org.jscience.mathematics.geometry
Class PureBezierSurface3D

java.lang.Object
  extended by org.jscience.mathematics.geometry.GeometryElement
      extended by org.jscience.mathematics.geometry.AbstractParametricSurface
          extended by org.jscience.mathematics.geometry.ParametricSurface3D
              extended by org.jscience.mathematics.geometry.BoundedSurface3D
                  extended by org.jscience.mathematics.geometry.FreeformSurfaceWithControlPoints3D
                      extended by org.jscience.mathematics.geometry.PureBezierSurface3D
All Implemented Interfaces:
java.io.Serializable

public class PureBezierSurface3D
extends FreeformSurfaceWithControlPoints3D

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

        m = U ����?���_��?� - 1
        n = V ����?���_��?� - 1
        bi,j = controlPoints[i][j]
        wi,j = weights[i][j]
 
�Ƃ���?A��L�?�x�W�G�Ȗʂ�
        P(u, v) = ((bi,j * Bm,i(u)) �̑?�a) * Bn,j(v) �̑?�a      (i = 0, ..., m, j = 0, ..., n)
 
�L�?�x�W�G�Ȗʂ�
                  ((wi,j * bi,j * Bm,i(u)) �̑?�a) * Bn,j(v) �̑?�a
        P(u, v) = -------------------------------------------------     (i = 0, ..., m, j = 0, ..., n)
                  ((wi,j * Bm,i(u)) �̑?�a) * Bn,j(v) �̑?�a
 
������ Bm,i(u), Bn,j(v) �̓o?[���X�^�C������?��ł���?B

See Also:
Serialized Form

Field Summary
 
Fields inherited from class org.jscience.mathematics.geometry.FreeformSurfaceWithControlPoints3D
controlPoints, weights
 
Constructor Summary
PureBezierSurface3D(Point3D[][] controlPoints)
          ?
PureBezierSurface3D(Point3D[][] controlPoints, double[][] weights)
          ?
 
Method Summary
 Point3D coordinates(double uParam, double vParam)
          ���̋Ȗʂ�?
protected  ParametricSurface3D doTransformBy(boolean reverseTransform, CartesianTransformationOperator3D transformationOperator, java.util.Hashtable transformedGeometries)
          ���̋Ȗʂ�?
 SurfaceDerivative3D evaluation(double uParam, double vParam)
          ���̋Ȗʂ�?
 IntersectionPoint3D[] intersect(ParametricCurve3D mate)
          ���̋ȖʂƑ��̋�?
 SurfaceSurfaceInterference3D[] intersect(ParametricSurface3D mate)
          ���̋ȖʂƑ��̋Ȗʂ̌�?
 BsplineSurface3D offsetByBsplineSurface(ParameterSection uPint, ParameterSection vPint, double magni, int side, ToleranceForDistance tol)
          ���̋Ȗʂ̎w��� (�p���??
protected  void output(java.io.PrintWriter writer, int indent)
          ?
 PointOnSurface3D[] projectFrom(Point3D point)
          �^����ꂽ�_���炱�̋Ȗʂւ̓��e�_��?
 Vector3D[] tangentVector(double uParam, double vParam)
          ���̋Ȗʂ�?
 BsplineSurface3D toBsplineSurface()
          ���� (��`�̃p���??
 BsplineSurface3D toBsplineSurface(ParameterSection uPint, ParameterSection vPint)
          ���̋Ȗʂ̎w��� (�p���??
 Mesh3D toMesh(ParameterSection uPint, ParameterSection vPint, ToleranceForDistance tol)
          ���̋Ȗʂ̎w��� (�p���??
 Mesh3D toMesh(ToleranceForDistance tol)
          ���� (��`�̃p���??
 java.util.Vector toNonStructuredPoints(ParameterSection uParameterSection, ParameterSection vParameterSection, double tolerance, double[] scalingFactor)
          ���̋Ȗʂ̎w��� (�p���??
 PureBezierSurface3D truncate(ParameterSection uSection, ParameterSection vSection)
          ���̃x�W�G�Ȗʂ�?
 int uDegree()
          ���̋Ȗʂ� U ���̎�?
 PureBezierSurface3D[] uDivide(double uParam)
          ���̋Ȗʂ�?
 PureBezierSurface3D uElevateOneDegree()
          ���̋Ȗʂ�?
 ParametricCurve3D uIsoParametricCurve(double uParam)
          ���̋Ȗʂ� U �p���??
 int vDegree()
          ���̋Ȗʂ� V ���̎�?
 PureBezierSurface3D[] vDivide(double vParam)
          ���̋Ȗʂ�?
 PureBezierSurface3D vElevateOneDegree()
          ���̋Ȗʂ�?
 ParametricCurve3D vIsoParametricCurve(double vParam)
          ���̋Ȗʂ� V �p���??
 
Methods inherited from class org.jscience.mathematics.geometry.FreeformSurfaceWithControlPoints3D
allocateDoubleArray, controlPointAt, controlPoints, convRational0Deriv, convRational1Deriv, convRational2Deriv, isFreeform, isPolynomial, isRational, makeUniformWeights, nControlPoints, setCoordinatesToDoubleArray, toDoubleArray, uNControlPoints, vNControlPoints, weightAt, weights
 
Methods inherited from class org.jscience.mathematics.geometry.BoundedSurface3D
fillet, offsetByBsplineSurface
 
Methods inherited from class org.jscience.mathematics.geometry.ParametricSurface3D
curvature, dimension, fillet, is3D, nearestProjectFrom, nearestProjectWithDistanceFrom, normalVector, pointToParameter, reverseTransformBy, transformBy, transformBy
 
Methods inherited from class org.jscience.mathematics.geometry.AbstractParametricSurface
checkUValidity, checkUValidity, checkVValidity, checkVValidity, isParametric, isSurface, isUFinite, isUInfinite, isUNonPeriodic, isUPeriodic, isValidUParameter, isValidVParameter, isVFinite, isVInfinite, isVNonPeriodic, isVPeriodic, uParameterDomain, vParameterDomain
 
Methods inherited from class org.jscience.mathematics.geometry.GeometryElement
getClassName, getToleranceForAngle, getToleranceForAngleAsObject, getToleranceForDistance, getToleranceForDistance2, getToleranceForDistanceAsObject, getToleranceForParameter, getToleranceForParameterAsObject, getToleranceForRealNumber, getToleranceForRealNumberAsObject, is1D, is2D, isCurve, isPlacement, isPoint, isTransformationOperator, isVector, makeIndent, output
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

PureBezierSurface3D

public PureBezierSurface3D(Point3D[][] controlPoints)
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Parameters:
controlPoints - ?���_�̔z��

PureBezierSurface3D

public PureBezierSurface3D(Point3D[][] controlPoints,
                           double[][] weights)
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���̃R���X�g���N�^��?A super(controlPoints, weights) ��Ă�?o���Ă��邾���ł���?B

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

uDegree

public int uDegree()
���̋Ȗʂ� U ���̎�?���Ԃ�?B

Returns:
U ���̎�?�

vDegree

public int vDegree()
���̋Ȗʂ� V ���̎�?���Ԃ�?B

Returns:
V ���̎�?�

coordinates

public Point3D coordinates(double uParam,
                           double vParam)
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Specified by:
coordinates in class ParametricSurface3D
Parameters:
uParam - U ���̃p���??[�^�l
vParam - V ���̃p���??[�^�l
Returns:
?W�l
See Also:
ParameterOutOfRange

tangentVector

public Vector3D[] tangentVector(double uParam,
                                double vParam)
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Specified by:
tangentVector in class ParametricSurface3D
Parameters:
uParam - U ���̃p���??[�^�l
vParam - V ���̃p���??[�^�l
Returns:
?ڃx�N�g��
See Also:
ParameterOutOfRange

evaluation

public SurfaceDerivative3D evaluation(double uParam,
                                      double vParam)
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Specified by:
evaluation in class ParametricSurface3D
Parameters:
uParam - U ���̃p���??[�^�l
vParam - V ���̃p���??[�^�l
Returns:
����?�
See Also:
ParameterOutOfRange

projectFrom

public PointOnSurface3D[] projectFrom(Point3D point)
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Specified by:
projectFrom in class ParametricSurface3D
Parameters:
point - ���e���̓_
Returns:
���e�_�̔z��

toMesh

public Mesh3D toMesh(ParameterSection uPint,
                     ParameterSection vPint,
                     ToleranceForDistance tol)
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�^����ꂽ�p���??[�^��Ԃ���`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Specified by:
toMesh in class ParametricSurface3D
Parameters:
uPint - U ���̃p���??[�^���
vPint - V ���̃p���??[�^���
tol - �����̋��e��?�
Returns:
���̋Ȗʂ̎w��̋�Ԃ𕽖ʋߎ�����i�q�_�Q
See Also:
PointOnSurface3D, ParameterOutOfRange, truncate(ParameterSection,ParameterSection), toMesh(ToleranceForDistance)

toMesh

public Mesh3D toMesh(ToleranceForDistance tol)
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Specified by:
toMesh in class BoundedSurface3D
Parameters:
tol - �����̋��e��?�
Returns:
���̗L� ȖʑS�̂𕽖ʋߎ�����i�q�_�Q
See Also:
PointOnSurface3D

toBsplineSurface

public BsplineSurface3D toBsplineSurface()
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Overrides:
toBsplineSurface in class BoundedSurface3D
Returns:
���̗L� ȖʑS�̂�?Č�����L�? Bspline �Ȗ�

toBsplineSurface

public BsplineSurface3D toBsplineSurface(ParameterSection uPint,
                                         ParameterSection vPint)
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�^����ꂽ�p���??[�^��Ԃ���`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Specified by:
toBsplineSurface in class ParametricSurface3D
Parameters:
uPint - U ���̃p���??[�^���
vPint - V ���̃p���??[�^���
Returns:
���̋Ȗʂ̎w��̋�Ԃ�?Č�����L�? Bspline �Ȗ�
See Also:
ParameterOutOfRange, truncate(ParameterSection,ParameterSection), toBsplineSurface()

intersect

public IntersectionPoint3D[] intersect(ParametricCurve3D mate)
                                throws IndefiniteSolutionException
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Specified by:
intersect in class ParametricSurface3D
Parameters:
mate - ���̋�?�
Returns:
��_�̔z��
Throws:
IndefiniteSolutionException - �⪕s��ł���

intersect

public SurfaceSurfaceInterference3D[] intersect(ParametricSurface3D mate)
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��Ȗʂ���?������?��ɂ‚��Ă�?A��?� (IntersectionCurve3D) ���Ԃ�?B

��Ȗʂ�?ڂ����?��ɂ‚��Ă�?A��_ (IntersectionPoint3D) ���Ԃ邱�Ƃ�����?B

Specified by:
intersect in class ParametricSurface3D
Parameters:
mate - ���̋Ȗ�
Returns:
��?� (�܂��͌�_) �̔z��
See Also:
IntersectionCurve3D, IntersectionPoint3D

offsetByBsplineSurface

public BsplineSurface3D offsetByBsplineSurface(ParameterSection uPint,
                                               ParameterSection vPint,
                                               double magni,
                                               int side,
                                               ToleranceForDistance tol)
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Specified by:
offsetByBsplineSurface in class ParametricSurface3D
Parameters:
uPint - U ���̃p���??[�^���
vPint - V ���̃p���??[�^���
magni - �I�t�Z�b�g��
side - �I�t�Z�b�g�̌� (WhichSide.FRONT/BACK)
tol - �����̋��e��?�
Returns:
���̋Ȗʂ̎w��̋�`��Ԃ̃I�t�Z�b�g�Ȗʂ�ߎ����� Bspline �Ȗ�
See Also:
WhichSide

uIsoParametricCurve

public ParametricCurve3D uIsoParametricCurve(double uParam)
Description copied from class: ParametricSurface3D
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Specified by:
uIsoParametricCurve in class ParametricSurface3D
Parameters:
uParam - U ���̃p���??[�^�l
Returns:
�w��� U �p���??[�^�l�ł̓��p���??[�^��?�

vIsoParametricCurve

public ParametricCurve3D vIsoParametricCurve(double vParam)
Description copied from class: ParametricSurface3D
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Specified by:
vIsoParametricCurve in class ParametricSurface3D
Parameters:
vParam - V ���̃p���??[�^�l
Returns:
�w��� V �p���??[�^�l�ł̓��p���??[�^��?�

uDivide

public PureBezierSurface3D[] uDivide(double uParam)
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Parameters:
uParam - U ���̃p���??[�^�l
Returns:
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See Also:
ParameterOutOfRange, vDivide(double)

vDivide

public PureBezierSurface3D[] vDivide(double vParam)
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Parameters:
vParam - V ���̃p���??[�^�l
Returns:
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See Also:
ParameterOutOfRange, uDivide(double)

truncate

public PureBezierSurface3D truncate(ParameterSection uSection,
                                    ParameterSection vSection)
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�^����ꂽ�p���??[�^��Ԃ���`���O��Ă���?�?��ɂ�?A ParameterOutOfRange �̗�O��?�����?B

Parameters:
uSection - ?ؒf���Ďc��������\�� U ���̃p���??[�^���
vSection - ?ؒf���Ďc��������\�� V ���̃p���??[�^���
Returns:
?ؒf���Ďc����������\���x�W�G�Ȗ�
See Also:
ParameterOutOfRange

uElevateOneDegree

public PureBezierSurface3D uElevateOneDegree()
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Returns:
����`?��?AU ���̎�?������?オ�B��Ȗ�

vElevateOneDegree

public PureBezierSurface3D vElevateOneDegree()
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Returns:
����`?��?AV ���̎�?������?オ�B��Ȗ�

toNonStructuredPoints

public java.util.Vector toNonStructuredPoints(ParameterSection uParameterSection,
                                              ParameterSection vParameterSection,
                                              double tolerance,
                                              double[] scalingFactor)
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?��?���ʂƂ��ē�����_�Q�͈�ʂ�?A�ʑ��I�ɂ�􉽓I�ɂ�?A�i�q?�ł͂Ȃ�?B

scalingFactor ��?A��͗p�ł͂Ȃ�?A?o�͗p�̈�?��ł���?B scalingFactor �ɂ�?A�v�f?� 2 �̔z���^����?B scalingFactor[0] �ɂ� U ����?k�ڔ{��?A scalingFactor[1] �ɂ� V ����?k�ڔ{�����Ԃ�?B �����̒l�͉��炩��?�Βl�ł͂Ȃ�?A �p���??[�^��?i�ޑ��x T �ɑ΂���?A U/V �����ɂ‚��Ď ��?�ŋȖ�?�̓_��?i�ޑ��x Pu/Pv ��\�����Βl�ł���?B �‚܂�?A�p���??[�^�� T ����?i�ނ�?A � ��?�ł̋Ȗ�?�̓_�� U ���ł� Pu (scalingFactor[0])?A V ���ł� Pv (scalingFactor[1]) ����?i�ނ��Ƃ�\���Ă���?B T �̑傫���͖�������Ȃ��̂�?A���̒l��Q?Ƃ���?ۂɂ�?A scalingFactor[0] �� scalingFactor[1] �̔䂾����p����ׂ��ł���?B �Ȃ�?A�����̒l�͂����܂ł�ڈł���?A�����ȑ��x����̂ł͂Ȃ�?B

���ʂƂ��ĕԂ� Vector �Ɋ܂܂��e�v�f�� ���̋Ȗʂ�x?[�X�Ƃ��� PointOnSurface3D �ł��邱�Ƃ���҂ł���?B

Specified by:
toNonStructuredPoints in class ParametricSurface3D
Parameters:
uParameterSection - U ���̃p���??[�^���
vParameterSection - V ���̃p���??[�^���
tolerance - �����̋��e��?�
scalingFactor - �_�Q��O�p�`��������?ۂɗL�p�Ǝv���� U/V ��?k�ڔ{��
Returns:
�_�Q��܂� Vector
See Also:
PointOnSurface3D

doTransformBy

protected ParametricSurface3D doTransformBy(boolean reverseTransform,
                                            CartesianTransformationOperator3D transformationOperator,
                                            java.util.Hashtable transformedGeometries)
���̋Ȗʂ�?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 ParametricSurface3D
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