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opennurbs_curve.h
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/* $NoKeywords: $ */
/*
//
// Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved.
// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert
// McNeel & Associates.
//
// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.
// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF
// MERCHANTABILITY ARE HEREBY DISCLAIMED.
//
// For complete openNURBS copyright information see <http://www.opennurbs.org>.
//
////////////////////////////////////////////////////////////////
*/
////////////////////////////////////////////////////////////////
//
// Definition of virtual parametric curve
//
////////////////////////////////////////////////////////////////
#if !defined(OPENNURBS_CURVE_INC_)
#define OPENNURBS_CURVE_INC_
////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////
class ON_CLASS ON_MeshCurveParameters
{
public:
ON_MeshCurveParameters();
// If main_seg_count <= 0, then both these parameters are ignored.
// If main_seg_count > 0, then sub_seg_count must be >= 1. In this
// case the curve will be broken into main_seg_count equally spaced
// chords. If needed, each of these chords can be split into as many
// sub_seg_count sub-parts if the subdivision is necessary for the
// mesh to meet the other meshing constraints. In particular, if
// sub_seg_count = 0, then the curve is broken into main_seg_count
// pieces and no further testing is performed.
int m_main_seg_count;
int m_sub_seg_count;
int m_reserved1;
int m_reserved2;
// Maximum angle (in radians) between unit tangents at adjacent
// vertices.
double m_max_ang_radians;
// Maximum permitted value of
// distance chord midpoint to curve) / (length of chord)
double m_max_chr;
// If max_aspect < 1.0, the parameter is ignored.
// If 1 <= max_aspect < sqrt(2), it is treated as if
// max_aspect = sqrt(2).
// This parameter controls the maximum permitted value of
// (length of longest chord) / (length of shortest chord)
double m_max_aspect;
// If tolerance = 0, the parameter is ignored.
// This parameter controls the maximum permitted value of the
// distance from the curve to the mesh.
double m_tolerance;
// If m_min_edge_length = 0, the parameter is ignored.
// This parameter controls the minimum permitted edge length.
double m_min_edge_length;
// If max_edge_length = 0, the parameter is ignored.
// This parameter controls the maximum permitted edge length.
double m_max_edge_length;
double m_reserved3;
double m_reserved4;
};
/*
Description:
ON_Curve is a pure virtual class for curve objects
- Any class derived from ON_Curve should have a
ON_OBJECT_DECLARE(ON_...);
at the beginning of its class definition and a
ON_OBJECT_IMPLEMENT( ON_..., ON_Curve );
in a .cpp file.
Example:
- See the definition of ON_NurbsCurve for an example.
*/
class ON_CLASS ON_Curve : public ON_Geometry
{
ON_OBJECT_DECLARE(ON_Curve);
public:
ON_Curve() ON_NOEXCEPT;
virtual ~ON_Curve();
ON_Curve(const ON_Curve&);
ON_Curve& operator=(const ON_Curve&);
#if defined(ON_HAS_RVALUEREF)
// rvalue copy constructor
ON_Curve( ON_Curve&& ) ON_NOEXCEPT;
// The rvalue assignment operator calls ON_Object::operator=(ON_Object&&)
// which could throw exceptions. See the implementation of
// ON_Object::operator=(ON_Object&&) for details.
ON_Curve& operator=( ON_Curve&& );
#endif
public:
// virtual ON_Object::DestroyRuntimeCache override
void DestroyRuntimeCache( bool bDelete = true ) override;
// virtual ON_Object::SizeOf override
unsigned int SizeOf() const override;
// virtual ON_Geometry override
bool EvaluatePoint( const class ON_ObjRef& objref, ON_3dPoint& P ) const override;
/*
Description:
Get a duplicate of the curve.
Returns:
A duplicate of the curve.
Remarks:
The caller must delete the returned curve.
For non-ON_CurveProxy objects, this simply duplicates the curve using
ON_Object::Duplicate.
For ON_CurveProxy objects, this duplicates the actual proxy curve
geometry and, if necessary, trims and reverse the result to that
the returned curve's parameterization and locus match the proxy curve's.
*/
virtual
ON_Curve* DuplicateCurve() const;
// Description:
// overrides virtual ON_Object::ObjectType.
// Returns:
// ON::curve_object
ON::object_type ObjectType() const override;
// virtual ON_Geometry GetTightBoundingBox override
bool GetTightBoundingBox( class ON_BoundingBox& tight_bbox, bool bGrowBox = false, const class ON_Xform* xform = nullptr ) const override;
/*
Description:
overrides virtual ON_Geometry::Transform().
ON_Curve::Transform() calls ON_Geometry::Transform(xform),
which calls ON_Object::TransformUserData(xform), and then
calls this->DestroyCurveTree().
Parameters:
xform - [in] transformation to apply to object.
Remarks:
Classes derived from ON_Curve should call
ON_Curve::Transform() to handle user data
transformations and curve tree destruction
and then transform their definition.
*/
bool Transform(
const ON_Xform& xform
) override;
////////////////////////////////////////////////////////////////////
// curve interface
// Description:
// Gets domain of the curve
// Parameters:
// t0 - [out]
// t1 - [out] domain is [*t0, *t1]
// Returns:
// true if successful.
bool GetDomain( double* t0, double* t1 ) const;
// Returns:
// domain of the curve.
virtual
ON_Interval Domain() const = 0;
/*
Description:
Set the domain of the curve.
Parameters:
domain - [in] increasing interval
Returns:
true if successful.
*/
bool SetDomain( ON_Interval domain );
// Description:
// Set the domain of the curve
// Parameters:
// t0 - [in]
// t1 - [in] new domain will be [t0,t1]
// Returns:
// true if successful.
virtual
bool SetDomain(
double t0,
double t1
);
/*
Description:
If this curve is closed, then modify it so that
the start/end point is at curve parameter t.
Parameters:
t - [in] curve parameter of new start/end point. The
returned curves domain will start at t.
min_dist - [in] Do not change if Crv(t) is within min_dist of the original seam
Returns:
true if successful, and seam was moved.
*/
bool ChangeClosedCurveSeam(
double t,
double min_dist
);
/*
Description:
If this curve is closed, then modify it so that
the start/end point is at curve parameter t.
Parameters:
t - [in] curve parameter of new start/end point. The
returned curves domain will start at t.
Returns:
true if successful.
*/
virtual
bool ChangeClosedCurveSeam(
double t
);
/*
Description:
Change the dimension of a curve.
Parameters:
desired_dimension - [in]
Returns:
true if the curve's dimension was already desired_dimension
or if the curve's dimension was successfully changed to
desired_dimension.
*/
virtual
bool ChangeDimension(
int desired_dimension
);
// Description:
// Get number of nonempty smooth (c-infinity) spans in curve
// Returns:
// Number of nonempty smooth (c-infinity) spans.
virtual
int SpanCount() const = 0;
// Description:
// Get number of parameters of "knots".
// Parameters:
// span_parameters - [out] an array of length SpanCount()+1 is filled in
// with the parameters where the curve is not smooth (C-infinity).
// Returns:
// true if successful
virtual
bool GetSpanVector(
double* span_parameters
) const = 0; //
//////////
// If t is in the domain of the curve, GetSpanVectorIndex() returns the
// span vector index "i" such that span_vector[i] <= t <= span_vector[i+1].
// The "side" parameter determines which span is selected when t is at the
// end of a span.
virtual
bool GetSpanVectorIndex(
double t , // [IN] t = evaluation parameter
int side, // [IN] side 0 = default, -1 = from below, +1 = from above
int* span_vector_index, // [OUT] span vector index
ON_Interval* span_domain // [OUT] domain of the span containing "t"
) const;
// Description:
// Returns maximum algebraic degree of any span
// or a good estimate if curve spans are not algebraic.
// Returns:
// degree
virtual
int Degree() const = 0;
// Description:
// Returns maximum algebraic degree of any span
// or a good estimate if curve spans are not algebraic.
// Returns:
// degree
virtual
bool GetParameterTolerance( // returns tminus < tplus: parameters tminus <= s <= tplus
double t, // [IN] t = parameter in domain
double* tminus, // [OUT] tminus
double* tplus // [OUT] tplus
) const;
// Description:
// Test a curve to see if the locus if its points is a line segment.
// Parameters:
// tolerance - [in] // tolerance to use when checking linearity
// Returns:
// true if the ends of the curve are farther than tolerance apart
// and the maximum distance from any point on the curve to
// the line segment connecting the curve's ends is <= tolerance.
virtual
bool IsLinear(
double tolerance = ON_ZERO_TOLERANCE
) const;
/*
Description:
Several types of ON_Curve can have the form of a polyline including
a degree 1 ON_NurbsCurve, an ON_PolylineCurve, and an ON_PolyCurve
all of whose segments are some form of polyline. IsPolyline tests
a curve to see if it can be represented as a polyline.
Parameters:
pline_points - [out] if not nullptr and true is returned, then the
points of the polyline form are returned here.
t - [out] if not nullptr and true is returned, then the parameters of
the polyline points are returned here.
Returns:
@untitled table
0 curve is not some form of a polyline
>=2 number of points in polyline form
*/
virtual
int IsPolyline(
ON_SimpleArray<ON_3dPoint>* pline_points = nullptr,
ON_SimpleArray<double>* pline_t = nullptr
) const;
// Description:
// Test a curve to see if the locus if its points is an arc or circle.
// Parameters:
// plane - [in] if not nullptr, test is performed in this plane
// arc - [out] if not nullptr and true is returned, then arc parameters
// are filled in
// tolerance - [in] tolerance to use when checking
// Returns:
// ON_Arc.m_angle > 0 if curve locus is an arc between
// specified points. If ON_Arc.m_angle is 2.0*ON_PI, then the curve
// is a circle.
virtual
bool IsArc(
const ON_Plane* plane = nullptr,
ON_Arc* arc = nullptr,
double tolerance = ON_ZERO_TOLERANCE
) const;
/*
Description:
Parameters:
t - [in] curve parameter
plane - [in]
if not nullptr, test is performed in this plane
arc - [out]
if not nullptr and true is returned, then arc parameters
are filled in
tolerance - [in]
tolerance to use when checking
t0 - [out]
if not nullptr, and then *t0 is set to the parameter
at the start of the G2 curve segment that was
tested.
t1 - [out]
if not nullptr, and then *t0 is set to the parameter
at the start of the G2 curve segment that was
tested.
Returns:
True if the paramter t is on a arc segment of the curve.
*/
bool IsArcAt(
double t,
const ON_Plane* plane = 0,
ON_Arc* arc = 0,
double tolerance = ON_ZERO_TOLERANCE,
double* t0 = 0,
double* t1 = 0
) const;
virtual
bool IsEllipse(
const ON_Plane* plane = nullptr,
ON_Ellipse* ellipse = nullptr,
double tolerance = ON_ZERO_TOLERANCE
) const;
// Description:
// Test a curve to see if it is planar.
// Parameters:
// plane - [out] if not nullptr and true is returned,
// the plane parameters are filled in.
// tolerance - [in] tolerance to use when checking
// Returns:
// true if there is a plane such that the maximum distance from
// the curve to the plane is <= tolerance.
virtual
bool IsPlanar(
ON_Plane* plane = nullptr,
double tolerance = ON_ZERO_TOLERANCE
) const;
// Description:
// Test a curve to see if it lies in a specific plane.
// Parameters:
// test_plane - [in]
// tolerance - [in] tolerance to use when checking
// Returns:
// true if the maximum distance from the curve to the
// test_plane is <= tolerance.
virtual
bool IsInPlane(
const ON_Plane& test_plane,
double tolerance = ON_ZERO_TOLERANCE
) const = 0;
/*
Description:
Decide if it makes sense to close off this curve by moving
the endpoint to the start based on start-end gap size and length
of curve as approximated by chord defined by 6 points.
Parameters:
tolerance - [in] maximum allowable distance between start and end.
if start - end gap is greater than tolerance, returns false
min_abs_size - [in] if greater than 0.0 and none of the interior sampled
points are at least min_abs_size from start, returns false.
min_rel_size - [in] if greater than 1.0 and chord length is less than
min_rel_size*gap, returns false.
Returns:
true if start and end points are close enough based on above conditions.
*/
bool IsClosable(
double tolerance,
double min_abs_size = 0.0,
double min_rel_size = 10.0
) const;
// Description:
// Test a curve to see if it is closed.
// Returns:
// true if the curve is closed.
virtual
bool IsClosed() const;
// Description:
// Test a curve to see if it is periodic.
// Returns:
// true if the curve is closed and at least C2 at the start/end.
virtual
bool IsPeriodic() const;
/*
Description:
Search for a derivatitive, tangent, or curvature
discontinuity.
Parameters:
c - [in] type of continity to test for.
t0 - [in] Search begins at t0. If there is a discontinuity
at t0, it will be ignored. This makes it
possible to repeatedly call GetNextDiscontinuity
and step through the discontinuities.
t1 - [in] (t0 != t1) If there is a discontinuity at t1 is
will be ingored unless c is a locus discontinuity
type and t1 is at the start or end of the curve.
t - [out] if a discontinuity is found, then *t reports the
parameter at the discontinuity.
hint - [in/out] if GetNextDiscontinuity will be called
repeatedly, passing a "hint" with initial value *hint=0
will increase the speed of the search.
dtype - [out] if not nullptr, *dtype reports the kind of
discontinuity found at *t. A value of 1 means the first
derivative or unit tangent was discontinuous. A value
of 2 means the second derivative or curvature was
discontinuous. A value of 0 means teh curve is not
closed, a locus discontinuity test was applied, and
t1 is at the start of end of the curve.
If 'c', the type of continuity to test for
is ON::continuity::Gsmooth_continuous and the curvature changes
from curved to 0 or 0 to curved and there is no
tangency kink dtype is returns 3
cos_angle_tolerance - [in] default = cos(1 degree) Used only
when c is ON::continuity::G1_continuous or ON::continuity::G2_continuous. If the
cosine of the angle between two tangent vectors is
<= cos_angle_tolerance, then a G1 discontinuity is reported.
curvature_tolerance - [in] (default = ON_SQRT_EPSILON) Used
only when c is ON::continuity::G2_continuous. If K0 and K1 are
curvatures evaluated from above and below and
|K0 - K1| > curvature_tolerance, then a curvature
discontinuity is reported.
Returns:
Parametric continuity tests c = (C0_continuous, ..., G2_continuous):
true if a parametric discontinuity was found strictly
between t0 and t1. Note well that all curves are
parametrically continuous at the ends of their domains.
Locus continuity tests c = (C0_locus_continuous, ...,G2_locus_continuous):
true if a locus discontinuity was found strictly between
t0 and t1 or at t1 is the at the end of a curve.
Note well that all open curves (IsClosed()=false) are locus
discontinuous at the ends of their domains. All closed
curves (IsClosed()=true) are at least C0_locus_continuous at
the ends of their domains.
*/
virtual
bool GetNextDiscontinuity(
ON::continuity c,
double t0,
double t1,
double* t,
int* hint=nullptr,
int* dtype=nullptr,
double cos_angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE_COSINE,
double curvature_tolerance=ON_SQRT_EPSILON
) const;
/*
Description:
Test continuity at a curve parameter value.
Parameters:
c - [in] type of continuity to test for. Read ON::continuity
comments for details.
t - [in] parameter to test
hint - [in] evaluation hint
point_tolerance - [in] if the distance between two points is
greater than point_tolerance, then the curve is not C0.
d1_tolerance - [in] if the difference between two first derivatives is
greater than d1_tolerance, then the curve is not C1.
d2_tolerance - [in] if the difference between two second derivatives is
greater than d2_tolerance, then the curve is not C2.
cos_angle_tolerance - [in] default = cos(1 degree) Used only when
c is ON::continuity::G1_continuous or ON::continuity::G2_continuous. If the cosine
of the angle between two tangent vectors
is <= cos_angle_tolerance, then a G1 discontinuity is reported.
curvature_tolerance - [in] (default = ON_SQRT_EPSILON) Used only when
c is ON::continuity::G2_continuous or ON::continuity::Gsmooth_continuous.
ON::continuity::G2_continuous:
If K0 and K1 are curvatures evaluated
from above and below and |K0 - K1| > curvature_tolerance,
then a curvature discontinuity is reported.
ON::continuity::Gsmooth_continuous:
If K0 and K1 are curvatures evaluated from above and below
and the angle between K0 and K1 is at least twice angle tolerance
or ||K0| - |K1|| > (max(|K0|,|K1|) > curvature_tolerance,
then a curvature discontinuity is reported.
Returns:
true if the curve has at least the c type continuity at
the parameter t.
*/
virtual
bool IsContinuous(
ON::continuity c,
double t,
int* hint = nullptr,
double point_tolerance=ON_ZERO_TOLERANCE,
double d1_tolerance=ON_ZERO_TOLERANCE,
double d2_tolerance=ON_ZERO_TOLERANCE,
double cos_angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE_COSINE,
double curvature_tolerance=ON_SQRT_EPSILON
) const;
// Description:
// Reverse the direction of the curve.
// Returns:
// true if curve was reversed.
// Remarks:
// If reveresed, the domain changes from [a,b] to [-b,-a]
virtual
bool Reverse()=0;
/*
Description:
Force the curve to start at a specified point.
Parameters:
start_point - [in]
Returns:
true if successful.
Remarks:
Some end points cannot be moved. Be sure to check return
code.
ON_Curve::SetStartPoint() returns true if start_point is the same as the start of the curve,
false otherwise.
See Also:
ON_Curve::SetEndPoint
ON_Curve::PointAtStart
ON_Curve::PointAtEnd
*/
virtual
bool SetStartPoint(
ON_3dPoint start_point
);
/*
Description:
Force the curve to end at a specified point.
Parameters:
end_point - [in]
Returns:
true if successful.
Remarks:
Some end points cannot be moved. Be sure to check return
code.
ON_Curve::SetEndPoint() returns true if end_point is the same as the end of the curve,
false otherwise.
See Also:
ON_Curve::SetStartPoint
ON_Curve::PointAtStart
ON_Curve::PointAtEnd
*/
virtual
bool SetEndPoint(
ON_3dPoint end_point
);
// Description:
// Evaluate point at a parameter.
// Parameters:
// t - [in] evaluation parameter
// Returns:
// Point (location of curve at the parameter t).
// Remarks:
// No error handling.
// See Also:
// ON_Curve::EvPoint
// ON_Curve::PointAtStart
// ON_Curve::PointAtEnd
ON_3dPoint PointAt(
double t
) const;
// Description:
// Evaluate point at the start of the curve.
// Parameters:
// t - [in] evaluation parameter
// Returns:
// Point (location of the start of the curve.)
// Remarks:
// No error handling.
// See Also:
// ON_Curve::PointAt
ON_3dPoint PointAtStart() const;
// Description:
// Evaluate point at the end of the curve.
// Parameters:
// t - [in] evaluation parameter
// Returns:
// Point (location of the end of the curve.)
// Remarks:
// No error handling.
// See Also:
// ON_Curve::PointAt
ON_3dPoint PointAtEnd() const;
// Description:
// Evaluate first derivative at a parameter.
// Parameters:
// t - [in] evaluation parameter
// Returns:
// First derivative of the curve at the parameter t.
// Remarks:
// No error handling.
// See Also:
// ON_Curve::Ev1Der
ON_3dVector DerivativeAt(
double t
) const;
// Description:
// Evaluate unit tangent vector at a parameter.
// Parameters:
// t - [in] evaluation parameter
// Returns:
// Unit tangent vector of the curve at the parameter t.
// Remarks:
// No error handling.
// See Also:
// ON_Curve::EvTangent
ON_3dVector TangentAt(
double t
) const;
// Description:
// Evaluate the curvature vector at a parameter.
// Parameters:
// t - [in] evaluation parameter
// Returns:
// curvature vector of the curve at the parameter t.
// Remarks:
// No error handling.
// See Also:
// ON_Curve::EvCurvature
ON_3dVector CurvatureAt(
double t
) const;
// Description:
// Return a 3d frame at a parameter.
// Parameters:
// t - [in] evaluation parameter
// plane - [out] the frame is returned here
// Returns:
// true if successful
// See Also:
// ON_Curve::PointAt, ON_Curve::TangentAt,
// ON_Curve::Ev1Der, Ev2Der
bool FrameAt( double t, ON_Plane& plane) const;
// Description:
// Evaluate point at a parameter with error checking.
// Parameters:
// t - [in] evaluation parameter
// point - [out] value of curve at t
// side - [in] optional - determines which side to evaluate from
// =0 default
// <0 to evaluate from below,
// >0 to evaluate from above
// hint - [in/out] optional evaluation hint used to speed repeated evaluations
// Returns:
// false if unable to evaluate.
// See Also:
// ON_Curve::PointAt
// ON_Curve::EvTangent
// ON_Curve::Evaluate
bool EvPoint(
double t,
ON_3dPoint& point,
int side = 0,
int* hint = 0
) const;
// Description:
// Evaluate first derivative at a parameter with error checking.
// Parameters:
// t - [in] evaluation parameter
// point - [out] value of curve at t
// first_derivative - [out] value of first derivative at t
// side - [in] optional - determines which side to evaluate from
// =0 default
// <0 to evaluate from below,
// >0 to evaluate from above
// hint - [in/out] optional evaluation hint used to speed repeated evaluations
// Returns:
// false if unable to evaluate.
// See Also:
// ON_Curve::EvPoint
// ON_Curve::Ev2Der
// ON_Curve::EvTangent
// ON_Curve::Evaluate
bool Ev1Der(
double t,
ON_3dPoint& point,
ON_3dVector& first_derivative,
int side = 0,
int* hint = 0
) const;
// Description:
// Evaluate second derivative at a parameter with error checking.
// Parameters:
// t - [in] evaluation parameter
// point - [out] value of curve at t
// first_derivative - [out] value of first derivative at t
// second_derivative - [out] value of second derivative at t
// side - [in] optional - determines which side to evaluate from
// =0 default
// <0 to evaluate from below,
// >0 to evaluate from above
// hint - [in/out] optional evaluation hint used to speed repeated evaluations
// Returns:
// false if unable to evaluate.
// See Also:
// ON_Curve::Ev1Der
// ON_Curve::EvCurvature
// ON_Curve::Evaluate
bool Ev2Der(
double t,
ON_3dPoint& point,
ON_3dVector& first_derivative,
ON_3dVector& second_derivative,
int side = 0,
int* hint = 0
) const;
/*
Description:
Evaluate unit tangent at a parameter with error checking.
Parameters:
t - [in] evaluation parameter
point - [out] value of curve at t
tangent - [out] value of unit tangent
side - [in] optional - determines which side to evaluate from
=0 default
<0 to evaluate from below,
>0 to evaluate from above
hint - [in/out] optional evaluation hint used to speed repeated evaluations
Returns:
false if unable to evaluate.
See Also:
ON_Curve::TangentAt
ON_Curve::Ev1Der
*/
bool EvTangent(
double t,
ON_3dPoint& point,
ON_3dVector& tangent,
int side = 0,
int* hint = 0
) const;
/*
Description:
Evaluate unit tangent and curvature at a parameter with error checking.
Parameters:
t - [in] evaluation parameter
point - [out] value of curve at t
tangent - [out] value of unit tangent
kappa - [out] value of curvature vector
side - [in] optional - determines which side to evaluate from
=0 default
<0 to evaluate from below,
>0 to evaluate from above
hint - [in/out] optional evaluation hint used to speed repeated evaluations
Returns:
false if unable to evaluate.
See Also:
ON_Curve::CurvatureAt
ON_Curve::Ev2Der
ON_EvCurvature
*/
bool EvCurvature(
double t,
ON_3dPoint& point,
ON_3dVector& tangent,
ON_3dVector& kappa,
int side = 0,
int* hint = 0
) const;
/*
Description:
This evaluator actually does all the work. The other ON_Curve
evaluation tools call this virtual function.
Parameters:
t - [in] evaluation parameter ( usually in Domain() ).
der_count - [in] (>=0) number of derivatives to evaluate
v_stride - [in] (>=Dimension()) stride to use for the v[] array
v - [out] array of length (der_count+1)*v_stride
curve(t) is returned in (v[0],...,v[m_dim-1]),
curve'(t) is retuned in (v[v_stride],...,v[v_stride+m_dim-1]),
curve"(t) is retuned in (v[2*v_stride],...,v[2*v_stride+m_dim-1]),
etc.
side - [in] optional - determines which side to evaluate from
=0 default
<0 to evaluate from below,
>0 to evaluate from above
hint - [in/out] optional evaluation hint used to speed repeated evaluations
Returns:
false if unable to evaluate.
See Also:
ON_Curve::EvPoint
ON_Curve::Ev1Der
ON_Curve::Ev2Der
*/
virtual
bool Evaluate(
double t,
int der_count,
int v_stride,
double* v,
int side = 0,
int* hint = 0
) const = 0;
/*
Parameters:
min_length -[in]
minimum length of a linear span
tolerance -[in]
distance tolerance to use when checking linearity.
Returns
true if the span is a non-degenrate line. This means:
- dimension = 2 or 3
- The length of the the line segment from the span's initial
point to the span's control point is >= min_length.
- The maximum distance from the line segment to the span
is <= tolerance and the span increases monotonically
in the direction of the line segment.
*/
bool FirstSpanIsLinear(
double min_length,
double tolerance
) const;
bool LastSpanIsLinear(
double min_length,
double tolerance
) const;
bool FirstSpanIsLinear(
double min_length,
double tolerance,
ON_Line* span_line
) const;
bool LastSpanIsLinear(
double min_length,
double tolerance,
ON_Line* span_line
) const;
// Description:
// Removes portions of the curve outside the specified interval.
// Parameters:
// domain - [in] interval of the curve to keep. Portions of the
// curve before curve(domain[0]) and after curve(domain[1]) are
// removed.
// Returns:
// true if successful.
virtual
bool Trim(
const ON_Interval& domain
);
// Description:
// Pure virtual function. Default returns false.
// Where possible, analytically extends curve to include domain.
// Parameters:
// domain - [in] if domain is not included in curve domain,
// curve will be extended so that its domain includes domain.
// Will not work if curve is closed. Original curve is identical
// to the restriction of the resulting curve to the original curve domain,
// Returns:
// true if successful.
virtual
bool Extend(
const ON_Interval& domain
);
/*
Description:
Splits (divides) the curve at the specified parameter.
The parameter must be in the interior of the curve's domain.
The pointers passed to Split must either be nullptr or point to
an ON_Curve object of the same type. If the pointer is nullptr,
then a curve will be created in Split(). You may pass "this"
as left_side or right_side.
Parameters:
t - [in] parameter to split the curve at in the
interval returned by Domain().
left_side - [out] left portion of curve returned here
right_side - [out] right portion of curve returned here
Returns:
true - The curve was split into two pieces.
false - The curve could not be split. For example if the parameter is
too close to an endpoint.
Example:
For example, if crv were an ON_NurbsCurve, then
ON_NurbsCurve right_side;
crv.Split( crv.Domain().Mid() &crv, &right_side );
would split crv at the parametric midpoint, put the left side
in crv, and return the right side in right_side.
*/
virtual
bool Split(
double t,
ON_Curve*& left_side,
ON_Curve*& right_side
) const;
/*
Description:
Get a NURBS curve representation of this curve.
Parameters:
nurbs_curve - [out] NURBS representation returned here
tolerance - [in] tolerance to use when creating NURBS
representation.
subdomain - [in] if not nullptr, then the NURBS representation
for this portion of the curve is returned.
Returns:
0 unable to create NURBS representation