KnotVector

java.lang.Object
- geomss.geom.nurbs.KnotVector

All Implemented Interfaces:

j2me.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:

November 28, 2015

Author:

Samuel Gerber, Date: May 14, 2009, Version 1.0.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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, Float64Vector 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 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).
    
    Overrides:
    
    clone in class java.lang.Object
    
    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()!

Class KnotVector

Method Summary

Methods inherited from class java.lang.Object

Method Detail

newInstance

newInstance

newInstance

bezierKnotVector

findSpan

basisFunctions

basisFunctions

basisFunctionDerivatives

getNu

length

getAll

get

getValue

getDegree

getNumberOfSegments

isOpen

isValid

findMultiplicity

reverse

copy

clone

equals

hashCode

toText

toString

recycle2DArray