Rhino C++ API
8.13
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#include <opennurbs_arc.h>
Public Member Functions | |
ON_Arc ()=default | |
Create a radius one arc with angle = 2*pi. More... | |
ON_Arc (const ON_2dPoint &start_point, const ON_2dPoint &interior_point, const ON_2dPoint &end_point) | |
ON_Arc (const ON_3dPoint ¢er, double radius, double angle_in_radians) | |
ON_Arc (const ON_3dPoint &start_point, const ON_3dPoint &interior_point, const ON_3dPoint &end_point) | |
ON_Arc (const ON_Arc &)=default | |
ON_Arc (const ON_Circle &circle, double angle_in_radians) | |
ON_Arc (const ON_Circle &circle, ON_Interval angle_interval_in_radians) | |
ON_Arc (const ON_Plane &plane, const ON_3dPoint ¢er, double radius, double angle_in_radians) | |
ON_Arc (const ON_Plane &plane, double radius, double angle_in_radians) | |
~ON_Arc ()=default | |
double | AngleDegrees () const |
double | AngleRadians () const |
ON_BoundingBox | BoundingBox () const |
ON_3dPoint | ClosestPointTo (const ON_3dPoint &test_point) const |
bool | ClosestPointTo (const ON_3dPoint &test_point, double *t) const |
bool | Create (const ON_2dPoint &start_point, const ON_2dPoint &interior_point, const ON_2dPoint &end_point) |
bool | Create (const ON_2dPoint &start_point, const ON_2dVector &dir_at_start, const ON_2dPoint &end_point) |
bool | Create (const ON_3dPoint ¢er, double radius, double angle_in_radians) |
bool | Create (const ON_3dPoint &start_point, const ON_3dPoint &interior_point, const ON_3dPoint &end_point) |
bool | Create (const ON_3dPoint &start_point, const ON_3dVector &dir_at_start, const ON_3dPoint &end_point) |
bool | Create (const ON_Circle &circle, double angle_in_radians) |
bool | Create (const ON_Circle &circle, ON_Interval angle_interval_in_radians) |
bool | Create (const ON_Plane &plane, const ON_3dPoint ¢er, double radius, double angle_in_radians) |
bool | Create (const ON_Plane &plane, double radius, double angle_in_radians) |
ON_Interval | Domain () const |
ON_Interval | DomainDegrees () const |
ON_Interval | DomainRadians () const |
void | Dump (ON_TextLog &dump) const |
ON_3dPoint | EndPoint () const |
bool | GetBoundingBox (ON_BoundingBox &bbox, int bGrowBox=false) const |
int | GetNurbForm (ON_NurbsCurve &nurbs_curve) const |
bool | GetNurbFormParameterFromRadian (double arc_radians_parameter, double *nurbs_parameter) const |
bool | GetRadianFromNurbFormParameter (double nurbs_parameter, double *arc_radians_parameter) const |
bool | GetTightBoundingBox (ON_BoundingBox &tight_bbox, bool bGrowBox=false, const ON_Xform *xform=nullptr) const |
bool | IsCircle () const |
bool | IsLinear (double tol) const |
bool | IsValid () const |
double | Length () const |
ON_3dPoint | MidPoint () const |
ON_Arc & | operator= (const ON_Arc &)=default |
ON_Arc & | operator= (const ON_Circle &) |
bool | Reverse () |
double | SectorArea () const |
ON_3dPoint | SectorAreaCentroid () const |
double | SegmentArea () const |
ON_3dPoint | SegmentAreaCentroid () const |
bool | SetAngleDegrees (double angle_in_degrees) |
bool | SetAngleIntervalRadians (ON_Interval angle_in_radians) |
bool | SetAngleRadians (double angle_in_radians) |
ON_3dPoint | StartPoint () const |
bool | Trim (ON_Interval domain_radian) |
Public Member Functions inherited from ON_Circle | |
ON_Circle ()=default | |
ON_Circle (const ON_2dPoint &P, const ON_2dPoint &Q, const ON_2dPoint &R) | |
ON_Circle (const ON_3dPoint ¢er, double radius) | |
ON_Circle (const ON_3dPoint &P, const ON_3dPoint &Q, const ON_3dPoint &R) | |
ON_Circle (const ON_Circle &)=default | |
ON_Circle (const ON_Plane &plane, const ON_3dPoint ¢er, double radius) | |
ON_Circle (const ON_Plane &plane, double radius) | |
~ON_Circle ()=default | |
ON_BoundingBox | BoundingBox () const |
const ON_3dPoint & | Center () const |
double | Circumference () const |
ON_3dPoint | ClosestPointTo (const ON_3dPoint &point) const |
returns point on circle that is closest to given point More... | |
bool | ClosestPointTo (const ON_3dPoint &point, double *t) const |
returns parameters of point on circle that is closest to given point More... | |
bool | Create (const ON_2dPoint &P, const ON_2dPoint &Q, const ON_2dPoint &R) |
bool | Create (const ON_2dPoint &P, const ON_2dVector &tangent_at_P, const ON_2dPoint &Q) |
bool | Create (const ON_3dPoint ¢er, double radius) |
bool | Create (const ON_3dPoint &P, const ON_3dPoint &Q, const ON_3dPoint &R) |
bool | Create (const ON_3dPoint &P, const ON_3dVector &tangent_at_P, const ON_3dPoint &Q) |
bool | Create (const ON_Plane &plane, const ON_3dPoint ¢er, double radius) |
bool | Create (const ON_Plane &plane, double radius) |
ON_3dVector | DerivativeAt (int, double) const |
double | Diameter () const |
double | EquationAt (const ON_2dPoint &plane_point) const |
evaluate circle's implicit equation in plane More... | |
int | GetNurbForm (ON_NurbsCurve &nurbs_curve) const |
bool | GetNurbFormParameterFromRadian (double circle_radians_parameter, double *nurbs_parameter) const |
bool | GetRadianFromNurbFormParameter (double nurbs_parameter, double *circle_radians_parameter) const |
bool | GetTightBoundingBox (ON_BoundingBox &tight_bbox, bool bGrowBox=false, const ON_Xform *xform=nullptr) const |
ON_2dVector | GradientAt (const ON_2dPoint &plane_point) const |
bool | IsInPlane (const ON_Plane &, double=ON_ZERO_TOLERANCE) const |
bool UpdatePoints(); ///< sets m_point[] to have valid points More... | |
bool | IsValid () const |
A Valid circle has m_radius>0 and m_plane.IsValid(). More... | |
double | MaximumCoordinate () const |
///< absolute value of maximum coordinate More... | |
const ON_3dVector & | Normal () const |
ON_Circle & | operator= (const ON_Circle &)=default |
const ON_Plane & | Plane () const |
plane containing circle More... | |
ON_3dPoint | PointAt (double) const |
double | Radius () const |
bool | Reverse () |
bool | Rotate (double angle_in_radians, const ON_3dVector &axis_of_rotation) |
bool | Rotate (double angle_in_radians, const ON_3dVector &axis_of_rotation, const ON_3dPoint ¢er_of_rotation) |
bool | Rotate (double sin_angle, double cos_angle, const ON_3dVector &axis_of_rotation) |
rotate circle about its center More... | |
bool | Rotate (double sin_angle, double cos_angle, const ON_3dVector &axis_of_rotation, const ON_3dPoint ¢er_of_rotation) |
rotate circle about a point and axis More... | |
ON_3dVector | TangentAt (double) const |
bool | Transform (const ON_Xform &) |
bool | Translate (const ON_3dVector &delta) |
Static Public Attributes | |
static const ON_Arc | UnitCircle |
unit circle in the xy plane More... | |
Static Public Attributes inherited from ON_Circle | |
static const ON_Circle | UnitCircle |
unit circle in the xy plane More... | |
Friends | |
bool | ON_BinaryArchive::ReadArc (ON_Arc &) |
bool | ON_BinaryArchive::WriteArc (const ON_Arc &) |
Additional Inherited Members | |
Public Attributes inherited from ON_Circle | |
ON_Plane | plane = ON_Plane::World_xy |
double | radius = 1.0 |
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. Description: An ON_Arc is a subcurve of 3d circle. Details: The curve is parameterized by an angle expressed in radians. For an IsValid() arc the total subtended angle AngleRadians() = Domain()(1) - Domain()(0) must satisfy 0< AngleRadians() <2*Pi .
The parameterization of the ON_Arc is inherited from the ON_Circle it is derived from. In particular t -> center + cos(t)*radius*xaxis + sin(t)*radius*yaxis
where xaxis and yaxis, (part of ON_Circle::m_plane) form an orthonormal frame of the plane containing the circle.
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Create a radius one arc with angle = 2*pi.
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ON_Arc::ON_Arc | ( | const ON_Circle & | circle, |
double | angle_in_radians | ||
) |
Description: Construct an arc from a circle and an angle in radians Parameters: circle - [in] angle_in_radians - [in]
ON_Arc::ON_Arc | ( | const ON_Circle & | circle, |
ON_Interval | angle_interval_in_radians | ||
) |
Parameters: circle - [in] angle_interval_in_radians - [in] increasing angle interval in radians with angle_interval_in_radians.Length() <= 2.0*ON_PI.
ON_Arc::ON_Arc | ( | const ON_Plane & | plane, |
double | radius, | ||
double | angle_in_radians | ||
) |
Description: Construct an arc from a plane, radius and an angle in radians. The center of the arc is at the plane's origin. Parameters: plane - [in] circle is in this plane with center at m_origin center - [in] circle's center point radius - [in] angle_in_radians - [in]
ON_Arc::ON_Arc | ( | const ON_3dPoint & | center, |
double | radius, | ||
double | angle_in_radians | ||
) |
Description: Construct an arc parallel to the world XY plane from a center point, radius, and angle in radians. The arc starts at center+(radius,0,0). Parameters: center - [in] radius - [in] angle_in_radians - [in]
ON_Arc::ON_Arc | ( | const ON_Plane & | plane, |
const ON_3dPoint & | center, | ||
double | radius, | ||
double | angle_in_radians | ||
) |
Description: Construct an arc parallel to plane from a center point, radius, and angle in radians.
The arc starts at center+radius*plane.xaxis. Parameters: plane - [in] The plane x, y and z axis are used to defines the circle plane's x, y and z axis. The plane origin is ignored. center - [in] circle's center point radius - [in] angle_in_radians - [in]
ON_Arc::ON_Arc | ( | const ON_2dPoint & | start_point, |
const ON_2dPoint & | interior_point, | ||
const ON_2dPoint & | end_point | ||
) |
Description: Construct an arc that passes through three 2d points. Parameters: start_point - [in] interior_point - [in] end_point - [in]
ON_Arc::ON_Arc | ( | const ON_3dPoint & | start_point, |
const ON_3dPoint & | interior_point, | ||
const ON_3dPoint & | end_point | ||
) |
Description: Construct an arc that passes through three 3d points. Parameters: start_point - [in] interior_point - [in] end_point - [in]
double ON_Arc::AngleDegrees | ( | ) | const |
Returns: The arc's subtended angle in degrees.
double ON_Arc::AngleRadians | ( | ) | const |
Returns: The arc's subtended angle in radians.
ON_BoundingBox ON_Arc::BoundingBox | ( | ) | const |
Description: Get arc's 3d axis aligned bounding box. Returns: 3d bounding box.
ON_3dPoint ON_Arc::ClosestPointTo | ( | const ON_3dPoint & | test_point | ) | const |
Description: Get the point on the arc that is closest to test_point. Parameters: test_point - [in] Returns: The point on the arc that is closest to test_point. If test_point is the center of the arc, then the starting point of the arc is returned.
bool ON_Arc::ClosestPointTo | ( | const ON_3dPoint & | test_point, |
double * | t | ||
) | const |
Description: Get the point on the arc that is closest to test_point. Parameters: test_point - [in] t - [out] parameter (in radians) of the point on the arc that is closest to test_point. If test_point is the center of the arc, then the starting point of the arc is (arc.Domain()[0]) returned.
bool ON_Arc::Create | ( | const ON_2dPoint & | start_point, |
const ON_2dPoint & | interior_point, | ||
const ON_2dPoint & | end_point | ||
) |
Description: Create an arc that passes through three 2d points. Parameters: start_point - [in] interior_point - [in] end_point - [in]
bool ON_Arc::Create | ( | const ON_2dPoint & | start_point, |
const ON_2dVector & | dir_at_start, | ||
const ON_2dPoint & | end_point | ||
) |
Description: Create an arc from a 2d start point, 2d start direction and a 2d end point. Parameters: start_point - [in] dir_at_start - [in] end_point - [in]
bool ON_Arc::Create | ( | const ON_3dPoint & | center, |
double | radius, | ||
double | angle_in_radians | ||
) |
Description: Create an arc parallel to the world XY plane from a center point, radius, and angle in radians. The arc starts at center+(radius,0,0). Parameters: center - [in] radius - [in] angle_in_radians - [in]
bool ON_Arc::Create | ( | const ON_3dPoint & | start_point, |
const ON_3dPoint & | interior_point, | ||
const ON_3dPoint & | end_point | ||
) |
Description: Create an arc that passes through three 3d points. Parameters: start_point - [in] interior_point - [in] end_point - [in]
bool ON_Arc::Create | ( | const ON_3dPoint & | start_point, |
const ON_3dVector & | dir_at_start, | ||
const ON_3dPoint & | end_point | ||
) |
Description: Create an arc from a 3d start point, 3d start direction and a 3d end point. Parameters: start_point - [in] dir_at_start - [in] end_point - [in]
bool ON_Arc::Create | ( | const ON_Circle & | circle, |
double | angle_in_radians | ||
) |
Description: Create an arc from a circle and an angle in radians Parameters: circle - [in] angle_in_radians - [in] Returns: true if input is valid and a valid arc is created.
bool ON_Arc::Create | ( | const ON_Circle & | circle, |
ON_Interval | angle_interval_in_radians | ||
) |
Description: Create an arc from a circle and an increasing angle interval Parameters: circle - [in] angle_interval_in_radians - [in] increasing angle interval in radians with angle_interval_in_radians.Length() <= 2.0*ON_PI Returns: true if input is valid and a valid arc is created.
bool ON_Arc::Create | ( | const ON_Plane & | plane, |
const ON_3dPoint & | center, | ||
double | radius, | ||
double | angle_in_radians | ||
) |
Description: Create an arc parallel to plane from a center point, radius, and angle in radians.
The arc starts at center+radius*plane.xaxis. Parameters: plane - [in] The plane x, y and z axis are used to defines the circle plane's x, y and z axis. The plane origin is ignored. center - [in] circle's center point radius - [in] angle_in_radians - [in]
bool ON_Arc::Create | ( | const ON_Plane & | plane, |
double | radius, | ||
double | angle_in_radians | ||
) |
Description: Create an arc from a plane, radius and an angle in radians. The center of the arc is at the plane's origin. Parameters: plane - [in] circle is in this plane with center at m_origin center - [in] circle's center point radius - [in] angle_in_radians - [in]
ON_Interval ON_Arc::Domain | ( | ) | const |
Description: Get evaluation domain. Returns: Evaluation domain (same as DomainRadians()).
ON_Interval ON_Arc::DomainDegrees | ( | ) | const |
Returns: The arc's domain in degrees.
ON_Interval ON_Arc::DomainRadians | ( | ) | const |
Returns: The arc's domain in radians.
void ON_Arc::Dump | ( | ON_TextLog & | dump | ) | const |
Description: Creates a text dump of the arc listing the normal, center radius, start point, end point, and angle. Remarks: Dump() is intended for debugging and is not suitable for creating high quality text descriptions of an arc.
ON_3dPoint ON_Arc::EndPoint | ( | ) | const |
Returns: Point at end of the arc.
bool ON_Arc::GetBoundingBox | ( | ON_BoundingBox & | bbox, |
int | bGrowBox = false |
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) | const |
Description: Get arc's 3d axis aligned bounding box or the union of the input box with the arc's bounding box. Parameters: bbox - [in/out] 3d axis aligned bounding box bGrowBox - [in] (default=false) If true, then the union of the input bbox and the arc's bounding box is returned in bbox.
If false, the arc's bounding box is returned in bbox. Returns: true if arc has bounding box and calculation was successful.
int ON_Arc::GetNurbForm | ( | ON_NurbsCurve & | nurbs_curve | ) | const |
Description: Get a rational degree 2 NURBS curve representation of the arc. Note that the parameterization of NURBS curve does not match arc's transcendental parameterization. Use GetRadianFromNurbFormParameter() and GetParameterFromRadian() to convert between the NURBS curve parameter and the transcendental parameter Parameters: nurbs_curve - [out] nurbs_curve returned here. Returns: 0 for failure and 2 for success.
bool ON_Arc::GetNurbFormParameterFromRadian | ( | double | arc_radians_parameter, |
double * | nurbs_parameter | ||
) | const |
Description: Convert a arc radians parameter to a NURBS curve arc parameter. Parameters: arc_radians_parameter - [in] 0.0 to 2.0*ON_PI nurbs_parameter - [out] Example:
ON_Arc arc = ...; double arc_t = 1.2345; ///< some number in interval (0,2.0*ON_PI). double nurbs_t; arc.GetNurbFormParameterFromRadian( arc_t, &nurbs_t ); ON_NurbsCurve nurbs_curve; arc.GetNurbsForm( nurbs_curve ); arc_pt = arc.PointAt(arc_t); nurbs_pt = nurbs_curve.PointAt(nurbs_t);
/ arc_pt and nurbs_pt will be the same
Remarks: The NURBS curve parameter is with respect to the NURBS curve created by ON_Arc::GetNurbForm. At radian values of 0.0, 0.5*ON_PI, ON_PI, 1.5*ON_PI, and 2.0*ON_PI, the nurbs parameter and radian parameter are the same. At all other values the nurbs and radian parameter values are different. See Also: ON_Arc::GetNurbFormParameterFromRadian
bool ON_Arc::GetRadianFromNurbFormParameter | ( | double | nurbs_parameter, |
double * | arc_radians_parameter | ||
) | const |
Description: Convert a NURBS curve arc parameter to a arc radians parameter. Parameters: nurbs_parameter - [in] arc_radians_parameter - [out] Example:
ON_Arc arc = ...; double nurbs_t = 1.2345; ///< some number in interval (0,2.0*ON_PI). double arc_t; arc.GetRadianFromNurbFormParameter( nurbs_t, &arc_t ); ON_NurbsCurve nurbs_curve; arc.GetNurbsForm( nurbs_curve ); arc_pt = arc.PointAt(arc_t); nurbs_pt = nurbs_curve.PointAt(nurbs_t);
/ arc_pt and nurbs_pt will be the same
Remarks: The NURBS curve parameter is with respect to the NURBS curve created by ON_Arc::GetNurbForm. At nurbs parameter values of 0.0, 0.5*ON_PI, ON_PI, 1.5*ON_PI, and 2.0*ON_PI, the nurbs parameter and radian parameter are the same. At all other values the nurbs and radian parameter values are different. See Also: ON_Arc::GetNurbFormParameterFromRadian
bool ON_Arc::GetTightBoundingBox | ( | ON_BoundingBox & | tight_bbox, |
bool | bGrowBox = false , |
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const ON_Xform * | xform = nullptr |
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) | const |
Description: Get tight bounding box. Parameters: tight_bbox - [in/out] tight bounding box bGrowBox -[in] (default=false)
If true and the input tight_bbox is valid, then returned tight_bbox is the union of the input tight_bbox and the arc's tight bounding box. xform -[in] (default=nullptr) If not nullptr, the tight bounding box of the transformed arc is calculated. The arc is not modified. Returns: True if a valid tight_bbox is returned.
bool ON_Arc::IsCircle | ( | ) | const |
Returns: true if the arc is a complete circle; i.e., the arc's angle is 360 degrees.
bool ON_Arc::IsLinear | ( | double | tol | ) | const |
Returns: True if the arc is within tol of the chord and chord is longer than tol
bool ON_Arc::IsValid | ( | ) | const |
Description: Checks an arc to make sure it is valid. Detail: Radius>0 and 0<AngleRadians()<=2 ON_PI Returns: true if the arc is valid.
double ON_Arc::Length | ( | ) | const |
Returns: Length of the arc = radius*(subtended angle in radians).
ON_3dPoint ON_Arc::MidPoint | ( | ) | const |
Returns: Point at middle of the arc.
bool ON_Arc::Reverse | ( | ) |
Description: Reverse the orientation of the arc. Changes the domain from [a,b] to [-b.-a].
double ON_Arc::SectorArea | ( | ) | const |
Returns: Area of the arc's sector.
Remarks: The arc's sector is the region bounded by the arc, the line segment from the arc's end to the center, and the line segment from the center to the arc's start.
ON_3dPoint ON_Arc::SectorAreaCentroid | ( | ) | const |
Returns: Area centroid of the arc's sector.
Remarks: The arc's sector is the region bounded by the arc, the line segment from the arc's end to the center, and the line segment from the center to the arc's start.
double ON_Arc::SegmentArea | ( | ) | const |
Returns: Area of the arc's segment. Remarks: The arc's segment is the region bounded by the arc and the line segment from the arc's end to the arc's start.
ON_3dPoint ON_Arc::SegmentAreaCentroid | ( | ) | const |
Returns: Area centroid of the arc's segment.
Remarks: The arc's segment is the region bounded by the arc and the line segment from the arc's end to the arc's start.
bool ON_Arc::SetAngleDegrees | ( | double | angle_in_degrees | ) |
Description: Set arc's subtended angle in degrees. Parameters: angle_in_degrees - [in] 0 < angle_in_degrees <= 360
bool ON_Arc::SetAngleIntervalRadians | ( | ON_Interval | angle_in_radians | ) |
Description: Set arc's angle interval in radians. Parameters: angle_in_radians - [in] increasing interval with start and end angle in radians. Length of the interval <= 2.0*ON_PI. Returns: true if successful.
bool ON_Arc::SetAngleRadians | ( | double | angle_in_radians | ) |
Description: Set arc's subtended angle in radians. Parameters: angle_in_radians - [in] 0 <= angle_in_radians <= 2.0*ON_PI
ON_3dPoint ON_Arc::StartPoint | ( | ) | const |
Returns: Point at start of the arc.
bool ON_Arc::Trim | ( | ON_Interval | domain_radian | ) |
Description: Set arc's domain as a subdomain of the circle. Parameters: domain_radian - [in] 0 < domain_radian[1] - domain_radian[0] <= 2.0 * ON*PI
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unit circle in the xy plane