Class ArcsSet

java.lang.Object
org.apache.commons.math3.geometry.partitioning.AbstractRegion<Sphere1D,Sphere1D>
org.apache.commons.math3.geometry.spherical.oned.ArcsSet
All Implemented Interfaces:
Iterable<double[]>, Region<Sphere1D>
public class ArcsSet extends AbstractRegion<Sphere1D,Sphere1D> implements Iterable<double[]>
This class represents a region of a circle: a set of arcs.

Note that due to the wrapping around \(2 \pi\), barycenter is ill-defined here. It was defined only in order to fulfill the requirements of the Region interface, but its use is discouraged.

Since:
3.3

  • Constructor Details

    • ArcsSet

      public ArcsSet(double tolerance)
      Build an arcs set representing the whole circle.
      Parameters:
      tolerance - tolerance below which close sub-arcs are merged together

    • ArcsSet

      public ArcsSet(double lower, double upper, double tolerance) throws NumberIsTooLargeException
      Build an arcs set corresponding to a single arc.

      If either lower is equals to upper or the interval exceeds \( 2 \pi \), the arc is considered to be the full circle and its initial defining boundaries will be forgotten. lower is not allowed to be greater than upper (an exception is thrown in this case).

      Parameters:
      lower - lower bound of the arc
      upper - upper bound of the arc
      tolerance - tolerance below which close sub-arcs are merged together
      Throws:
      NumberIsTooLargeException - if lower is greater than upper

    • ArcsSet

      public ArcsSet(BSPTree<Sphere1D> tree, double tolerance) throws ArcsSet.InconsistentStateAt2PiWrapping
      Build an arcs set from an inside/outside BSP tree.

      The leaf nodes of the BSP tree must have a Boolean attribute representing the inside status of the corresponding cell (true for inside cells, false for outside cells). In order to avoid building too many small objects, it is recommended to use the predefined constants Boolean.TRUE and Boolean.FALSE

      Parameters:
      tree - inside/outside BSP tree representing the arcs set
      tolerance - tolerance below which close sub-arcs are merged together
      Throws:
      ArcsSet.InconsistentStateAt2PiWrapping - if the tree leaf nodes are not consistent across the \( 0, 2 \pi \) crossing

    • ArcsSet

      public ArcsSet(Collection<SubHyperplane<Sphere1D>> boundary, double tolerance) throws ArcsSet.InconsistentStateAt2PiWrapping
      Build an arcs set from a Boundary REPresentation (B-rep).

      The boundary is provided as a collection of sub-hyperplanes. Each sub-hyperplane has the interior part of the region on its minus side and the exterior on its plus side.

      The boundary elements can be in any order, and can form several non-connected sets (like for example polygons with holes or a set of disjoints polyhedrons considered as a whole). In fact, the elements do not even need to be connected together (their topological connections are not used here). However, if the boundary does not really separate an inside open from an outside open (open having here its topological meaning), then subsequent calls to the checkPoint method will not be meaningful anymore.

      If the boundary is empty, the region will represent the whole space.

      Parameters:
      boundary - collection of boundary elements
      tolerance - tolerance below which close sub-arcs are merged together
      Throws:
      ArcsSet.InconsistentStateAt2PiWrapping - if the tree leaf nodes are not consistent across the \( 0, 2 \pi \) crossing

  • Method Details

    • buildTree

      private static BSPTree<Sphere1D> buildTree(double lower, double upper, double tolerance) throws NumberIsTooLargeException
      Build an inside/outside tree representing a single arc.
      Parameters:
      lower - lower angular bound of the arc
      upper - upper angular bound of the arc
      tolerance - tolerance below which close sub-arcs are merged together
      Returns:
      the built tree
      Throws:
      NumberIsTooLargeException - if lower is greater than upper

    • check2PiConsistency

      private void check2PiConsistency() throws ArcsSet.InconsistentStateAt2PiWrapping
      Check consistency.
      Throws:
      ArcsSet.InconsistentStateAt2PiWrapping - if the tree leaf nodes are not consistent across the \( 0, 2 \pi \) crossing

    • getFirstLeaf

      private BSPTree<Sphere1D> getFirstLeaf(BSPTree<Sphere1D> root)
      Get the first leaf node of a tree.
      Parameters:
      root - tree root
      Returns:
      first leaf node (i.e. node corresponding to the region just after 0.0 radians)

    • getLastLeaf

      private BSPTree<Sphere1D> getLastLeaf(BSPTree<Sphere1D> root)
      Get the last leaf node of a tree.
      Parameters:
      root - tree root
      Returns:
      last leaf node (i.e. node corresponding to the region just before \( 2 \pi \) radians)

    • getFirstArcStart

      private BSPTree<Sphere1D> getFirstArcStart()
      Get the node corresponding to the first arc start.
      Returns:
      smallest internal node (i.e. first after 0.0 radians, in trigonometric direction), or null if there are no internal nodes (i.e. the set is either empty or covers the full circle)

    • isArcStart

      private boolean isArcStart(BSPTree<Sphere1D> node)
      Check if an internal node corresponds to the start angle of an arc.
      Parameters:
      node - internal node to check
      Returns:
      true if the node corresponds to the start angle of an arc

    • isArcEnd

      private boolean isArcEnd(BSPTree<Sphere1D> node)
      Check if an internal node corresponds to the end angle of an arc.
      Parameters:
      node - internal node to check
      Returns:
      true if the node corresponds to the end angle of an arc

    • nextInternalNode

      private BSPTree<Sphere1D> nextInternalNode(BSPTree<Sphere1D> node)
      Get the next internal node.
      Parameters:
      node - current internal node
      Returns:
      next internal node in trigonometric order, or null if this is the last internal node

    • previousInternalNode

      private BSPTree<Sphere1D> previousInternalNode(BSPTree<Sphere1D> node)
      Get the previous internal node.
      Parameters:
      node - current internal node
      Returns:
      previous internal node in trigonometric order, or null if this is the first internal node

    • leafBefore

      private BSPTree<Sphere1D> leafBefore(BSPTree<Sphere1D> node)
      Find the leaf node just before an internal node.
      Parameters:
      node - internal node at which the sub-tree starts
      Returns:
      leaf node just before the internal node

    • leafAfter

      private BSPTree<Sphere1D> leafAfter(BSPTree<Sphere1D> node)
      Find the leaf node just after an internal node.
      Parameters:
      node - internal node at which the sub-tree starts
      Returns:
      leaf node just after the internal node

    • isBeforeParent

      private boolean isBeforeParent(BSPTree<Sphere1D> node)
      Check if a node is the child before its parent in trigonometric order.
      Parameters:
      node - child node considered
      Returns:
      true is the node has a parent end is before it in trigonometric order

    • isAfterParent

      private boolean isAfterParent(BSPTree<Sphere1D> node)
      Check if a node is the child after its parent in trigonometric order.
      Parameters:
      node - child node considered
      Returns:
      true is the node has a parent end is after it in trigonometric order

    • childBefore

      private BSPTree<Sphere1D> childBefore(BSPTree<Sphere1D> node)
      Find the child node just before an internal node.
      Parameters:
      node - internal node at which the sub-tree starts
      Returns:
      child node just before the internal node

    • childAfter

      private BSPTree<Sphere1D> childAfter(BSPTree<Sphere1D> node)
      Find the child node just after an internal node.
      Parameters:
      node - internal node at which the sub-tree starts
      Returns:
      child node just after the internal node

    • isDirect

      private boolean isDirect(BSPTree<Sphere1D> node)
      Check if an internal node has a direct limit angle.
      Parameters:
      node - internal node to check
      Returns:
      true if the limit angle is direct

    • getAngle

      private double getAngle(BSPTree<Sphere1D> node)
      Get the limit angle of an internal node.
      Parameters:
      node - internal node to check
      Returns:
      limit angle

    • buildNew

      public ArcsSet buildNew(BSPTree<Sphere1D> tree)
      Build a region using the instance as a prototype.

      This method allow to create new instances without knowing exactly the type of the region. It is an application of the prototype design pattern.

      The leaf nodes of the BSP tree must have a Boolean attribute representing the inside status of the corresponding cell (true for inside cells, false for outside cells). In order to avoid building too many small objects, it is recommended to use the predefined constants Boolean.TRUE and Boolean.FALSE. The tree also must have either null internal nodes or internal nodes representing the boundary as specified in the getTree method).

      Specified by:
      buildNew in interface Region<Sphere1D>
      Specified by:
      buildNew in class AbstractRegion<Sphere1D,Sphere1D>
      Parameters:
      tree - inside/outside BSP tree representing the new region
      Returns:
      the built region

    • computeGeometricalProperties

      protected void computeGeometricalProperties()
      Compute some geometrical properties.

      The properties to compute are the barycenter and the size.

      Specified by:
      computeGeometricalProperties in class AbstractRegion<Sphere1D,Sphere1D>

    • projectToBoundary

      public BoundaryProjection<Sphere1D> projectToBoundary(Point<Sphere1D> point)
      Project a point on the boundary of the region.
      Specified by:
      projectToBoundary in interface Region<Sphere1D>
      Overrides:
      projectToBoundary in class AbstractRegion<Sphere1D,Sphere1D>
      Parameters:
      point - point to check
      Returns:
      projection of the point on the boundary
      Since:
      3.3

    • asList

      public List<Arc> asList()
      Build an ordered list of arcs representing the instance.

      This method builds this arcs set as an ordered list of Arc elements. An empty tree will build an empty list while a tree representing the whole circle will build a one element list with bounds set to \( 0 and 2 \pi \).

      Returns:
      a new ordered list containing Arc elements

    • iterator

      public Iterator<double[]> iterator()

      The iterator returns the limit angles pairs of sub-arcs in trigonometric order.

      The iterator does not support the optional remove operation.

      Specified by:
      iterator in interface Iterable<double[]>

    • side

      @Deprecated public Side side(Arc arc)
      Deprecated.
      as of 3.6, replaced with split(Arc).ArcsSet.Split.getSide()
      Compute the relative position of the instance with respect to an arc.

      The Side.MINUS side of the arc is the one covered by the arc.

      Parameters:
      arc - arc to check instance against
      Returns:
      one of Side.PLUS, Side.MINUS, Side.BOTH or Side.HYPER

    • split

      public ArcsSet.Split split(Arc arc)
      Split the instance in two parts by an arc.
      Parameters:
      arc - splitting arc
      Returns:
      an object containing both the part of the instance on the plus side of the arc and the part of the instance on the minus side of the arc

    • addArcLimit

      private void addArcLimit(BSPTree<Sphere1D> tree, double alpha, boolean isStart)
      Add an arc limit to a BSP tree under construction.
      Parameters:
      tree - BSP tree under construction
      alpha - arc limit
      isStart - if true, the limit is the start of an arc

    • createSplitPart

      private ArcsSet createSplitPart(List<Double> limits)
      Create a split part.

      As per construction, the list of limit angles is known to have an even number of entries, with start angles at even indices and end angles at odd indices.

      Parameters:
      limits - limit angles of the split part
      Returns:
      split part (may be null)