java.lang.Object
- WildMagic.LibFoundation.Curves.Curve3f

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

MultipleCurve3, SingleCurve3f
```
public abstract class Curve3f
extends java.lang.Object
implements java.io.Serializable
```
This is an abstract interface for a curve in 3D. The curve is defined as a function of time over an interval. The position, 1st derivative, and 2nd derivative is computed for any point along the curve as selected by an input value in the time domain. The tangent at any point is computed as direction of the 1st derivative vector and the speed is computed as the length of the 1st derivative vector. The arc length of any subinterval of the curve can be computed. The curve can be re-parameterized as function of arc length where the length at the minimum interval time is zero and the length at the maximum interval time is the total length of the curve. This means that given an arc length, the corresponding input time within the curve's time interval is determined. Extensions of this class provide the implementation based on the particular type of curve.

See Also:

Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type Class Description

protected class Curve3f.PointList
Utility class used in SubdivideByVariation()

Field Summary

Fields
Modifier and Type	Field	Description
`protected float`	`m_fTMax`	curve parameter is t where tmin <= t <= tmax
`protected float`	`m_fTMin`	curve parameter is t where tmin <= t <= tmax
`private static long`	`serialVersionUID`

Constructor Summary

Constructors
Constructor Description

Curve3f(float fTMin, float fTMax)
Create a generalized curve over the specified time interval.

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method	Description
`Vector3f`	`GetBinormal(float fTime)`	Binormal at a point on the curve.
`float`	`GetCurvature(float fTime)`	Curvature at a point on the curve.
`abstract 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.
`void`	`GetFrame(float fTime, Vector3f rkPosition, Vector3f rkTangent, Vector3f rkNormal, Vector3f rkBinormal)`	Several quantities at once at a point on the curve.
`abstract float`	`GetLength(float fT0, float fT1)`	Get the length of the curve for the specified time subinterval.
`float`	`GetMaxTime()`	Get the maximum time value for which this curve is defined.
`float`	`GetMinTime()`	Get the minimum time value for which this curve is defined.
`Vector3f`	`GetNormal(float fTime)`	Normal at a point on the curve.
`abstract Vector3f`	`GetPosition(float fTime)`	Get the 3D coordinates of the position along the curve evaluated for the input time value.
`abstract 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.
`float`	`GetSpeed(float fTime)`	Get the speed at the point along the curve evaluated for the input time value.
`Vector3f`	`GetTangent(float fTime)`	Get the 3D coordinates of the tangent vector at the point along the curve evaluated for the input time value.
`abstract Vector3f`	`GetThirdDerivative(float fTime)`
`float`	`GetTime(float fLength)`	Locate the time value associated with this arc length along the curve.
`abstract float`	`GetTime(float fLength, int iIterations, float fTolerance)`	Re-parameterize the curve where the time value is defined as a function of arc length.
`float`	`GetTorsion(float fTime)`	Torsion at a point on the curve.
`float`	`GetTotalLength()`	Get the length total length of the curve from start to end.
`abstract float`	`GetVariation(float fT0, float fT1, Vector3f pkP0, Vector3f pkP1)`	Subdivision by variation.
`void`	`SetTimeInterval(float fTMin, float fTMax)`	If you are interested in only a subinterval of the actual domain of the curve, you may set that subinterval with SetTimeInterval.
`void`	`SubdivideByLength(int iNumPoints, Vector3f[] rakPoint)`	Perform subdivision
`void`	`SubdivideByTime(int iNumPoints, Vector3f[] rakPoint)`	Perform subdivision
`void`	`SubdivideByVariation(float fMinVariation, int iMaxLevel, int riNumPoints, Vector3f[] rakPoint)`
`protected void`	`SubdivideByVariation(float fT0, Vector3f rkP0, float fT1, Vector3f rkP1, float fMinVariation, int iLevel, int riNumPoints, Curve3f.PointList rpkList)`	Subdivision by variation.

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_fTMin
```
protected float m_fTMin
```
    curve parameter is t where tmin <= t <= tmax
  - m_fTMax
```
protected float m_fTMax
```
    curve parameter is t where tmin <= t <= tmax
- Constructor Detail
  - Curve3f
```
public Curve3f(float fTMin,
               float fTMax)
```
    Create a generalized curve over the specified time interval.
    
    Parameters:
    
    fTMin - Minimum time value for the interval.
    
    fTMax - Maximum time value for the interval.
- Method Detail
  - GetBinormal
```
public Vector3f GetBinormal(float fTime)
```
    Binormal at a point on the curve. @see GetTangent
  - GetCurvature
```
public float GetCurvature(float fTime)
```
    Curvature at a point on the curve. @see GetTangent
  - GetFirstDerivative
```
public abstract 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.
    
    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.
  - GetFrame
```
public void GetFrame(float fTime,
                     Vector3f rkPosition,
                     Vector3f rkTangent,
                     Vector3f rkNormal,
                     Vector3f rkBinormal)
```
    Several quantities at once at a point on the curve. @see GetTangent
  - GetLength
```
public abstract float GetLength(float fT0,
                                float fT1)
```
    Get the length of the curve for the specified time subinterval.
    
    Parameters:
    
    fT0 - Minimum time of the subinterval. Clipped to getMinTime() if less than it.
    
    fT1 - Minimum time of the subinterval. Clipped to getMaxTime() if greater than it.
    
    Returns:
    
    Computed length curve for the specified time subinterval.
  - GetMaxTime
```
public float GetMaxTime()
```
    Get the maximum time value for which this curve is defined.
    
    Returns:
    
    Maximum time value for curve.
  - GetMinTime
```
public float GetMinTime()
```
    Get the minimum time value for which this curve is defined.
    
    Returns:
    
    Minimum time value for curve.
  - GetNormal
```
public Vector3f GetNormal(float fTime)
```
    Normal at a point on the curve. @see GetTangent
  - GetPosition
```
public abstract Vector3f GetPosition(float fTime)
```
    Get the 3D coordinates of the position along the curve evaluated for the input time value.
    
    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 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 abstract 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.
    
    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.
  - GetSpeed
```
public float GetSpeed(float fTime)
```
    Get the speed at the point along the curve evaluated for the input time value. The speed is the length of the 1st derivative vector.
    
    Parameters:
    
    fTime - Input time value which must be within the range for which this curve is defined.
    
    Returns:
    
    The computed speed. If the time value is less than getMinTime() then the speed at the start of the curve is returned. If the time value is greater than getMaxTime() then the speed at the end of the curve is returned.
  - GetTangent
```
public Vector3f GetTangent(float fTime)
```
    Get the 3D coordinates of the tangent vector at the point along the curve evaluated for the input time value. The tangent vector is the normalized direction of the 1st derivative vector.
    
    Parameters:
    
    fTime - float Input time value which must be within the range for which this curve is defined.
    
    Returns:
    
    Vector3f New instance created to contain the 3D coordinates of the computed tangent vector. If the time value is less than getMinTime() then the tangent vector at the start of the curve is returned. If the time value is greater than getMaxTime() then the tangent vector at the end of the curve is returned.
  - GetThirdDerivative
```
public abstract Vector3f GetThirdDerivative(float fTime)
```
  - GetTime
```
public float GetTime(float fLength)
```
    Locate the time value associated with this arc length along the curve. Use 32 iterations and tolerance of 1e-06
    
    Parameters:
    
    fLength - Input arc length
    
    Returns:
    
    Time value
    
    See Also:
    
    GetTime(float, int, float)
  - GetTime
```
public abstract float GetTime(float fLength,
                              int iIterations,
                              float fTolerance)
```
    Re-parameterize the curve where the time value is defined as a function of arc length. Location the time value associated with this arc length along the curve.
    
    Parameters:
    
    fLength - Input arc length for which the associated time is to be determined. This length is measured from the starting point of the curve which is at the getMinTime().
    
    iIterations - iterations to run Newton's method
    
    fTolerance - tolerance for early termination
    
    Returns:
    
    Time value associated with this arc length along the curve. The returned value is always within the range of getMinTime() and getMaxTime().
  - GetTorsion
```
public float GetTorsion(float fTime)
```
    Torsion at a point on the curve. @see GetTangent
  - GetTotalLength
```
public float GetTotalLength()
```
    Get the length total length of the curve from start to end.
    
    Returns:
    
    Length of the entire curve.
  - GetVariation
```
public abstract float GetVariation(float fT0,
                                   float fT1,
                                   Vector3f pkP0,
                                   Vector3f pkP1)
```
    Subdivision by variation. The pointers pkP0 and pkP1 correspond to the curve points at fT0 and fT1. If the pointer values are not null, the assumption is that the caller has passed in the curve points. Otherwise, the function computes the curve points.
    
    Parameters:
    
    fT0 - point 0
    
    pkP0 - curvature at point 0, may be null
    
    fT1 - point 1
    
    pkP1 - curvature at point 1, may be null
    
    See Also:
    
    SubdivideByVariation(float, int, int, Vector3f[])
  - SetTimeInterval
```
public void SetTimeInterval(float fTMin,
                            float fTMax)
```
    If you are interested in only a subinterval of the actual domain of the curve, you may set that subinterval with SetTimeInterval. This function requires that fTMin < fTMax.
    
    Parameters:
    
    fTMin - min time
    
    fTMax - max time
  - SubdivideByLength
```
public void SubdivideByLength(int iNumPoints,
                              Vector3f[] rakPoint)
```
    Perform subdivision
  - SubdivideByTime
```
public void SubdivideByTime(int iNumPoints,
                            Vector3f[] rakPoint)
```
    Perform subdivision
  - SubdivideByVariation
```
public void SubdivideByVariation(float fMinVariation,
                                 int iMaxLevel,
                                 int riNumPoints,
                                 Vector3f[] rakPoint)
```
  - SubdivideByVariation
```
protected void SubdivideByVariation(float fT0,
                                    Vector3f rkP0,
                                    float fT1,
                                    Vector3f rkP1,
                                    float fMinVariation,
                                    int iLevel,
                                    int riNumPoints,
                                    Curve3f.PointList rpkList)
```
    Subdivision by variation. The pointers pkP0 and pkP1 correspond to the curve points at fT0 and fT1. If the pointer values are not null, the assumption is that the caller has passed in the curve points. Otherwise, the function computes the curve points.
    
    Parameters:
    
    fT0 - point 0
    
    rkP0 - curvature at point 0
    
    fT1 - point 1
    
    rkP1 - curvature at point 1
    
    fMinVariation -
    
    iLevel -
    
    riNumPoints - number of points in list
    
    rpkList - may be null

Class Curve3f

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

serialVersionUID

m_fTMin

m_fTMax

Constructor Detail

Curve3f

Method Detail

GetBinormal

GetCurvature

GetFirstDerivative

GetFrame

GetLength

GetMaxTime

GetMinTime

GetNormal

GetPosition

GetSecondDerivative

GetSpeed

GetTangent

GetThirdDerivative

GetTime

GetTime

GetTorsion

GetTotalLength

GetVariation

SetTimeInterval

SubdivideByLength

SubdivideByTime

SubdivideByVariation

SubdivideByVariation