param name="curve"></param>
private static CircularLinkedListNode <UV> AddPointsInList(CircularLinkedList <UV> points, IntersectionResultArray resultArray, Curve curve)
{
UV p0 = VectorManipulator.ProjectInPlaneXY(curve.GetEndPoint(0));
CircularLinkedListNode <UV> newNode = null;
CircularLinkedListNode <UV> node = FindPoint(points, p0);
IntersectionResultArrayIterator iterator = resultArray.ForwardIterator();
iterator.Reset();
while (iterator.MoveNext())
{
IntersectionResult result = iterator.Current as IntersectionResult;
UV intersectionPoint = VectorManipulator.ProjectInPlaneXY(result.XYZPoint);
newNode = points.AddAfter(node, intersectionPoint);
}
if (newNode.Next.Value.IsAlmostEqualTo(newNode.Value))
{
points.Remove(newNode.Next.Value);
}
else if (newNode.Previous.Value.IsAlmostEqualTo(newNode.Value))
{
points.Remove(newNode.Previous.Value);
}
return(newNode);
}
/// <summary>
/// Get the vertices of the CurveArray
/// </summary>
/// <param name="curveArray">
/// The CurveArray must be closed.
/// </param>
/// <returns>
/// Returns a Linked List of UV points ordered in clock wise order.
/// </returns>
private CircularLinkedList <UV> GetPoints()
{
CircularLinkedList <UV> points = new CircularLinkedList <UV>();
foreach (Curve curve in curveArray)
{
UV point2D = VectorManipulator.ProjectInPlaneXY(curve.GetEndPoint(0));
points.AddLast(point2D);
}
return(points);
}
/// <summary>
/// Create a sub group of the linkedList that starts with node 'first' and ends with node 'last'.
/// </summary>
/// <param name="first"></param>
/// <param name="last"></param>
/// <returns>
/// Returns the vertives of the new polygon.
/// </returns>
private CircularLinkedList <UV> CreatePolygonBetweenVertices(CircularLinkedListNode <UV> first, CircularLinkedListNode <UV> last)
{
CircularLinkedList <UV> polygon = new CircularLinkedList <UV>();
CircularLinkedListNode <UV> node = first;
do
{
polygon.AddLast(node.Value);
node = node.Next;
} while (node != last);
polygon.AddLast(node.Value);
return(polygon);
}
private UV CalculatePolygonCentroid(CircularLinkedList <UV> vertices)
{
CircularLinkedListNode <UV> node = vertices.Head;
UV sum = UV.Zero;
do
{
UV vertex = node.Value;
sum += vertex;
node = node.Next;
} while (node != vertices.Head);
sum /= vertices.Count;
return(sum);
}
/// <summary>
/// Eliminates a notch by creating a new line between the notch and an edge of the polygon.
/// </summary>
/// <param name="notch">Coordinates of the notch.</param>
/// <param name="curveArray">The polygon.</param>
/// <param name="points">The vertices of the polygon.</param>
/// <param name="preferredOrientation">The method will try to make a cut that is parallel to this vector.</param>
/// <param name="cutLine">The line that cut the polygon.</param>
/// <returns>
/// Returns the list of the CurveArrays.
/// </returns>
private List <CurveArray> EliminateNotch(UV notch, CurveArray curveArray, CircularLinkedList <UV> points, XYZ preferredOrientation, out Line cutLine)
{
XYZ notche3D = VectorManipulator.TransformUVinXYZ(notch);
Line line1 = Line.CreateUnbound(notche3D, preferredOrientation);
XYZ otherOrientation = new XYZ(preferredOrientation.Y, preferredOrientation.X, 0);
Line line2 = Line.CreateUnbound(notche3D, otherOrientation);
CircularLinkedListNode <UV> notchNode = FindPoint(points, notch);
// get the posible curves for the new point
CurveArray posibleCurves = new CurveArray();
foreach (Curve curve in curveArray)
{
if (PosibleCurve(curve, notchNode))
{
posibleCurves.Append(curve);
}
}
// iterate for each possible curve, and if
// a intersection is found, the point will
// added in the linked list
CircularLinkedListNode <UV> newNode;
newNode = FindNewNode(ref points, line1, posibleCurves, notch);
if (newNode == null)
{
newNode = FindNewNode(ref points, line2, posibleCurves, notch);
}
// generates the 2 new polygons
CircularLinkedList <UV> polygonA = CreatePolygonBetweenVertices(newNode, notchNode);
CircularLinkedList <UV> polygonB = CreatePolygonBetweenVertices(notchNode, newNode);
// creates the curves
List <CurveArray> list = new List <CurveArray>
{
CreateCurveArrayFromPoints(polygonA),
CreateCurveArrayFromPoints(polygonB)
};
// returns the cutLine
cutLine = Line.CreateBound(notche3D, VectorManipulator.TransformUVinXYZ(newNode.Value));
return(list);
}
/// <summary>
/// Finds a point that
/// </summary>
/// <param name="points"></param>
/// <param name="line1"></param>
/// <param name="posibleCurves"></param>
/// <returns></returns>
private static CircularLinkedListNode <UV> FindNewNode(ref CircularLinkedList <UV> points, Line line, CurveArray posibleCurves, UV notch)
{
// iterate for each possible curve, and if
// a intersection is found, the point will
// be added in the linked list
CircularLinkedListNode <UV> newNode = null;
// get the closest point
UV newPoint = null, previousPoint = null;
double minDistance = double.MaxValue;
foreach (Curve curve in posibleCurves)
{
SetComparisonResult intersection = curve.Intersect(line, out IntersectionResultArray resultArray);
if (intersection == SetComparisonResult.Overlap)
{
IntersectionResultArrayIterator iterator = resultArray.ForwardIterator();
iterator.Reset();
while (iterator.MoveNext())
{
IntersectionResult result = iterator.Current as IntersectionResult;
UV point = VectorManipulator.ProjectInPlaneXY(result.XYZPoint);
double distance = point.DistanceTo(notch);
if (distance < minDistance)
{
minDistance = distance;
newPoint = point;
previousPoint = VectorManipulator.ProjectInPlaneXY(curve.GetEndPoint(0));
}
}
}
}
// insert the new point in the list
CircularLinkedListNode <UV> node = FindPoint(points, previousPoint);
newNode = points.AddAfter(node, newPoint);
if (newNode.Next.Value.IsAlmostEqualTo(newNode.Value))
{
points.Remove(newNode.Next.Value);
}
else if (newNode.Previous.Value.IsAlmostEqualTo(newNode.Value))
{
points.Remove(newNode.Previous.Value);
}
return(newNode);
}
/// <summary>
/// Creates a Curve Array given the Boundary Segments.
/// </summary>
/// <param name="offset">
/// A positive value that represents the offset that the curve array will have in a direction.
/// If this value is 0, the user may not pass an offsetVector.
/// <returns>
/// Returns the offseted Curve Array.
/// </returns>
public CurveArray CreateOffsetedCurveArray(double offset, List <Line> unchangedLines)
{
if (offset < 0 || curveArray.Size < 3)
{
return(null);
}
Normalize();
CircularLinkedList <UV> points = GetPoints();
CircularLinkedList <UV> offsetedPoints = OffsetPolygon(points, offset, unchangedLines);
CircularLinkedList <UV> linkedOffsetedPoints = new CircularLinkedList <UV>(offsetedPoints);
CurveArray offsetedCurveArray = CreateCurveArrayFromPoints(linkedOffsetedPoints);
return(offsetedCurveArray);
}
/// <summary>
/// Searches for a point in the LinkedList
/// </summary>
/// <returns>
/// Returns the node.
/// </returns>
private static CircularLinkedListNode <UV> FindPoint(CircularLinkedList <UV> points, UV key)
{
CircularLinkedListNode <UV> node = points.Head;
do
{
UV point = node.Value;
if (point.IsAlmostEqualTo(key, 0.01))
{
return(node);
}
node = node.Next;
} while (node != points.Head);
return(null);
}
private static CircularLinkedListNode <UV> AddPointBetween(CircularLinkedList <UV> points, UV p0, UV p1, UV newPoint)
{
CircularLinkedListNode <UV> p0Node = FindPoint(points, p0);
CircularLinkedListNode <UV> p1Node = FindPoint(points, p1);
if (p0Node.Next.Equals(p1Node))
{
return(points.AddAfter(p0Node, newPoint));
}
if (p1Node.Next.Equals(p0Node))
{
return(points.AddAfter(p1Node, newPoint));
}
throw new ArgumentException("The points are not sequential.");
}
/// <summary>
/// Create a CurveArray given its vertices.
/// </summary>
public CurveArray CreateCurveArrayFromPoints(CircularLinkedList <UV> points)
{
CurveArray curveArray = new CurveArray();
CircularLinkedListNode <UV> node = points.Head;
Line line;
do
{
// for the cases that the 2 lines are colinear
if (!node.Value.IsAlmostEqualTo(node.Next.Value))
{
line = Line.CreateBound(VectorManipulator.TransformUVinXYZ(node.Value), VectorManipulator.TransformUVinXYZ(node.Next.Value));
curveArray.Append(line);
}
node = node.Next;
} while (node != points.Head);
return(curveArray);
}
/// <summary>
/// Decompose a non convex perimiter into its convex components. There is no
/// garantee that it will be the mininum number of convex polygons. All the
/// angles of the perimeter must be a multiple of PI/2 radians.
/// </summary>
/// <returns>
/// Returns a List of CurveArrays that represents the convex compenents.
/// </returns>
public List <CurveArray> GetConvexPerimeters(XYZ preferredOrientation, List <Line> cutLines)
{
CircularLinkedList <UV> points = GetPoints();
List <UV> notches = GetNotches(points);
List <CurveArray> perimeters = new List <CurveArray>();
if (notches.Count == 0)
{
perimeters.Add(curveArray);
return(perimeters);
}
List <CurveArray> result = EliminateNotch(notches[0], curveArray, points, preferredOrientation, out Line line);
cutLines.Add(line);
foreach (CurveArray array in result)
{
Polygon p = new Polygon(array);
perimeters.AddRange(p.GetConvexPerimeters(preferredOrientation, cutLines));
}
perimeters.Sort(new SortingDescendingArea());
return(perimeters);
}
/// <summary>
/// Offset a polygon in all directions, except the edge of this polygon that is equal to the unchangedLine parameter.
/// </summary>
/// <param name="vertices">A list of 2D coordinates that represents the vertices of the polygon. The list must be ordered counter-clockwise</param>
/// <param name="offset">The offset value.</param>
/// <param name="unchangedLine">If an edge of the polygon is collinear to this line, that edge will remain unchanged.</param>
/// <returns>Returns a List of 2D coordinates that represents the offseted polygon.</returns>
private static CircularLinkedList <UV> OffsetPolygon(CircularLinkedList <UV> vertices, double offset, List <Line> unchangedLines)
{
if (offset == 0)
{
return(vertices);
}
CircularLinkedList <UV> adjusted_points = new CircularLinkedList <UV>();
CircularLinkedListNode <UV> node = vertices.Head;
do
{
//find the points before and after our target point.
UV vertexI = node.Previous.Value;
UV vertexJ = node.Value;
UV vertexK = node.Next.Value;
//the next step is to push out each point based on the position of its surrounding points and then
//figure out the intersections of the pushed out points
UV v1 = vertexJ - vertexI;
UV v2 = vertexK - vertexJ;
// verifies if one of the segments ij, ji, jk or kj is the unchangedLine
if (unchangedLines != null)
{
foreach (Line l in unchangedLines)
{
UV p0 = VectorManipulator.ProjectInPlaneXY(l.GetEndPoint(0));
UV p1 = VectorManipulator.ProjectInPlaneXY(l.GetEndPoint(1));
if ((vertexI.IsAlmostEqualTo(p0) && vertexJ.IsAlmostEqualTo(p1)) ||
(vertexJ.IsAlmostEqualTo(p0) && vertexI.IsAlmostEqualTo(p1)))
{
v1 = UV.Zero;
break;
}
if ((vertexJ.IsAlmostEqualTo(p0) && vertexK.IsAlmostEqualTo(p1)) ||
(vertexK.IsAlmostEqualTo(p0) && vertexJ.IsAlmostEqualTo(p1)))
{
v2 = UV.Zero;
break;
}
}
}
v1 = v1.Normalize() * offset;
v2 = v2.Normalize() * offset;
// creates a shifted line that is parallel to the vector v1
UV n1 = new UV(-v1.V, v1.U);
UV pij1 = vertexI + n1;
UV pij2 = vertexJ + n1;
Line line1 = Line.CreateBound(VectorManipulator.TransformUVinXYZ(pij1), VectorManipulator.TransformUVinXYZ(pij2));
line1.MakeUnbound();
// creates a shifted line that is parallel to the vector v2
UV n2 = new UV(-v2.V, v2.U);
UV pjk1 = vertexJ + n2;
UV pjk2 = vertexK + n2;
Line line2 = Line.CreateBound(VectorManipulator.TransformUVinXYZ(pjk1), VectorManipulator.TransformUVinXYZ(pjk2));
line2.MakeUnbound();
//see where the shifted lines 1 and 2 intersect
SetComparisonResult comparisonResult = line1.Intersect(line2, out IntersectionResultArray intersection);
if (comparisonResult == SetComparisonResult.Overlap)
{
IntersectionResult result = intersection.get_Item(0);
UV intersection_point = VectorManipulator.ProjectInPlaneXY(result.XYZPoint);
//add the intersection as our adjusted vert point
adjusted_points.AddLast(new UV(intersection_point.U, intersection_point.V));
}
node = node.Next;
} while (node != vertices.Head);
return(adjusted_points);
}
