object Quadrangulation

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Type Members

  1. case class BaryCenter(face: Polygon) extends Vertex with Product with Serializable
  2. case class QuadEdge(face: Polygon, index: Int, positivelyOriented: Boolean) extends OrientedEdge with Product with Serializable
  3. case class QuadFace(face: Polygon, flipFace: Polygon, indexOfEdge: Int, indexOfFlip: Int) extends Polygon with Product with Serializable

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  1. final def !=(arg0: Any): Boolean
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  2. final def ##(): Int
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  3. final def ==(arg0: Any): Boolean
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  4. def apply(twoComplex: TwoComplex): Quadrangulation
  5. final def asInstanceOf[T0]: T0
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  6. def clone(): AnyRef
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  7. final def eq(arg0: AnyRef): Boolean
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  8. def equals(arg0: AnyRef): Boolean
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  9. def finalize(): Unit
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  10. final def getClass(): Class[_ <: AnyRef]
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  11. def hashCode(): Int
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  12. final def isInstanceOf[T0]: Boolean
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  13. def isQuadrangulation(twoComplex: TwoComplex): Boolean
  14. def mod(m: Int, n: Int): Int
  15. final def ne(arg0: AnyRef): Boolean
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  16. final def notify(): Unit
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  17. final def notifyAll(): Unit
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  18. def quadrangulate(twoComplex: TwoComplex): (TwoComplex, ((EdgePath) => EdgePath, (EdgePath) => EdgePath))

    Gives the quadrangulation of a twocomplex along maps from edgepaths from the twocomplex to paths in the quadragulation.

    Gives the quadrangulation of a twocomplex along maps from edgepaths from the twocomplex to paths in the quadragulation. The forWard EdgePath method turns every edge in the original twoComplex into an EdgePath of length two in the corresponding face in the quadrangulation. The backWard EdgePath method only works if the EdgePath in the quadrangulation starts and ends at pre existing vertices, or is a loop on a barycenter of length more than one. In the first case it returns a fixed end point homotopic path in the original TwoComplex. In the second case if returns a freely homotopic path in the original TwoComplex. In the first case the backWard EdgePath map considers edges in the quadragulation in Pairs. Because the pre existing vertices and the barycenters form a bipartite set in the quadrangulation, a consequtive pair of edges in the quadragulation (say u and v), starting from a (which is a pre existing vertex), passing through b (which is a barycenter) and ending at c (which is a pre existing vertex) is homotopic to a sequence of edges in the face corresponding to b. So we can take such a path. In the second case because the pre existing vertices and the barycenters form a bipartite set in the quadrangulation, shifting the basepoint makes the loop start and end at a pre existing vertex.

  19. final def synchronized[T0](arg0: => T0): T0
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  20. def toString(): String
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  21. final def wait(): Unit
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  22. final def wait(arg0: Long, arg1: Int): Unit
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  23. final def wait(arg0: Long): Unit
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