Package org.tinfour.common

Class Thresholds

  • public class Thresholds
extends Object
    Provides a standard calculation of threshold values appropriate for use in an incremental TIN implementation based on nominal point spacing. With the exception of vertex tolerance, all thresholds are computed using a small multiplier times the Unit of Least Precision (ULP) computed from the nominal point spacing. The vertex tolerance is a fixed fraction of the nominal point spacing.

    • Constructor Summary

      Constructors 
      Constructor Description
      Thresholds()
      Constructs thresholds for a nominal point spacing of 1.
      Thresholds​(double nominalPointSpacing)
      Constructs threshold values for the specified nominalPointSpacing.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double getCircumcircleDeterminantThreshold()
      Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for for computing a determinant to be used in determining a set of circumcircle center coordinates and radius.
      double getDelaunayThreshold()
      Gets the computed value for evaluating whether a triangle pair is within sufficient tolerance when testing to see if they approximately meet the Delaunay criterion using the in-circle calculation.
      double getHalfPlaneThreshold()
      Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for determining on which side of a point a plane lies (the "half-plane calculation").
      double getInCircleThreshold()
      Gets the threshold value indicating when an extended-precision calculation must be used for the in-circle determination.
      double getNominalPointSpacing()
      Gets the nominal point spacing value specified in the constructor.
      double getPrecisionThreshold()
      Get a threshold value giving guidelines for the smallest absolute value result from a geometric calculations that can be accepted without concern for an excessive loss of precision.
      double getVertexTolerance()
      Gets a threshold value indicating the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.
      double getVertexTolerance2()
      Gets a threshold value indicating the square of the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.

    • Field Detail

      • PRECISION_THRESHOLD_FACTOR

        public static final double PRECISION_THRESHOLD_FACTOR
        Factor for computing precision threshold.
        See Also:
        Constant Field Values

      • HALF_PLANE_THRESHOLD_FACTOR

        public static final double HALF_PLANE_THRESHOLD_FACTOR
        Factor for computing the half-plane threshold.
        See Also:
        Constant Field Values

      • DELAUNAY_THRESHOLD_FACTOR

        public static final double DELAUNAY_THRESHOLD_FACTOR
        Factor for computing the Delaunay threshold.
        See Also:
        Constant Field Values

      • IN_CIRCLE_THRESHOLD_FACTOR

        public static final double IN_CIRCLE_THRESHOLD_FACTOR
        Factor for computing the in-circle threshold.
        See Also:
        Constant Field Values

      • VERTEX_TOLERANCE_FACTOR_DEFAULT

        public static final double VERTEX_TOLERANCE_FACTOR_DEFAULT
        Factor for computing the vertex tolerance.
        See Also:
        Constant Field Values

    • Constructor Detail

      • Thresholds

        public Thresholds()
        Constructs thresholds for a nominal point spacing of 1.

      • Thresholds

        public Thresholds​(double nominalPointSpacing)
        Constructs threshold values for the specified nominalPointSpacing. In general, the nominal point spacing is a rough estimate of the mean distance between neighboring points (or vertices). It is used for estimating threshold values for logic used by the IncrementalTin and related classes. A perfect value is not necessary. An estimate within a couple orders of magnitude of the actual value is sufficient.
        Parameters:
        nominalPointSpacing - a positive, non-zero value

    • Method Detail

      • getInCircleThreshold

        public double getInCircleThreshold()
        Gets the threshold value indicating when an extended-precision calculation must be used for the in-circle determination.
        Returns:
        a positive value scaled according to the nominal point spacing of the TIN.

      • getVertexTolerance

        public double getVertexTolerance()
        Gets a threshold value indicating the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.
        Returns:
        a distance in the system of units consistent with the TIN.

      • getVertexTolerance2

        public double getVertexTolerance2()
        Gets a threshold value indicating the square of the distance at which a pair of (x,y) coordinates will be treated as effectively a match for a vertex.
        Returns:
        a distance squared in the system of units consistent with the TIN.

      • getPrecisionThreshold

        public double getPrecisionThreshold()
        Get a threshold value giving guidelines for the smallest absolute value result from a geometric calculations that can be accepted without concern for an excessive loss of precision. This value is based on general assumptions about the what constitutes a significant distance given the nominal point spacing of the vertices in the TIN.
        Returns:
        a small, positive value.

      • getNominalPointSpacing

        public double getNominalPointSpacing()
        Gets the nominal point spacing value specified in the constructor. In general, this value is a rough estimate of the mean distance between neighboring points (or vertices).
        Returns:
        a positive, non-zero value.

      • getDelaunayThreshold

        public double getDelaunayThreshold()
        Gets the computed value for evaluating whether a triangle pair is within sufficient tolerance when testing to see if they approximately meet the Delaunay criterion using the in-circle calculation. A positive (non-zero) in-circle value indicates that the pair violates the criterion, but for case where floating-point limitations may result in conflicts, a very small positive value may be acceptable for approximation purposes.

        This value is primarily used in test procedures that evaluate the correctness of a TIN constructed by the IncrementalTin class.

        Returns:
        A positive value much smaller than the nominal point spacing.

      • getHalfPlaneThreshold

        public double getHalfPlaneThreshold()
        Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for determining on which side of a point a plane lies (the "half-plane calculation"). If the absolute value of the result is smaller than this threshold, extended-precision arithmetic is advised.
        Returns:
        a positive, non-zero value much smaller than the nominal point spacing.

      • getCircumcircleDeterminantThreshold

        public double getCircumcircleDeterminantThreshold()
        Gets a threshold value giving guidelines for the smallest absolute value result that can be trusted in geometric calculations for for computing a determinant to be used in determining a set of circumcircle center coordinates and radius. If the absolute value of the determinant result is smaller than this threshold, extended-precision arithmetic is advised.
        Returns:
        a positive, non-zero value significantly smaller than the nominal point spacing.