org.jscience.mathematics.geometry
Class PureBezierCurve3D

java.lang.Object
  extended by org.jscience.mathematics.geometry.GeometryElement
      extended by org.jscience.mathematics.geometry.AbstractParametricCurve
          extended by org.jscience.mathematics.geometry.ParametricCurve3D
              extended by org.jscience.mathematics.geometry.BoundedCurve3D
                  extended by org.jscience.mathematics.geometry.FreeformCurveWithControlPoints3D
                      extended by org.jscience.mathematics.geometry.PureBezierCurve3D
All Implemented Interfaces:
java.io.Serializable

public class PureBezierCurve3D
extends FreeformCurveWithControlPoints3D

�R���� : ��L�? (��?���) �x�W�G��?��їL�?�x�W�G��?��\���N���X

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�x�W�G��?�̃p���??[�^��`��� [0, 1] �ƂȂ�?B

t ��p���??[�^�Ƃ���x�W�G��?� P(t) �̃p���?�g���b�N�\����?A�ȉ��̒ʂ�?B

        n = ?���_��?� - 1
        bi = controlPoints[i]
        wi = weights[i]
 
�Ƃ���?A��L�?�x�W�G��?��
        P(t) =  (bi * Bn,i(t)) �̑?�a            (i = 0, ..., n)
 
�L�?�x�W�G��?��
                (wi * bi * Bn,i(t)) �̑?�a
        P(t) =  --------------------------      (i = 0, ..., n)
                (wi * Bn,i(t)) �̑?�a
 
������ Bn,i(t) �̓o?[���X�^�C������?��ł���?B

See Also:
Serialized Form

Field Summary
 
Fields inherited from class org.jscience.mathematics.geometry.FreeformCurveWithControlPoints3D
controlPoints, weights
 
Constructor Summary
PureBezierCurve3D(Point3D[] controlPoints)
          ?
PureBezierCurve3D(Point3D[] controlPoints, double[] weights)
          ?
PureBezierCurve3D(Point3D[] controlPoints, double[] weights, boolean doCheck)
          ?
 
Method Summary
 Point3D blossoming(double[] parameters)
          ���̋�?
 Point3D coordinates(double param)
          ���̋�?
 CurveCurvature3D curvature(double param)
          ���̋�?
 int degree()
          ���̋�?
 PureBezierCurve3D[] divide(double param)
          ���̃x�W�G��?
protected  ParametricCurve3D doTransformBy(boolean reverseTransform, CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)
          ���̋�?
 PureBezierCurve3D elevateOneDegree()
          ���̋�?
 Point3D endPoint()
          ���̗L� �?
 CurveDerivative3D evaluation(double param)
          ���̋�?
 PointOnCurve3D[] inflexion()
          ���̋�?
 CurveCurveInterference3D[] interfere(BoundedCurve3D mate)
          ���̗L� �?
 IntersectionPoint3D[] intersect(ElementarySurface3D mate)
          ���̋�?
 IntersectionPoint3D[] intersect(ParametricCurve3D mate)
          ���̋�?
 IntersectionPoint3D[] intersect(ParametricSurface3D mate)
          ���̋�?
 double length(ParameterSection pint)
          �^����ꂽ�p���??
protected  void output(java.io.PrintWriter writer, int indent)
          ?
 ParametricCurve3D parallelTranslate(Vector3D moveVec)
          ���̋�?
 DoublePolynomial[] polynomial(boolean isPoly)
          ���̋�?
 PolynomialCurve3D polynomialCurve(boolean isPoly)
          ���̋�?
 PointOnCurve3D[] projectFrom(Point3D mate)
          �^����ꂽ�_���炱�̋�?
 PointOnCurve3D[] singular()
          ���̋�?
 Point3D startPoint()
          ���̗L� �?
 Vector3D tangentVector(double param)
          ���̋�?
 BsplineCurve3D toBsplineCurve()
          ���̗L� �?
 BsplineCurve3D toBsplineCurve(ParameterSection pint)
          ���̋�?
 Polyline3D toPolyline(ParameterSection section, ToleranceForDistance tolerance)
          ���̋�?
 double torsion(double param)
          ���̋�?
 PureBezierCurve3D truncate(ParameterSection section)
          ���̃x�W�G��?
 
Methods inherited from class org.jscience.mathematics.geometry.FreeformCurveWithControlPoints3D
allocateDoubleArray, controlPointAt, controlPoints, convRational0Deriv, convRational1Deriv, convRational2Deriv, convRational3Deriv, isFreeform, isPolynomial, isRational, makeUniformWeights, nControlPoints, setCoordinatesToDoubleArray, toDoubleArray, weightAt, weights
 
Methods inherited from class org.jscience.mathematics.geometry.BoundedCurve3D
length, toPolyline
 
Methods inherited from class org.jscience.mathematics.geometry.ParametricCurve3D
checkProjection, dimension, hasPolyline, identicalParameter, is3D, isComposedOfOnlyPolylines, nearestProjectFrom, nearestProjectWithDistanceFrom, pointToParameter, reverseTransformBy, transformBy, transformBy
 
Methods inherited from class org.jscience.mathematics.geometry.AbstractParametricCurve
checkValidity, checkValidity, isClosed, isCurve, isFinite, isInfinite, isNonPeriodic, isOpen, isParametric, isPeriodic, isValid, parameterDomain
 
Methods inherited from class org.jscience.mathematics.geometry.GeometryElement
getClassName, getToleranceForAngle, getToleranceForAngleAsObject, getToleranceForDistance, getToleranceForDistance2, getToleranceForDistanceAsObject, getToleranceForParameter, getToleranceForParameterAsObject, getToleranceForRealNumber, getToleranceForRealNumberAsObject, is1D, is2D, isPlacement, isPoint, isSurface, isTransformationOperator, isVector, makeIndent, output
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

PureBezierCurve3D

public PureBezierCurve3D(Point3D[] controlPoints)
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���̃R���X�g���N�^��?A super(controlPoints) ��Ă�?o���Ă��邾���ł���?B

Parameters:
controlPoints - ?���_�̔z��

PureBezierCurve3D

public PureBezierCurve3D(Point3D[] controlPoints,
                         double[] weights)
?���_���?d�ݗ��^���ėL�?��?�Ƃ��ăI�u�W�F�N�g��?\�z����?B

���̃R���X�g���N�^��?A super(controlPoints, weights) ��Ă�?o���Ă��邾���ł���?B

Parameters:
controlPoints - ?���_�̔z��
weights - ?d�݂̔z��

PureBezierCurve3D

public PureBezierCurve3D(Point3D[] controlPoints,
                         double[] weights,
                         boolean doCheck)
?���_���?d�ݗ��^���� ��?�����?� (���邢�͗L�?��?�) �Ƃ��ăI�u�W�F�N�g��?\�z����?B

���̃R���X�g���N�^��?A super(controlPoints, weights, doCheck) ��Ă�?o���Ă��邾���ł���?B

Parameters:
controlPoints - ?���_�̔z��?B
weights - ?d�݂̔z��
doCheck - ��?��̃`�F�b�N�ⷂ邩�ǂ���
Method Detail

degree

public int degree()
���̋�?�̎�?���Ԃ�?B

Returns:
��?�

polynomial

public DoublePolynomial[] polynomial(boolean isPoly)
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�L�?��?��?�?�?A R[0] �� WX ?���?A R[1] �� WY ?��� R[2] �� WZ ?��� R[3] �� W ?��� �̑�?����\����\��?B

Parameters:
isPoly - ��L�?�ł��邩�ǂ���
Returns:
��?����̔z��
See Also:
polynomialCurve(boolean)

polynomialCurve

public PolynomialCurve3D polynomialCurve(boolean isPoly)
���̋�?��?Č����鑽?�����?��Ԃ�?B

Parameters:
isPoly - ��L�?�ł��邩�ǂ���
Returns:
��?�����?�
See Also:
polynomial(boolean)

length

public double length(ParameterSection pint)
�^����ꂽ�p���??[�^��Ԃɂ����邱�̋�?�̎ ��?�ł̒��� (���̂�) ��Ԃ�?B

pint �̑?���l�͕��ł©�܂�Ȃ�?B

�^����ꂽ�p���??[�^��Ԃ����̋�?�̒�`���O��Ă���?�?��ɂ� ParameterOutOfRange �̗�O��?�����?B

Specified by:
length in class AbstractParametricCurve
Parameters:
pint - ��?�̒�����?�߂�p���??[�^���
Returns:
�w�肳�ꂽ�p���??[�^��Ԃɂ������?�̒���
See Also:
ParameterOutOfRange

coordinates

public Point3D coordinates(double param)
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�^����ꂽ�p���??[�^�l����`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Specified by:
coordinates in class ParametricCurve3D
Parameters:
param - �p���??[�^�l
Returns:
?W�l
See Also:
ParameterOutOfRange

tangentVector

public Vector3D tangentVector(double param)
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�^����ꂽ�p���??[�^�l����`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Specified by:
tangentVector in class ParametricCurve3D
Parameters:
param - �p���??[�^�l
Returns:
?ڃx�N�g��
See Also:
ParameterOutOfRange

curvature

public CurveCurvature3D curvature(double param)
���̋�?��?A�^����ꂽ�p���??[�^�l�ł̋ȗ���Ԃ�?B

�^����ꂽ�p���??[�^�l����`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Specified by:
curvature in class ParametricCurve3D
Parameters:
param - �p���??[�^�l
Returns:
�ȗ�
See Also:
ParameterOutOfRange

torsion

public double torsion(double param)
���̋�?��?A�^����ꂽ�p���??[�^�l�ł̃��C����Ԃ�?B

�^����ꂽ�p���??[�^�l����`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Specified by:
torsion in class ParametricCurve3D
Parameters:
param - �p���??[�^�l
Returns:
���C��
See Also:
ParameterOutOfRange

evaluation

public CurveDerivative3D evaluation(double param)
���̋�?��?A�^����ꂽ�p���??[�^�l�ł̓���?���Ԃ�?B

�^����ꂽ�p���??[�^�l����`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Specified by:
evaluation in class ParametricCurve3D
Parameters:
param - �p���??[�^�l
Returns:
����?�
See Also:
ParameterOutOfRange

blossoming

public Point3D blossoming(double[] parameters)
���̋�?��?A�^����ꂽ�p���??[�^��ɑ΂���u�?�b�T�~���O�̌��ʂ�Ԃ�?B

parameters �̗v�f?���?A���̋�?�̎�?��Ɉ�v���Ă���K�v������?B

�^����ꂽ�p���??[�^�l����`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Parameters:
parameters - �p���??[�^�l�̔z��
Returns:
�u�?�b�T�~���O�̌��ʂł���?W�l
See Also:
ParameterOutOfRange

singular

public PointOnCurve3D[] singular()
                          throws IndefiniteSolutionException
���̋�?�̓Hٓ_��Ԃ�?B

�Hٓ_����?݂��Ȃ��Ƃ��͒��� 0 �̔z���Ԃ�?B

Specified by:
singular in class ParametricCurve3D
Returns:
�Hٓ_�̔z��
Throws:
IndefiniteSolutionException - ��?�S�̂�?k�ނ��Ă���

inflexion

public PointOnCurve3D[] inflexion()
                           throws IndefiniteSolutionException
���̋�?�̕ϋȓ_��Ԃ�?B

�ϋȓ_����?݂��Ȃ��Ƃ��͒��� 0 �̔z���Ԃ�?B

Specified by:
inflexion in class ParametricCurve3D
Returns:
�ϋȓ_�̔z��
Throws:
IndefiniteSolutionException - �⪕s��ł��� (���̋�?�͒�?�?�ł���)

toBsplineCurve

public BsplineCurve3D toBsplineCurve()
���̗L� �?�S�̂쵖���?Č�����L�? Bspline ��?��Ԃ�?B

Overrides:
toBsplineCurve in class BoundedCurve3D
Returns:
���̋�?�S�̂�?Č�����L�? Bspline ��?�

toBsplineCurve

public BsplineCurve3D toBsplineCurve(ParameterSection pint)
���̋�?�̎w��̋�Ԃ쵖���?Č�����L�? Bspline ��?��Ԃ�?B

Specified by:
toBsplineCurve in class ParametricCurve3D
Parameters:
pint - �L�? Bspline ��?��?�����p���??[�^���
Returns:
���̋�?�̎w��̋�Ԃ�?Č�����L�? Bspline ��?�

intersect

public IntersectionPoint3D[] intersect(ParametricCurve3D mate)
                                throws IndefiniteSolutionException
���̋�?�Ƒ��̋�?�̌�_��?�߂�?B

��_����?݂��Ȃ��Ƃ��͒��� 0 �̔z���Ԃ�?B

Specified by:
intersect in class ParametricCurve3D
Parameters:
mate - ���̋�?�
Returns:
��_�̔z��
Throws:
IndefiniteSolutionException - �⪕s��ł���

intersect

public IntersectionPoint3D[] intersect(ParametricSurface3D mate)
                                throws IndefiniteSolutionException
���̋�?�Ƒ��̋Ȗʂ̌�_��?�߂�?B

��_����?݂��Ȃ��Ƃ��͒��� 0 �̔z���Ԃ�?B

Specified by:
intersect in class ParametricCurve3D
Parameters:
mate - ���̋Ȗ�
Returns:
��_�̔z��
Throws:
IndefiniteSolutionException - �⪕s��ł���

intersect

public IntersectionPoint3D[] intersect(ElementarySurface3D mate)
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��_����?݂��Ȃ��Ƃ��͒��� 0 �̔z���Ԃ�?B

Parameters:
mate - ���̋Ȗ� (��?͋Ȗ�)
Returns:
��_�̔z��

interfere

public CurveCurveInterference3D[] interfere(BoundedCurve3D mate)
���̗L� �?�Ƒ��̗L� �?�̊�?‚�?�߂�?B

��?‚���?݂��Ȃ�?�?��ɂ͒��� 0 �̔z���Ԃ�?B

Specified by:
interfere in class BoundedCurve3D
Parameters:
mate - ���̋�?�
Returns:
���?�̊�?‚̔z��

divide

public PureBezierCurve3D[] divide(double param)
���̃x�W�G��?��?A�^����ꂽ�p���??[�^�l�œ�‚ɕ�������?B

param �̒l��?A���̃x�W�G��?�̒�`���O��Ă���?�?��ɂ� ParameterOutOfRange �̗�O��?�����?B

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Parameters:
param - �p���??[�^�l
Returns:
������̃x�W�G��?��܂ޔz��
See Also:
ParameterOutOfRange

truncate

public PureBezierCurve3D truncate(ParameterSection section)
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section �̑?���l������?�?��ɂ�?A?i?s���]�����x�W�G��?��Ԃ�?B

section �̒l��?A���̃x�W�G��?�̒�`���O��Ă���?�?��ɂ� ParameterOutOfRange �̗�O��?�����?B

Parameters:
section - ?ؒf���Ďc��������\���p���??[�^���
Returns:
?ؒf���Ďc����������\���x�W�G��?�
See Also:
ParameterOutOfRange

projectFrom

public PointOnCurve3D[] projectFrom(Point3D mate)
�^����ꂽ�_���炱�̋�?�ւ̓��e�_��?�߂�?B

���e�_����?݂��Ȃ��Ƃ��͒��� 0 �̔z���Ԃ�?B

[�Ք?��?]
��?�?�̂���_ P(t) ����^����ꂽ�_�֌�x�N�g���� P(t) �ɂ�����?ڃx�N�g�� P'(t) �̓�?ς�\����?��� D(t) ��?�?���?A �����?��ӂƂ����?���� D(t) = 0 ��⢂Ă���?B

Specified by:
projectFrom in class ParametricCurve3D
Parameters:
point - ���e���̓_
Returns:
���e�_�̔z��

toPolyline

public Polyline3D toPolyline(ParameterSection section,
                             ToleranceForDistance tolerance)
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���ʂƂ��ĕԂ����|�����C����?\?�����_�� ���̋�?��x?[�X�Ƃ��� PointOnCurve3D �� ���邱�Ƃ��҂ł���?B

section �̒l��?A���̃x�W�G��?�̒�`���O��Ă���?�?��ɂ� ParameterOutOfRange �̗�O��?�����?B

Specified by:
toPolyline in class ParametricCurve3D
Parameters:
section - ��?�ߎ�����p���??[�^���
tolerance - �����̋��e��?�
Returns:
���̋�?�̎w��̋�Ԃ�?�ߎ�����|�����C��
See Also:
ParameterOutOfRange

startPoint

public Point3D startPoint()
���̗L� �?�̊J�n�_��Ԃ�?B

Overrides:
startPoint in class BoundedCurve3D
Returns:
�J�n�_

endPoint

public Point3D endPoint()
���̗L� �?��?I���_��Ԃ�?B

Overrides:
endPoint in class BoundedCurve3D
Returns:
?I���_

parallelTranslate

public ParametricCurve3D parallelTranslate(Vector3D moveVec)
���̋�?��?A�^����ꂽ�x�N�g����?]�Bĕ�?s�ړ�������?��Ԃ�?B

Specified by:
parallelTranslate in class ParametricCurve3D
Parameters:
moveVec - ��?s�ړ��̕��Ɨʂ�\���x�N�g��
Returns:
��?s�ړ���̋�?�

elevateOneDegree

public PureBezierCurve3D elevateOneDegree()
���̋�?��?A�`?�⻂̂܂܂ɂ���?A��?�����?グ����?��Ԃ�?B

Returns:
����`?��?A��?������?オ�B���?�

doTransformBy

protected ParametricCurve3D doTransformBy(boolean reverseTransform,
                                          CartesianTransformationOperator3D transformationOperator,
                                          java.util.Hashtable transformedGeometries)
���̋�?��?A�^����ꂽ�􉽓I�ϊ����Z�q�ŕϊ�����?B

transformedGeometries ��?A �ϊ��O�̊􉽗v�f��L?[�Ƃ�?A �ϊ���̊􉽗v�f��l�Ƃ���n�b�V���e?[�u���ł���?B

this �� transformedGeometries ��ɃL?[�Ƃ��đ�?݂��Ȃ�?�?��ɂ�?A this �� transformationOperator �ŕϊ�������̂�Ԃ�?B ����?ۂɃ?�\�b�h�Ք�ł� this ��L?[?A �ϊ����ʂ�l�Ƃ��� transformedGeometries �ɒljB���?B

this �� transformedGeometries ��Ɋ�ɃL?[�Ƃ��đ�?݂���?�?��ɂ�?A ��?ۂ̕ϊ���?s�Ȃ킸?A���̃L?[�ɑΉ�����l��Ԃ�?B ����?��?��?ċA�I��?s�Ȃ���?B

transformedGeometries �� null �ł�?\��Ȃ�?B transformedGeometries �� null ��?�?��ɂ�?A ?�� this �� transformationOperator �ŕϊ�������̂�Ԃ�?B

Specified by:
doTransformBy in class ParametricCurve3D
Parameters:
reverseTransform - �t�ϊ�����̂ł���� true?A�����łȂ���� false
transformationOperator - �􉽓I�ϊ����Z�q
transformedGeometries - ��ɓ��l�̕ϊ���{�����􉽗v�f��܂ރn�b�V���e?[�u��
Returns:
�ϊ���̊􉽗v�f

output

protected void output(java.io.PrintWriter writer,
                      int indent)
?o�̓X�g��?[���Ɍ`?�?���?o�͂���?B

Specified by:
output in class GeometryElement
Parameters:
writer - PrintWriter
indent - �C���f���g��?[��
See Also:
GeometryElement