Class S2FractalBuilder

java.lang.Object
com.google.common.geometry.S2FractalBuilder
@GwtCompatible public class S2FractalBuilder extends Object
A simple class that generates "Koch snowflake" fractals (see Wikipedia for an introduction). There is an option to control the fractal dimension (between 1.0 and 2.0); values between 1.02 and 1.50 are reasonable simulations of various coastlines. The default dimension (about 1.26) corresponds to the standard Koch snowflake. (The west coast of Britain has a fractal dimension of approximately 1.25)

The fractal is obtained by starting with an equilateral triangle and recursively subdividing each edge into four segments of equal length. Therefore the shape at level 'n' consists of 3 * (4^n) edges. Multi-level fractals are also supported: if you set minLevel() to a non-negative value, then the recursive subdivision has an equal probability of stopping at any of the levels between the given min and max (inclusive). This yields a fractal where the perimeter of the original triangle is approximately equally divided between fractals at the various possible levels. If there are k distinct levels {min, ..., max}, the expected number of edges at each level 'i' is approximately 3 * (4 ^ i) / k.

  • Constructor Summary

    Constructors
    Constructor
    Description
    S2FractalBuilder(Random rand)
    You must call setMaxLevel() or setLevelForApproxMaxMedges() before calling makeLoop().

  • Method Summary

    Modifier and Type
    Method
    Description
    S2Loop
    makeLoop(com.google.common.geometry.Matrix3x3 frame, S1Angle nominalRadius)
    Returns a fractal loop centered around the a-axis of the given coordinate frame, with the first vertex in the direction of the positive x-axis, and the given nominal radius.
    List<S2Point>
    makeVertices(com.google.common.geometry.Matrix3x3 frame, S1Angle nominalRadius)
    As makeLoop(Matrix3x3, S1Angle) except it returns the vertices instead of loop.
    double
    maxRadiusFactor()
    Returns the ratio (Rmax / R), where 'R' is the radius passed to makeLoop() and 'Rmax' is the maximum distance from the fractal boundary to its center.
    double
    minRadiusFactor()
    Returns a lower bound on the ratio (Rmin / R), where 'R' is the radius passed to makeLoop() and 'Rmin' is the minimum distance from the fractal boundary to its center.
    void
    setFractalDimension(double dimension)
    Sets the fractal dimension.
    void
    setLevelForApproxMaxEdges(int maxEdges)
     
    void
    setLevelForApproxMinEdges(int minEdges)
    The following two functions set the min and/or max level to produce approximately the given number of edges.
    void
    setMaxLevel(int maxLevel)
    Sets the maximum subdivision level for the fractal (see above).
    void
    setMinLevel(int minLevelArg)
    Sets the minimum subdivision level for the fractal (see above).

    Methods inherited from class Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • S2FractalBuilder

      public S2FractalBuilder(Random rand)
      You must call setMaxLevel() or setLevelForApproxMaxMedges() before calling makeLoop().

  • Method Details

    • setMaxLevel

      public void setMaxLevel(int maxLevel)
      Sets the maximum subdivision level for the fractal (see above).

    • setMinLevel

      public void setMinLevel(int minLevelArg)
      Sets the minimum subdivision level for the fractal (see above). The default value of -1 causes the min and max levels to be the same. A minLevel of 0 should be avoided since this creates a significant chance that none of the three original edges will be subdivided at all.

    • setFractalDimension

      public void setFractalDimension(double dimension)
      Sets the fractal dimension. The default value of approximately 1.26 corresponds to the standard Koch curve. The value must lie in the range [1.0, 2.0).

    • setLevelForApproxMinEdges

      public void setLevelForApproxMinEdges(int minEdges)
      The following two functions set the min and/or max level to produce approximately the given number of edges. (The values are rounded to a nearby value of 3 * (4 ^ n).)

    • setLevelForApproxMaxEdges

      public void setLevelForApproxMaxEdges(int maxEdges)

    • minRadiusFactor

      public double minRadiusFactor()
      Returns a lower bound on the ratio (Rmin / R), where 'R' is the radius passed to makeLoop() and 'Rmin' is the minimum distance from the fractal boundary to its center. This can be used to inscribe another geometric figure within the fractal without intersection.

    • maxRadiusFactor

      public double maxRadiusFactor()
      Returns the ratio (Rmax / R), where 'R' is the radius passed to makeLoop() and 'Rmax' is the maximum distance from the fractal boundary to its center. This can be used to inscribe the fractal within some other geometric figure without intersection.

    • makeLoop

      public S2Loop makeLoop(com.google.common.geometry.Matrix3x3 frame, S1Angle nominalRadius)
      Returns a fractal loop centered around the a-axis of the given coordinate frame, with the first vertex in the direction of the positive x-axis, and the given nominal radius.

    • makeVertices

      public List<S2Point> makeVertices(com.google.common.geometry.Matrix3x3 frame, S1Angle nominalRadius)
      As makeLoop(Matrix3x3, S1Angle) except it returns the vertices instead of loop.