WildMagic.LibFoundation.Curves

Class BSplineBasisf

java.lang.Object

WildMagic.LibFoundation.Curves.BSplineBasisf

All Implemented Interfaces:

Serializable

Direct Known Subclasses:

BSplineBasisDiscretef

public class BSplineBasisf
extends Object
implements Serializable

Basis functions for B-Splines

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected float[][]	m_aafBD0 Storage for the basis functions.
protected float[][]	m_aafBD1 Storage for first three derivatives.
protected float[][]	m_aafBD2 bd2[d+1][n+d+1]
protected float[][]	m_aafBD3 bd3[d+1][n+d+1]
protected float[]	m_afKnot knot[n+d+2]
protected boolean	m_bOpen flags
protected boolean	m_bUniform flags
protected int	m_iDegree d
protected int	m_iNumCtrlPoints n+1
protected int	m_iNumKnots number of knots
private static long	serialVersionUID

Constructor Summary

Constructors

Constructor and Description
BSplineBasisf() Empty default constructor.
BSplineBasisf(int iNumCtrlPoints, int iDegree) Open uniform.
BSplineBasisf(int iNumCtrlPoints, int iDegree, boolean bOpen) Open uniform or periodic uniform.
BSplineBasisf(int iNumCtrlPoints, int iDegree, float[] afKnot) Open nonuniform.

Method Summary

Methods

Modifier and Type	Method and Description
private float[][]	Allocate() Position and derivative storage allocation.
int	Compute(float fU, float[] afBD0, float[] afBD1, float[] afBD2) Evaluate basis functions for the given input and return the knot index i for which knot[i] <= fU < knot[i+1].
void	Compute(float fTime, int uiOrder, int[] riMinIndex, int[] riMaxIndex) evaluate basis functions and their derivatives
void	Create(int iNumCtrlPoints, int iDegree, boolean bOpen) Open uniform or periodic uniform.
void	Create(int iNumCtrlPoints, int iDegree, float[] afKnot) Open nonuniform.
void	dispose() release resources
float	GetD0(int i)
float	GetD1(int i)
float	GetD2(int i)
float	GetD3(int i)
int	GetDegree()
int	GetKey(float[] rfTime) Determine knot index i for which knot[i] <= rfTime < knot[i+1].
float	GetKnot(int i) Knot access for nonuniform splines
int	GetKnotIndex(float fU) Return the knot index i for which knot[i] <= fU < knot[i+1].
static int	GetMinNumControlPoints(int iDegree) Given a BSpline degree, return the minimum number of control points that is required.
int	GetNumCtrlPoints()
private int	Initialize(int iNumCtrlPoints, int iDegree, boolean bOpen) Common initialization.
boolean	IsOpen()
boolean	IsSameAs(BSplineBasisf that) Return indication of whether two BSpline basis instances are the same.
boolean	IsUniform()
void	SetKnot(int i, float fKnot) Knot access for nonuniform splines

Methods inherited from class java.lang.Object

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

Field Detail

serialVersionUID

private static final long serialVersionUID

See Also:

Constant Field Values

m_iNumCtrlPoints

protected int m_iNumCtrlPoints

n+1

m_iDegree

protected int m_iDegree

d

m_afKnot

protected float[] m_afKnot

knot[n+d+2]

m_iNumKnots

protected int m_iNumKnots

number of knots

m_bOpen

protected boolean m_bOpen

flags

m_bUniform

protected boolean m_bUniform

flags

m_aafBD0

protected float[][] m_aafBD0

Storage for the basis functions. The basis array is always allocated by the constructor calls. bd0[d+1][n+d+1]

m_aafBD1

protected float[][] m_aafBD1

Storage for first three derivatives. A derivative basis array is allocated on the first call to a derivative member function. bd1[d+1][n+d+1]

m_aafBD2

protected float[][] m_aafBD2

bd2[d+1][n+d+1]

m_aafBD3

protected float[][] m_aafBD3

bd3[d+1][n+d+1]

Constructor Detail

BSplineBasisf

public BSplineBasisf()

Empty default constructor. Call Create()...

BSplineBasisf

public BSplineBasisf(int iNumCtrlPoints,
             int iDegree)

Open uniform.

Parameters:

iNumCtrlPoints - number of spline control points, 2 or more.

iDegree - polynomial degree, between 1 and iNumCtrlPoints - 1

See Also:

Create(int, int, boolean)

BSplineBasisf

public BSplineBasisf(int iNumCtrlPoints,
             int iDegree,
             boolean bOpen)

Open uniform or periodic uniform.

Parameters:

iNumCtrlPoints - number of spline control points, 2 or more.

iDegree - polynomial degree, between 1 and iNumCtrlPoints - 1

bOpen - true for open uniform, false for periodic uniform.

See Also:

Create(int, int, boolean)

BSplineBasisf

public BSplineBasisf(int iNumCtrlPoints,
             int iDegree,
             float[] afKnot)

Open nonuniform.

Parameters:

iNumCtrlPoints - number of spline control points, 2 or more.

iDegree - polynomial degree, between 1 and iNumCtrlPoints - 1

afKnot - The knot array must have n-d elements. The elements must be nondecreasing. Each element must be in [0,1].

See Also:

Create(int, int, float[])

Method Detail

GetMinNumControlPoints

public static int GetMinNumControlPoints(int iDegree)

Given a BSpline degree, return the minimum number of control points that is required.

Parameters:

iDegree - Input degree of the BSpline.

Returns:

Minimum number of control points required.

Compute

public int Compute(float fU,
          float[] afBD0,
          float[] afBD1,
          float[] afBD2)

Evaluate basis functions for the given input and return the knot index i for which knot[i] <= fU < knot[i+1]. It is then that indexes i-degree <= k <= i have non-zero basis evaluations.

Parameters:

fU - float Input value in the [0,1] range. Clamped if not.

afBD0 - float[] Array to be filled with position basis evaluation at each of the knot values for the given fU input. This array must have enough elements to store a value for each control point. This array must not be null.

afBD1 - float[] Array to be filled with first derivative basis evaluation at each of the knot values for the given fU input. This array may be null meaning that the first derivative basis evaluation is not computed, but if the array is defined it must have enough elements to store a value for each control point. If this array is null, then the afBD2 array must also be null.

afBD2 - float[] Array to be filled with second derivative basis evaluation at each of the knot values for the given fU input. This array may be null meaning that the second derivative basis evaluation is not computed, but if the array is defined it must have enough elements to store a value for each control point. If this array is not null, then the afBD1 array must not be null.

Returns:

The knot index i for which knot[i] <= fU < knot[i+1].

Throws:

IllegalArgumentException - when afBD0 is null

Compute

public void Compute(float fTime,
           int uiOrder,
           int[] riMinIndex,
           int[] riMaxIndex)

evaluate basis functions and their derivatives

Create

public void Create(int iNumCtrlPoints,
          int iDegree,
          boolean bOpen)

Open uniform or periodic uniform. The knot array is internally generated with equally spaced elements.

Parameters:

iNumCtrlPoints - number of spline control points, 2 or more.

iDegree - polynomial degree, between 1 and iNumCtrlPoints - 1

bOpen - true for open uniform, false for periodic uniform.

Create

public void Create(int iNumCtrlPoints,
          int iDegree,
          float[] afKnot)

Open nonuniform. An internal copy is made of afKnot, so to dynamically change knots you must use the SetKnot function.

Parameters:

iNumCtrlPoints - number of spline control points, 2 or more.

iDegree - polynomial degree, between 1 and iNumCtrlPoints - 1

afKnot - The knot array must have n-d elements. The elements must be nondecreasing. Each element must be in [0,1].

dispose

public void dispose()

release resources

GetD0

public float GetD0(int i)

Parameters:

i - control point

Returns:

position

GetD1

public float GetD1(int i)

Parameters:

i - control point

Returns:

first derivative

GetD2

public float GetD2(int i)

Parameters:

i - control point

Returns:

second derivative

GetD3

public float GetD3(int i)

Parameters:

i - control point

Returns:

third derivative

GetDegree

public int GetDegree()

Returns:

polynomial degree

GetKey

public int GetKey(float[] rfTime)

Determine knot index i for which knot[i] <= rfTime < knot[i+1].

GetKnot

public float GetKnot(int i)

Knot access for nonuniform splines

Parameters:

i - knot index

Returns:

knot value

GetKnotIndex

public int GetKnotIndex(float fU)

Return the knot index i for which knot[i] <= fU < knot[i+1].

Parameters:

fU - Input value in the [0,1] range.

Returns:

Knot index in the range [0,getNumKnots()-1].

GetNumCtrlPoints

public int GetNumCtrlPoints()

Returns:

number of control points

IsOpen

public boolean IsOpen()

Returns:

Open flag

IsSameAs

public boolean IsSameAs(BSplineBasisf that)

Return indication of whether two BSpline basis instances are the same.

Parameters:

that - BSplineBasisf BSpline basis instance to check for similarity.

Returns:

boolean True if the two BSpline basis instances represent the same set of functions.

IsUniform

public boolean IsUniform()

Returns:

Uniform flag

SetKnot

public void SetKnot(int i,
           float fKnot)

Knot access for nonuniform splines

Parameters:

i - knot index

fKnot - knot value

Allocate

private float[][] Allocate()

Position and derivative storage allocation.

Returns:

2D array of correct size

Initialize

private int Initialize(int iNumCtrlPoints,
             int iDegree,
             boolean bOpen)

Common initialization.

Parameters:

iNumCtrlPoints - number of spline control points, 2 or more.

iDegree - polynomial degree, between 1 and iNumCtrlPoints - 1

bOpen - true for open uniform, false for periodic uniform.

Returns:

number of knots.

See Also:

Create(int, int, boolean)