Package geomss.geom.nurbs

Class KnotVector

  • All Implemented Interfaces:
    java.io.Serializable, java.lang.Cloneable, javolution.lang.Immutable, javolution.lang.ValueType, javolution.xml.XMLSerializable
    public class KnotVector
extends java.lang.Object
implements java.lang.Cloneable, javolution.xml.XMLSerializable, javolution.lang.ValueType
    An immutable collection of knot values that are associated with a NURBS curve or surface.

    Modified by: Joseph A. Huwaldt

    Version:
    February 17, 2025
    Author:
    Samuel Gerber, Date: May 14, 2009, Version 1.0.
    See Also:
    Serialized Form

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double[][] basisFunctionDerivatives​(int span, double s, int grade)
      Calculates all the derivatives of all the unweighted basis functions from 0 up to the given grade, d^{grade}Nik(s)/d^{grade}s.
      double[] basisFunctions​(double s)
      Returns the basis function values for the given parameter value (Nik(s)).
      double[] basisFunctions​(int span, double s)
      Returns the unweighted basis function values for the given parameter value (Nik(s)), when the span that the parameter value lies in is already known.
      static KnotVector bezierKnotVector​(int degree)
      Return a knot vector that can be used to create a Bezier curve segment of the specified degree using the BasicNurbsCurve class.
      java.lang.Object clone()
      Returns a copy of this KnotVector instance allocated by the calling thread (possibly on the stack).
      KnotVector copy()
      Returns a copy of this KnotVector instance allocated by the calling thread (possibly on the stack).
      boolean equals​(java.lang.Object obj)
      Compares this ControlPoint against the specified object for strict equality (same values and same units).
      int findMultiplicity​(int index)
      Find the multiplicity of the knot with the specified index in this knot vector.
      int findSpan​(double s)
      Returns the span (position of corresponding knot values in knot vector) a given parameter value belongs to.
      Float64 get​(int i)
      Return the knot at the specified index.
      Float64Vector getAll()
      Return the knot values as an vector of Float64 values.
      int getDegree()
      Return the degree of the KnotVector
      int getNu()
      Return the length of the knot vector (nu).
      int getNumberOfSegments()
      Return the number of segments in the knot vector.
      double getValue​(int i)
      Return the knot value at a specific index as a double.
      int hashCode()
      Returns the hash code for this parameter.
      boolean isOpen()
      Return true if the knot vector is open and false if it is closed.
      boolean isValid()
      Return true if this KnotVector contains valid and finite numerical components.
      int length()
      Return the number of elements in the knot vector.
      static KnotVector newInstance​(int degree, double... knots)
      Create a KnotVector from the given knot values of the desired degree.
      static KnotVector newInstance​(int degree, java.util.List<java.lang.Double> knots)
      Create a KnotVector from the given list of knot values of the desired degree.
      static KnotVector newInstance​(int degree, Float64Vector knots)
      Create a KnotVector from the given knot values of the desired degree.
      static void recycle2DArray​(double[][] arr)
      Recycle any 2D array of doubles that was created by this classes factory methods.
      KnotVector reverse()
      Return a copy of this knot vector with the parameterization reversed.
      java.lang.String toString()
      Returns the string representation of this knot vector that consists of the degree followed by the knot values.
      javolution.text.Text toText()
      Returns the text representation of this knot vector that consists of the degree followed by the knot values.

      • Methods inherited from class java.lang.Object

        getClass, notify, notifyAll, wait, wait, wait

    • Method Detail

      • newInstance

        public static KnotVector newInstance​(int degree,
                                     Float64Vector knots)
        Create a KnotVector from the given knot values of the desired degree.
        Parameters:
        degree - degree of NURBS curve
        knots - knot values. May not be null.
        Returns:
        A KnotVector consisting of the given knots and degree.
        Throws:
        java.lang.IllegalArgumentException - if the knot vector is not valid.

      • newInstance

        public static KnotVector newInstance​(int degree,
                                     java.util.List<java.lang.Double> knots)
                              throws java.lang.IllegalArgumentException
        Create a KnotVector from the given list of knot values of the desired degree.
        Parameters:
        degree - degree of NURBS curve
        knots - A list of knot values. May not be null.
        Returns:
        A KnotVector consisting of the given knots and degree.
        Throws:
        java.lang.IllegalArgumentException - if the knot vector is not valid.

      • newInstance

        public static KnotVector newInstance​(int degree,
                                     double... knots)
                              throws java.lang.IllegalArgumentException
        Create a KnotVector from the given knot values of the desired degree.
        Parameters:
        degree - degree of NURBS curve
        knots - knot values. May not be null.
        Returns:
        A KnotVector consisting of the given knots and degree.
        Throws:
        java.lang.IllegalArgumentException - if the knot vector is not valid.

      • bezierKnotVector

        public static KnotVector bezierKnotVector​(int degree)
        Return a knot vector that can be used to create a Bezier curve segment of the specified degree using the BasicNurbsCurve class.
        Parameters:
        degree - The degree of the knot vector to return.
        Returns:
        A knot vector appropriate for creating a Bezier curve segment.

      • findSpan

        public int findSpan​(double s)
        Returns the span (position of corresponding knot values in knot vector) a given parameter value belongs to.
        Parameters:
        s - parameter value to find the span for
        Returns:
        Position of span.

      • basisFunctions

        public double[] basisFunctions​(double s)
        Returns the basis function values for the given parameter value (Nik(s)). This function first calculates the span which is needed in order to calculate the basis functions values.
        Parameters:
        s - Parameter value to calculate basis functions for.
        Returns:
        basis function values. WARNING: the returned array will likely be longer than [0..degree], so do NOT depend on array.length in any iterations over the array!. The additional array elements will contain garbage and should not be used. The returned array was allocated using javolution.context.ArrayFactory.DOUBLES_FACTORY and could be recycled by the user when no longer needed.

      • basisFunctions

        public double[] basisFunctions​(int span,
                               double s)
        Returns the unweighted basis function values for the given parameter value (Nik(s)), when the span that the parameter value lies in is already known.
        Parameters:
        span - The span s lies in
        s - The parameter value to calculate basis functions for.
        Returns:
        basis function values. WARNING: the returned array will likely be longer than [0..degree], so do NOT depend on array.length in any iterations over the array!. The additional array elements will contain garbage and should not be used. The returned array was allocated using javolution.context.ArrayFactory.DOUBLES_FACTORY and could be recycled by the user when no longer needed.

      • basisFunctionDerivatives

        public double[][] basisFunctionDerivatives​(int span,
                                           double s,
                                           int grade)
        Calculates all the derivatives of all the unweighted basis functions from 0 up to the given grade, d^{grade}Nik(s)/d^{grade}s.

        Examples:
        1st derivative (grade = 1), this returns [Nik(s), dNik(s)/ds];
        2nd derivative (grade = 2), this returns [Nik(s), dNik(s)/ds, d^2Nik(s)/d^2s]; etc.

        Parameters:
        span - The span s lies in
        s - The parameter value to calculate basis functions for.
        grade - The grade to calculate the derivatives for (1=1st derivative, 2=2nd derivative, etc).
        Returns:
        Basis function derivative values. WARNING: the returned array is recycled and will likely be longer than [0..grade+1][0..degree+1], so do NOT depend on array.length in any iterations over the array!. The additional array elements will contain garbage and should not be used. The returned array could be recycled by calling KnotVector.recycle2DArray(arr) when no longer needed.
        Throws:
        java.lang.IllegalArgumentException - if the grade is < 0.
        See Also:
        basisFunctions(double), recycle2DArray(double[][])

      • getNu

        public int getNu()
        Return the length of the knot vector (nu).
        Returns:
        The length of the knot vector.

      • length

        public int length()
        Return the number of elements in the knot vector.
        Returns:
        The number of elements in the knot vector.

      • getAll

        public Float64Vector getAll()
        Return the knot values as an vector of Float64 values.
        Returns:
        the vector of knot values

      • get

        public Float64 get​(int i)
        Return the knot at the specified index.
        Parameters:
        i - Index to get knot value for
        Returns:
        the knot value at index i

      • getValue

        public double getValue​(int i)
        Return the knot value at a specific index as a double.
        Parameters:
        i - Index to get knot value for
        Returns:
        the knot value at index i returned as a double.

      • getDegree

        public int getDegree()
        Return the degree of the KnotVector
        Returns:
        Degree of the KnotVector

      • getNumberOfSegments

        public int getNumberOfSegments()
        Return the number of segments in the knot vector.
        Returns:
        The number of segments in the knot vector.

      • isOpen

        public boolean isOpen()
        Return true if the knot vector is open and false if it is closed.
        Returns:
        true if the knot vector is open.

      • isValid

        public boolean isValid()
        Return true if this KnotVector contains valid and finite numerical components. A value of false will be returned if any of the knot values are NaN or Inf.
        Returns:
        true if the KnotVector contains valid and finite values.

      • findMultiplicity

        public int findMultiplicity​(int index)
        Find the multiplicity of the knot with the specified index in this knot vector.
        Parameters:
        index - the index of the knot to observe (the largest index of a repeated series of knots).
        Returns:
        the multiplicity of the knot

      • reverse

        public KnotVector reverse()
        Return a copy of this knot vector with the parameterization reversed.
        Returns:
        A copy of this KnotVector with the parameterization reversed.

      • copy

        public KnotVector copy()
        Returns a copy of this KnotVector instance allocated by the calling thread (possibly on the stack).
        Specified by:
        copy in interface javolution.lang.ValueType
        Returns:
        an identical and independent copy of this point.

      • clone

        public java.lang.Object clone()
                       throws java.lang.CloneNotSupportedException
        Returns a copy of this KnotVector instance allocated by the calling thread (possibly on the stack).
        Returns:
        an identical and independent copy of this point.
        Throws:
        java.lang.CloneNotSupportedException - Never thrown.

      • equals

        public boolean equals​(java.lang.Object obj)
        Compares this ControlPoint against the specified object for strict equality (same values and same units).
        Overrides:
        equals in class java.lang.Object
        Parameters:
        obj - the object to compare with.
        Returns:
        true if this point is identical to that point; false otherwise.

      • hashCode

        public int hashCode()
        Returns the hash code for this parameter.
        Overrides:
        hashCode in class java.lang.Object
        Returns:
        the hash code value.

      • toText

        public javolution.text.Text toText()
        Returns the text representation of this knot vector that consists of the degree followed by the knot values. For example: 
           {degree=2,{0.0, 0.0, 0.0, 1.0, 1.0, 1.0}}
        Returns:
        the text representation of this geometry element.

      • toString

        public java.lang.String toString()
        Returns the string representation of this knot vector that consists of the degree followed by the knot values. For example: 
           {degree=2,{0.0, 0.0, 0.0, 1.0, 1.0, 1.0}}
        Overrides:
        toString in class java.lang.Object
        Returns:
        the text representation of this geometry element.

      • recycle2DArray

        public static void recycle2DArray​(double[][] arr)
        Recycle any 2D array of doubles that was created by this classes factory methods.
        Parameters:
        arr - The array to be recycled. The array must have been created by this class or by CurveUtils.allocate2DArray()!