Package WildMagic.LibFoundation.Curves

Class 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
      protected float m_fTMin
      curve parameter is t where tmin
      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

      • m_fTMin

        protected float m_fTMin
        curve parameter is t where tmin

        • m_fTMax

          protected float m_fTMax
          curve parameter is t where tmin

          • 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
              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