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opennurbs_curve.h
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opennurbs_curve.h
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//
// Copyright (c) 1993-2022 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;
/// <summary>
/// The curve's span vector is a stricltly monotone increasing list of doubles
/// that are the intervals on which the curve is C-infinity.
/// </summary>
/// <returns>
/// The curve's span vector.
/// </returns>
const ON_SimpleArray<double> SpanVector() 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 parameter 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 checkin
// Note:
// If the curve is a simple planar closed curve the plane
// orientation agrees with the curve orientation.
// 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 derivative, 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 ignored 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 the 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 reversed, 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:
// Evaluate the signed curvature of a planar curve at a parameter.
// Parameters:
// t - [in] evaluation parameter
// plane_normal - [in] oriented plane unit normal,
// defaults to ON_3dVector(0,0,1) for curve in xy-plane
// Returns:
// signed curvature of a planar curve at the parameter t.
// Remarks:
// No error handling.
// See Also:
// ON_Curve::EvSignedCurvature
double SignedCurvatureAt(
double t,
const ON_3dVector* plane_normal = nullptr
) 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:
Evaluate unit tangent and signed curvature (also called oriented curvature) of a planar
curve 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 signed curvature
normal - [in] oriented unit normal of the plane containing the curve.
default of nullptr is interpreted as ON_3dVector(0,0,1)
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.
Notes:
Computes the Triple product T o ( K X N)
where T is the unit tangent, K is the curvature vector
and N is the plane unit normal. If the curve is planar this is the signed curvature for the given
plane orientation. The normal defaults to (0,0,1) for curves in the x-y plane.
See Also:
ON_Curve::CurvatureAt
ON_Curve::Ev2Der
ON_EvCurvature
*/
bool EvSignedCurvature(
double t,
ON_3dPoint& point,
ON_3dVector& tangent,
double& kappa,
const ON_3dVector* normal = nullptr,
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 returned in (v[v_stride],...,v[v_stride+m_dim-1]),
curve"(t) is returned 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-degenerate 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.