p

superficial

package superficial

Ordering
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Visibility
  1. Public
  2. Protected

Type Members

  1. case class BoundaryEdge(pb: PantsBoundary, top: Boolean, positivelyOriented: Boolean) extends OrientedEdge with Product with Serializable
  2. case class BoundaryVertex(pb: PantsBoundary, first: Boolean) extends Vertex with Product with Serializable
  3. case class ClosedSurface(n: Int) extends StandardSurface with Product with Serializable
  4. trait CollectionOfHomotopyClasses extends AnyRef
  5. case class Curve(left: PantsBoundary, right: PantsBoundary) extends Product with Serializable
  6. case class CurveEdge(curve: Curve, top: Boolean, positivelyOriented: Boolean) extends OrientedEdge with Product with Serializable
  7. case class CurveVertex(curve: Curve, first: Boolean) extends Vertex with Product with Serializable
  8. trait Edge extends AnyRef

    An oriented edge in a two-complex

  9. class EdgePair extends AnyRef
  10. sealed trait EdgePath extends AnyRef
  11. trait EquivalenceClass extends AnyRef
  12. case class FormalSum[A](coeffs: Map[A, Int]) extends Product with Serializable

    A formal sum of elements of A with coefficients integers.

  13. sealed trait Generator extends AnyRef

    Contribution of Ankit-Jaiswal and Soumyo Biswas, independent of the rest of the code.

    Contribution of Ankit-Jaiswal and Soumyo Biswas, independent of the rest of the code.

    This program basically abstracts : (i) OrientableSurface (i.e. a connected compact 2-manifold) parametrized by g and r. where, g is its genus and r is the number of components in its boundary. (ii) Surfaces' fundamental group Generators along with the 'relation' over them, (iii) Closed curves/Words (on the surfaces) in terms of Generators, And, verifies whether a given word is homotopic to a simple closed curve.

    NOTE: This program works for surfaces which are not sphere(where g = 0 as well as r = 0).

    Reference:: "Simple Closed Curves on Surfaces" by D.R.J. Chillingworth

  14. trait Hexagon extends Polygon
  15. trait HomotopyClassesOfPaths extends AnyRef
  16. trait Intersection extends AnyRef
  17. trait NonPosQuad extends TwoComplex
  18. case class NormalArc(initial: Index, terminal: Index, face: Polygon) extends Product with Serializable

    A normal arc in a face

    A normal arc in a face

    initial

    the edge containing the initial point

    terminal

    the edge containing the final point

    face

    the face containing the arc

  19. case class NormalPath(edges: Vector[NormalArc]) extends Product with Serializable
  20. case class OrientableSurface(g: Int, r: Int) extends Product with Serializable

    Contribution of Ankit-Jaiswal and Soumyo Biswas, independent of the rest of the code.

    Contribution of Ankit-Jaiswal and Soumyo Biswas, independent of the rest of the code.

    'a' and 'b' are the two Generators of a OrientableSurface, parametrized by the genus number. And 's' is the generator corressponding to surface's boundary, parametrized by r, the number of components. Because their inverse can also generate the fundamental group; therefore they are also being considered as Generators.

  21. trait OrientedEdge extends Edge
  22. case class PantsBoundary(pants: Index, direction: Z3) extends Product with Serializable

    index for boundary of pants, may be in the curve system or the boundary of the surface

    index for boundary of pants, may be in the curve system or the boundary of the surface

    pants

    the index of the pair of pants

    direction

    the prong of the pair of pants

  23. case class PantsHexagon(pants: Index, top: Boolean, cs: Set[Curve]) extends Hexagon with Product with Serializable
  24. case class PantsSeam(pants: Index, initial: Vertex, terminal: Vertex, positivelyOriented: Boolean = true) extends OrientedEdge with Product with Serializable
  25. case class PantsSurface(numPants: Index, cs: Set[Curve]) extends PureTwoComplex with Product with Serializable
  26. trait Polygon extends TwoComplex

    Abstract polygon, with given edges and vertices, i.e.

    Abstract polygon, with given edges and vertices, i.e. a two-complex with a single face.

  27. case class PureComplex(polys: Set[Polygon]) extends PureTwoComplex with Product with Serializable
  28. trait PureTwoComplex extends TwoComplex

    A two-complex with all vertices and edges contained in faces, hence determined by its faces.

  29. class QuadPlot extends AnyRef
  30. trait Quadrangulation extends TwoComplex
  31. trait Quadrilateral extends Polygon

    a quadrilateral is a polygon with four edges.

  32. case class QuotientEdge(edges: Set[Edge]) extends Edge with Product with Serializable

    An edge obtained by identifications

  33. case class QuotientVertex(vertices: Set[Vertex]) extends Vertex with Product with Serializable

    A vertex obtained by identifications

  34. case class SkewCurve(left: PantsBoundary, right: PantsBoundary, twist: Double, length: Double) extends Product with Serializable
  35. case class SkewCurveEdge(curve: SkewCurve, position: Double, positivelyOriented: Boolean) extends OrientedEdge with Product with Serializable
  36. case class SkewCurveVertex(curve: SkewCurve, position: Double) extends Vertex with Product with Serializable
  37. case class SkewPantsHexagon(pants: Index, top: Boolean, cs: Set[SkewCurve]) extends Polygon with Product with Serializable
  38. case class SkewPantsSurface(numPants: Index, cs: Set[SkewCurve]) extends PureTwoComplex with Product with Serializable
  39. class StandardSurface extends TwoComplex
  40. trait TwoComplex extends AnyRef

    A polyheadral two complex, with faces polygons, a collection of edges and

  41. class Vertex extends AnyRef

    A vertex in a two-complex

  42. case class Z3(n: Int) extends Product with Serializable

Value Members

  1. object CheckQuadrangulation
  2. object Clockwise
  3. object ClosedSurface extends Serializable
  4. object CollectionOfHomotopyClasses
  5. object Edge
  6. object EdgePair
  7. object EdgePath
  8. object EquivalenceClass
  9. object Examples
  10. object FormalSum extends Serializable
  11. object Generator
  12. object Hexagon
  13. object HomotopyClassesOfPaths
  14. object Intersection
  15. object NonPosQuad
  16. object NormalArc extends Serializable
  17. object NormalPath extends Serializable
  18. object PantsSurface extends Serializable
  19. object Polygon
  20. object Quadrangulation
  21. object SkewCurve extends Serializable
  22. object SkewPantsSurface extends Serializable
  23. object SphereComplex
  24. object StandardSurface
  25. object SvgPlot
  26. object Triangles
  27. object TwoComplex
  28. object Vertex
  29. object Z3 extends Serializable

Ungrouped