WildMagic.LibFoundation.Curves

Class BSplineCurve3f

java.lang.Object

WildMagic.LibFoundation.Curves.Curve3f

WildMagic.LibFoundation.Curves.SingleCurve3f

WildMagic.LibFoundation.Curves.BSplineCurve3f

All Implemented Interfaces:

Serializable, IntegrateInterface

public class BSplineCurve3f
extends SingleCurve3f
implements Serializable

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class WildMagic.LibFoundation.Curves.Curve3f

Curve3f.PointList

Field Summary

Fields

Modifier and Type	Field and Description
protected Vector3f[]	m_akCtrlPoint Set of control points
protected boolean	m_bLoop Loop flag
protected int	m_iNumCtrlPoints Larger than basis control points, because of replication
protected int	m_iReplicate the number of replicated control points
protected BSplineBasisf	m_kBasis Spline basis
private static long	serialVersionUID

Fields inherited from class WildMagic.LibFoundation.Curves.Curve3f

m_fTMax, m_fTMin

Constructor Summary

Constructors

Constructor and Description
BSplineCurve3f(int iNumCtrlPoints, Vector3f[] akCtrlPoint, int iDegree, boolean bLoop, boolean bOpen) Construction and destruction.
BSplineCurve3f(int iNumCtrlPoints, Vector3f[] akCtrlPoint, int iDegree, boolean bLoop, float[] afKnot) Open, nonuniform spline.

Method Summary

Methods

Modifier and Type	Method and Description
static BSplineCurve3f	CreateApproximation(float[] akValue, int iNumControlPoints, int iDegree) Create a BSpline curve which best fits a set of 3D points.
static BSplineCurve3f	CreateApproximation(Vector3f[] akPoint, int iNumControlPoints, int iDegree) Create a BSpline curve which best fits a set of 3D points.
private void	CreateControl(Vector3f[] akCtrlPoint) Allocate our control points, with replication
void	dispose() release resources
void	Get(float fTime, Vector3f pkPos, Vector3f pkDer1, Vector3f pkDer2, Vector3f pkDer3) If you need position and derivatives at the same time, it is more efficient to call these functions.
BSplineBasisf	GetBasis() Access the basis function to compute it without control points.
Vector3f	GetControlPoint(int i) Retrieve a control point.
int	GetDegree()
Vector3f	GetFirstDerivative(float fTime) Get the 3D coordinates of the 1st derivative vector at the point along the curve evaluated for the input time value.
float	GetKnot(int i)
int	GetNumCtrlPoints()
Vector3f	GetPosition(float fTime) The spline is defined for 0 <= t <= 1.
Vector3f	GetSecondDerivative(float fTime) Get the 3D coordinates of the 2nd derivative vector at the point along the curve evaluated for the input time value.
Vector3f	GetThirdDerivative(float fTime)
float	GetVariation(float fT0, float fT1, Vector3f pkP0, Vector3f pkP1) TODO unimplemented
boolean	IsLoop()
boolean	IsOpen()
boolean	IsUniform()
void	SetControlPoint(int i, Vector3f rkCtrl) Control points may be changed at any time.
void	SetKnot(int i, float fKnot) The knot values can be changed only if the basis function is nonuniform and the input index is valid (0 <= i <= n-d-1).

Methods inherited from class WildMagic.LibFoundation.Curves.SingleCurve3f

GetLength, GetTime, Integrate

Methods inherited from class WildMagic.LibFoundation.Curves.Curve3f

GetBinormal, GetCurvature, GetFrame, GetMaxTime, GetMinTime, GetNormal, GetSpeed, GetTangent, GetTime, GetTorsion, GetTotalLength, SetTimeInterval, SubdivideByLength, SubdivideByTime, SubdivideByVariation, SubdivideByVariation

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

Larger than basis control points, because of replication

m_akCtrlPoint

protected Vector3f[] m_akCtrlPoint

Set of control points

m_bLoop

protected boolean m_bLoop

Loop flag

m_kBasis

protected BSplineBasisf m_kBasis

Spline basis

m_iReplicate

protected int m_iReplicate

the number of replicated control points

Constructor Detail

BSplineCurve3f

public BSplineCurve3f(int iNumCtrlPoints,
              Vector3f[] akCtrlPoint,
              int iDegree,
              boolean bLoop,
              boolean bOpen)

Construction and destruction. The caller is responsible for deleting the input arrays if they were dynamically allocated. Internal copies of the arrays are made, so to dynamically change control points or knots you must use the 'SetControlPoint', 'GetControlPoint', and 'Knot' member functions. Uniform spline. The number of control points is n+1 >= 2. The degree of the B-spline is d and must satisfy 1 <= d <= n. The knots are implicitly calculated in [0,1]. If bOpen is 'true', the spline is open and the knots are

       t[i] = 0,               0 <= i <= d
              (i-d)/(n+1-d),   d+1 <= i <= n
              1,               n+1 <= i <= n+d+1
 

If bOpen is 'false', the spline is periodic and the knots are

       t[i] = (i-d)/(n+1-d),   0 <= i <= n+d+1
 

If bLoop is 'true', extra control points are added to generate a closed curve. For an open spline, the control point array is reallocated and one extra control point is added, set to the first control point C[n+1] = C[0]. For a periodic spline, the control point array is reallocated and the first d points are replicated. In either case the knot array is calculated accordingly.

Parameters:

iNumCtrlPoints - number of control points is n+1 >= 2

akCtrlPoint - control point array

iDegree - degree of the B-spline is d and must satisfy 1 <= d <= n

bLoop - true to generate a closed loop

bOpen - true for open, false for periodic

BSplineCurve3f

public BSplineCurve3f(int iNumCtrlPoints,
              Vector3f[] akCtrlPoint,
              int iDegree,
              boolean bLoop,
              float[] afKnot)

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

Parameters:

iNumCtrlPoints - number of control points is n+1 >= 2

akCtrlPoint - control point array

iDegree - degree of the B-spline is d and must satisfy 1 <= d <= n

bLoop - true to generate a closed loop

afKnot - knot array

Method Detail

CreateApproximation

public static BSplineCurve3f CreateApproximation(float[] akValue,
                                 int iNumControlPoints,
                                 int iDegree)

Create a BSpline curve which best fits a set of 3D points.

Parameters:

akValue - float[] Array of values. The order of the points in the array defines a path.

iNumControlPoints - int Number of control points to use when creating the BSpline curve. The location of the control points are determined to provide a least squares best fit.

iDegree - int Degree of the basis functions to use when creating the BSpline curve.

Returns:

BSplineCurve3 New instance of the best fit BSpline curve. Even though the fit is for a single set of values, the curve that is created is for 3D set of values in which the x coordinates are used to representing the single value curve. The y and z coordinates are undefined.

CreateApproximation

public static BSplineCurve3f CreateApproximation(Vector3f[] akPoint,
                                 int iNumControlPoints,
                                 int iDegree)

Create a BSpline curve which best fits a set of 3D points.

Parameters:

akPoint - Point3f[] Array of 3D points. The order of the points in the array defines a path.

iNumControlPoints - Number of 3D control points to use when creating the BSpline curve. The location of the 3D control points are determined to provide a least squares best fit.

iDegree - Degree of the basis functions to use when creating the BSpline curve.

Returns:

BSplineCurve3 New instance of the best fit BSpline curve.

dispose

public void dispose()

release resources

Get

public void Get(float fTime,
       Vector3f pkPos,
       Vector3f pkDer1,
       Vector3f pkDer2,
       Vector3f pkDer3)

If you need position and derivatives at the same time, it is more efficient to call these functions. Pass the addresses of those quantities whose values you want. You may pass null in any argument whose value you do not want.

Parameters:

fTime - time

pkPos - output position

pkDer1 - output first derivative

pkDer2 - output second derivative

pkDer3 - output third derivative

GetBasis

public BSplineBasisf GetBasis()

Access the basis function to compute it without control points. This is useful for least squares fitting of curves.

Returns:

reference to basis

GetControlPoint

public Vector3f GetControlPoint(int i)

Retrieve a control point. The input index should be valid (0 <= i <= n). If it is invalid, GetControlPoint returns a vector whose components are all MAX_REAL.

Parameters:

i - index return control point

GetDegree

public int GetDegree()

Returns:

polynomial degree

GetFirstDerivative

public Vector3f GetFirstDerivative(float fTime)

Description copied from class: Curve3f

Get the 3D coordinates of the 1st derivative vector at the point along the curve evaluated for the input time value.

Specified by:

GetFirstDerivative in class Curve3f

Parameters:

fTime - Input time value which must be within the range for which this curve is defined.

Returns:

New instance created to contain the 3D coordinates of the computed 1st derivative vector. If the time value is less than getMinTime() then the 1st derivative vector at the start of the curve is returned. If the time value is greater than getMaxTime() then the 1st derivative vector at the end of the curve is returned.

See Also:

GetPosition(float fTime)

GetKnot

public float GetKnot(int i)

GetNumCtrlPoints

public int GetNumCtrlPoints()

Returns:

number of control points

GetPosition

public Vector3f GetPosition(float fTime)

The spline is defined for 0 <= t <= 1. If a t-value is outside [0,1], an open spline clamps t to [0,1]. That is, if t > 1, t is set to 1; if t < 0, t is set to 0. A periodic spline wraps to to [0,1]. That is, if t is outside [0,1], then t is set to t-floor(t).

Specified by:

GetPosition in class Curve3f

Parameters:

fTime - time

Returns:

New instance created to contain the 3D coordinates of the computed position. If the time value is less than getMinTime() then the coordinates of the point at the start of the curve is returned. If the time value is greater than getMaxTime() then the coordinates of the point at the end of the curve is returned.

GetSecondDerivative

public Vector3f GetSecondDerivative(float fTime)

Description copied from class: Curve3f

Get the 3D coordinates of the 2nd derivative vector at the point along the curve evaluated for the input time value.

Specified by:

GetSecondDerivative in class Curve3f

Parameters:

fTime - Input time value which must be within the range for which this curve is defined.

Returns:

New instance created to contain the 3D coordinates of the computed 1st derivative vector. If the time value is less than getMinTime() then the 2nd derivative vector at the start of the curve is returned. If the time value is greater than getMaxTime() then the 2nd derivative vector at the end of the curve is returned.

See Also:

GetPosition(float)

GetThirdDerivative

public Vector3f GetThirdDerivative(float fTime)

Specified by:

GetThirdDerivative in class Curve3f

See Also:

GetPosition(float fTime)

GetVariation

public float GetVariation(float fT0,
                 float fT1,
                 Vector3f pkP0,
                 Vector3f pkP1)

TODO unimplemented

Specified by:

GetVariation in class Curve3f

Parameters:

fT0 - point 0

fT1 - point 1

pkP0 - curvature at point 0, may be null

pkP1 - curvature at point 1, may be null

See Also:

Curve3f.SubdivideByVariation(float, int, int, Vector3f[])

IsLoop

public boolean IsLoop()

Returns:

loop flag

IsOpen

public boolean IsOpen()

Returns:

Open flag

IsUniform

public boolean IsUniform()

Returns:

Uniform flag

SetControlPoint

public void SetControlPoint(int i,
                   Vector3f rkCtrl)

Control points may be changed at any time. The input index should be valid (0 <= i <= n). If it is invalid, GetControlPoint returns a vector whose components are all MAX_REAL.

Parameters:

i - index

rkCtrl - new control point

SetKnot

public void SetKnot(int i,
           float fKnot)

The knot values can be changed only if the basis function is nonuniform and the input index is valid (0 <= i <= n-d-1). If these conditions are not satisfied, GetKnot returns MAX_REAL.

Parameters:

i - index

fKnot - new knot

CreateControl

private void CreateControl(Vector3f[] akCtrlPoint)

Allocate our control points, with replication

Parameters:

akCtrlPoint - starting points