Class BiarcList¶

Defined in File BiarcList.hxx

Inheritance Relationships¶

Base Type¶

public G2lib::BaseCurve (Class BaseCurve)

Class Documentation¶

class G2lib::BiarcList : public G2lib::BaseCurve ¶

Class to manage a list of biarc Curve (not necessarily G2 or G1 connected)

Public Functions

inline BiarcList()¶: Build an empty biarc spline.

inline ~BiarcList() override¶

inline BiarcList(BiarcList const &s)¶: Build a copy of another biarc spline.

void init()¶: Empty the the biarc list.

void reserve(int_type n)¶: Reserve memory for n biarcs.

void copy(BiarcList const &L)¶: Copy another biarc spline.

inline BiarcList const &operator=(BiarcList const &s)¶: Copy another biarc spline.

explicit BiarcList(LineSegment const &LS)¶: Build a biarc list from a line segment.

explicit BiarcList(CircleArc const &C)¶: Build a biarc list from a single circle arc.

explicit BiarcList(Biarc const &C)¶: Build a biarc list from a single biarc.

explicit BiarcList(PolyLine const &pl)¶: Build a biarc list from a single polyline.

explicit BiarcList(BaseCurve const &C)¶: Build a biarc list from another curve.

void push_back(LineSegment const &c)¶: Append a line segment to the biarc list (transformed to a degenerate biarc).

void push_back(CircleArc const &c)¶: Append a line circle to the biarc list (transformed to a degenerate biarc).

void push_back(Biarc const &c)¶: Append a biarc to the biarc list.

void push_back(PolyLine const &c)¶: Append a polyline to the biarc list (transformed to a list of degenerate biarc).

void push_back_G1(real_type x1, real_type y1, real_type theta1)¶

Construct a biarc passing from the points \( (x_0,y_0) \) to the point \( (x_1,y_1) \) with initial angle \( \theta_0 \) and final angle \( \theta_1 \) and append the biarc to the tail of biarc list. The initial point and angle is taken from the tail of the biarc list.

Parameters

x1 – [in] \( x_1 \)
y1 – [in] \( y_1 \)
theta1 – [in] \( \theta_1 \)

void push_back_G1(real_type x0, real_type y0, real_type theta0, real_type x1, real_type y1, real_type theta1)¶

Construct a biarc passing from the points \( (x_0,y_0) \) to the point \( (x_1,y_1) \) with initial angle \( \theta_0 \) and final angle \( \theta_1 \) and append the biarc to the tail of biarc list.

Parameters

x0 – [in] \( x_0 \)
y0 – [in] \( y_0 \)
theta0 – [in] \( \theta_0 \)
x1 – [in] \( x_1 \)
y1 – [in] \( y_1 \)
theta1 – [in] \( \theta_1 \)

bool build_G1(int_type n, real_type const *x, real_type const *y)¶

Construct a biarc list passing to the points \( (x_i,y_i) \).

Parameters

n – [in] number of points
x – [in] x-coordinates
y – [in] y-coordinates

bool build_G1(int_type n, real_type const *x, real_type const *y, real_type const *theta)¶

Construct a biarc list passing to the points \( (x_i,y_i) \) with angles \( \theta_i \).

Parameters

n – [in] number of points
x – [in] x-coordinates
y – [in] y-coordinates
theta – [in] angles at nodes

Biarc const &get(int_type idx) const¶: Get the idx-th biarc.

Biarc const &getAtS(real_type s) const¶: Get the biarc that contain the curvilinear coordinate s.

inline int_type numSegments() const¶: Return the number of biarc in the biarc list.

int_type findAtS(real_type &s) const¶: Get the of the biarc that contain the curvilinear coordinate s.

virtual real_type length() const override¶: The length of the curve

virtual real_type length_ISO(real_type offs) const override¶: The length of the curve with offset (ISO)

real_type segment_length(int_type nseg) const¶: The length of the nseg-th biarc.

real_type segment_length_ISO(int_type nseg, real_type offs) const¶: The length of the nseg-th biarc with offset offs.

virtual void bbTriangles_ISO(real_type offs, std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 6, real_type max_size = 1e100, int_type icurve = 0) const override¶

Build a cover with triangles of the curve with offset (ISO).

Parameters

offs – [out] curve offset
tvec – [out] list of covering triangles
max_angle – [out] maximum angle variation of the curve covered by a triangle
max_size – [out] maximum admissible size of the covering tirnagles
icurve – [out] index of the covering triangles

virtual void bbTriangles_SAE(real_type offs, std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 6, real_type max_size = 1e100, int_type icurve = 0) const override¶

Build a cover with triangles of the curve with offset (SAE).

Parameters

offs – [out] curve offset
tvec – [out] list of covering triangles
max_angle – [out] maximum angle variation of the arc covered by a triangle
max_size – [out] maximum admissible size of the covering tirnagles
icurve – [out] index of the covering triangles

virtual void bbTriangles(std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 6, real_type max_size = 1e100, int_type icurve = 0) const override¶

Build a cover with triangles of the curve.

Parameters

tvec – [out] list of covering triangles
max_angle – [out] maximum angle variation of the curve covered by a triangle
max_size – [out] maximum admissible size of the covering tirnagles
icurve – [out] index of the covering triangles

inline virtual void bbox(real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const override¶

Compute the bounding box of the curve.

Parameters

xmin – [out] left bottom
ymin – [out] left bottom
xmax – [out] right top
ymax – [out] right top

virtual void bbox_ISO(real_type offs, real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const override¶

Compute the bounding box of the curve with offset (ISO).

Parameters

offs – [in] curve offset
xmin – [out] left bottom
ymin – [out] left bottom
xmax – [out] right top
ymax – [out] right top

inline virtual real_type thetaBegin() const override¶: Initial angle of the curve.

inline virtual real_type thetaEnd() const override¶: Final angle of the curve.

inline virtual real_type xBegin() const override¶: Initial x-coordinate.

inline virtual real_type yBegin() const override¶: Initial y-coordinate.

inline virtual real_type xEnd() const override¶: Final x-coordinate.

inline virtual real_type yEnd() const override¶: Final y-coordinate.

inline virtual real_type xBegin_ISO(real_type offs) const override¶: Initial x-coordinate with offset (ISO standard).

inline virtual real_type yBegin_ISO(real_type offs) const override¶: Initial y-coordinate with offset (ISO standard).

inline virtual real_type xEnd_ISO(real_type offs) const override¶: Final x-coordinate with offset (ISO standard).

inline virtual real_type yEnd_ISO(real_type offs) const override¶: Final y-coordinate with offset (ISO standard).

inline virtual real_type tx_Begin() const override¶: Initial tangent x-coordinate.

inline virtual real_type ty_Begin() const override¶: Initial tangent y-coordinate.

inline virtual real_type tx_End() const override¶: Final tangent x-coordinate.

inline virtual real_type ty_End() const override¶: Final tangent y-coordinate.

inline virtual real_type nx_Begin_ISO() const override¶: Intial normal x-coordinate (ISO).

inline virtual real_type ny_Begin_ISO() const override¶: Intial normal y-coordinate (ISO).

inline virtual real_type nx_End_ISO() const override¶: Final normal x-coordinate (ISO).

inline virtual real_type ny_End_ISO() const override¶: Final normal y-coordinate (ISO).

virtual real_type theta(real_type) const override¶: Angle at curvilinear coodinate s.

virtual real_type theta_D(real_type) const override¶: Angle derivative (curvature) at curvilinear coodinate s.

virtual real_type theta_DD(real_type) const override¶: Angle second derivative (devitive of curvature) at curvilinear coodinate s.

virtual real_type theta_DDD(real_type) const override¶: Angle third derivative at curvilinear coodinate s.

virtual real_type tx(real_type) const override¶: Tangent x-coordinate at curvilinear coodinate s.

virtual real_type ty(real_type) const override¶: Tangent y-coordinate at curvilinear coodinate s.

virtual real_type tx_D(real_type) const override¶: Tangent derivative x-coordinate at curvilinear coodinate s.

virtual real_type ty_D(real_type) const override¶: Tangent derivative y-coordinate at curvilinear coodinate s.

virtual real_type tx_DD(real_type) const override¶: Tangent second derivative x-coordinate at curvilinear coodinate s.

virtual real_type ty_DD(real_type) const override¶: Tangent second derivative y-coordinate at curvilinear coodinate s.

virtual real_type tx_DDD(real_type) const override¶: Tangent third derivative x-coordinate at curvilinear coodinate s.

virtual real_type ty_DDD(real_type) const override¶: Tangent third derivative y-coordinate at curvilinear coodinate s.

virtual void tg(real_type s, real_type &tg_x, real_type &tg_y) const override¶: Tangent at curvilinear coodinate s.

virtual void tg_D(real_type s, real_type &tg_x_D, real_type &tg_y_D) const override¶: Tangent derivative at curvilinear coodinate s.

virtual void tg_DD(real_type s, real_type &tg_x_DD, real_type &tg_y_DD) const override¶: Tangent second derivative at curvilinear coodinate s.

virtual void tg_DDD(real_type s, real_type &tg_x_DDD, real_type &tg_y_DDD) const override¶: Tangent third derivative at curvilinear coodinate s.

virtual void evaluate(real_type s, real_type &th, real_type &k, real_type &x, real_type &y) const override¶

Evaluate curve at curvilinear coordinate s.

Parameters

s – [in] curvilinear coordinate
th – [out] angle
k – [out] curvature
x – [out] x-coordinate
y – [out] y-coordinate

virtual void evaluate_ISO(real_type s, real_type offs, real_type &th, real_type &k, real_type &x, real_type &y) const override¶

Evaluate curve with offset at curvilinear coordinate s (ISO).

Parameters

s – [in] curvilinear coordinate
offs – [in] offset
th – [out] angle
k – [out] curvature
x – [out] x-coordinate
y – [out] y-coordinate

virtual real_type X(real_type) const override¶: x-coordinate at curvilinear coordinate s.

virtual real_type Y(real_type) const override¶: y-coordinate at curvilinear coordinate s.

virtual real_type X_D(real_type) const override¶: x-coordinate derivative at curvilinear coordinate s.

virtual real_type Y_D(real_type) const override¶: y-coordinate derivative at curvilinear coordinate s.

virtual real_type X_DD(real_type) const override¶: x-coordinate second derivative at curvilinear coordinate s.

virtual real_type Y_DD(real_type) const override¶: y-coordinate second derivative at curvilinear coordinate s.

virtual real_type X_DDD(real_type) const override¶: x-coordinate third derivative at curvilinear coordinate s.

virtual real_type Y_DDD(real_type) const override¶: y-coordinate third derivative at curvilinear coordinate s.

virtual void eval(real_type s, real_type &x, real_type &y) const override¶: x and y-coordinate at curvilinear coordinate s.

virtual void eval_D(real_type s, real_type &x_D, real_type &y_D) const override¶: x and y-coordinate derivative at curvilinear coordinate s.

virtual void eval_DD(real_type s, real_type &x_DD, real_type &y_DD) const override¶: x and y-coordinate second derivative at curvilinear coordinate s.

virtual void eval_DDD(real_type s, real_type &x_DDD, real_type &y_DDD) const override¶: x and y-coordinate third derivative at curvilinear coordinate s.

virtual real_type X_ISO(real_type s, real_type offs) const override¶: x-coordinate at curvilinear coordinate s with offset offs (ISO).

virtual real_type Y_ISO(real_type s, real_type offs) const override¶: y-coordinate at curvilinear coordinate s with offset offs (ISO).

virtual real_type X_ISO_D(real_type s, real_type offs) const override¶: x-coordinate derivative at curvilinear coordinate s with offset offs (ISO).

virtual real_type Y_ISO_D(real_type s, real_type offs) const override¶: y-coordinate derivative at curvilinear coordinate s with offset offs (ISO).

virtual real_type X_ISO_DD(real_type s, real_type offs) const override¶: x-coordinate second derivative at curvilinear coordinate s with offset offs (ISO).

virtual real_type Y_ISO_DD(real_type s, real_type offs) const override¶: y-coordinate second derivative at curvilinear coordinate s with offset offs (ISO).

virtual real_type X_ISO_DDD(real_type s, real_type offs) const override¶: x-coordinate third derivative at curvilinear coordinate s with offset offs (ISO).

virtual real_type Y_ISO_DDD(real_type s, real_type offs) const override¶: y-coordinate third derivative at curvilinear coordinate s with offset offs (ISO).

virtual void eval_ISO(real_type s, real_type offs, real_type &x, real_type &y) const override¶

Compute curve at position s with offset offs (ISO).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x – [out] coordinate
y – [out] coordinate

virtual void eval_ISO_D(real_type s, real_type offs, real_type &x_D, real_type &y_D) const override¶

Compute derivative curve at position s with offset offs (ISO).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x_D – [out] x-coordinate
y_D – [out] y-coordinate

virtual void eval_ISO_DD(real_type s, real_type offs, real_type &x_DD, real_type &y_DD) const override¶

Compute second derivative curve at position s with offset offs (ISO).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x_DD – [out] x-coordinate second derivative
y_DD – [out] y-coordinate second derivative

virtual void eval_ISO_DDD(real_type s, real_type offs, real_type &x_DDD, real_type &y_DDD) const override¶

Compute third derivative curve at position s with offset offs (ISO).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x_DDD – [out] x-coordinate third derivative
y_DDD – [out] y-coordinate third derivative

virtual void translate(real_type tx, real_type ty) override¶: translate curve by \( (t_x,t_y) \)

virtual void rotate(real_type angle, real_type cx, real_type cy) override¶

Rotate curve by angle \( theta \) centered at point \( (c_x,c_y)\).

Parameters

angle – [in] angle \( theta \)
cx – [in] \( c_x\)
cy – [in] \( c_y\)

virtual void scale(real_type sc) override¶: Scale curve by factor sc.

virtual void reverse() override¶: Reverse curve parameterization.

virtual void changeOrigin(real_type newx0, real_type newy0) override¶: Translate curve so that origin will be (newx0, newy0).

virtual void trim(real_type s_begin, real_type s_end) override¶: Cut curve at parametrix coordinate s_begin and s_end.

virtual int_type closestPoint_ISO(real_type qx, real_type qy, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const override¶

Given a point find closest point on the curve.

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
x – x-coordinate of the projected point on the curve
y – y-coordinate of the projected point on the curve
s – parameter on the curve of the projection
t – curvilinear coordinate of the point x,y (if orthogonal projection)
dst – distance point projected point

Returns

1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

virtual int_type closestPoint_ISO(real_type qx, real_type qy, real_type offs, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const override¶

Given a point find closest point on the curve.

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
offs – offset of the curve
x – x-coordinate of the projected point on the curve
y – y-coordinate of the projected point on the curve
s – parameter on the curve of the projection
t – curvilinear coordinate of the point x,y (if orthogonal projection)
dst – distance point projected point

Returns

1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

inline virtual void info(ostream_type &stream) const override¶: Pretty print of the curve data.

void getSTK(real_type *s, real_type *theta, real_type *kappa) const¶

Return the biarc as a list of nodes angles and curvatures.

Parameters

s – [out] nodes
theta – [out] angles
kappa – [out] curvature

void getXY(real_type *x, real_type *y) const¶

Return the biarc XY nodes

Parameters

x – [out] x-nodes
y – [out] y-nodes

int_type findST1(real_type x, real_type y, real_type &s, real_type &t) const¶

Find parametric coordinate.

Parameters

x – x-coordinate point
y – y-coordinate point
s – value \( s \)
t – value \( t \)

Returns

idx the segment with point at minimal distance, otherwise -(idx+1) if (x,y) cannot be projected orthogonally on the segment

int_type findST1(int_type ibegin, int_type iend, real_type x, real_type y, real_type &s, real_type &t) const¶

Find parametric coordinate.

Parameters

ibegin – initial segment to compute the distance
iend – final segment to compute the distance
x – x-coordinate point
y – y-coordinate point
s – value \( s \)
t – value \( t \)

Returns

idx the segment with point at minimal distance, otherwise -(idx+1) if (x,y) cannot be projected orthogonally on the segment

bool collision(BiarcList const &C) const¶: Detect a collision with another biarc list.

bool collision_ISO(real_type offs, BiarcList const &CL, real_type offs_C) const¶

Detect a collision with another biarc list with offset.

Parameters

offs – [in] offset of first biarc
CL – [in] second biarc
offs_C – [in] offset of second biarc

inline void intersect(BiarcList const &CL, IntersectList &ilist, bool swap_s_vals) const¶

intersect a biarc list with another biarc list

Parameters

CL – [in] second biarc
ilist – [out] list of the intersection (as parameter on the curves)
swap_s_vals – [in] if true store (s2,s1) instead of (s1,s2) for each intersection

void intersect_ISO(real_type offs, BiarcList const &CL, real_type offs_obj, IntersectList &ilist, bool swap_s_vals) const¶

Intersect a biarc list with another biarc list with offset (ISO).

Parameters

offs – [in] offset of first biarc
CL – [in] second biarc
offs_obj – [in] offset of second biarc
ilist – [out] list of the intersection (as parameter on the curves)
swap_s_vals – [in] if true store (s2,s1) instead of (s1,s2) for each intersection

inline CurveType type() const¶: The name of the curve type

inline real_type length_SAE(real_type offs) const¶: The length of the curve with offset (SAE)

inline void bbox_SAE(real_type offs, real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const¶

Compute the bounding box of the curve (SAE).

Parameters

offs – [in] curve offset
xmin – [out] left bottom
ymin – [out] left bottom
xmax – [out] right top
ymax – [out] right top

inline virtual real_type kappaBegin() const¶: Initial curvature.

inline virtual real_type kappaEnd() const¶: Final curvature.

inline real_type xBegin_SAE(real_type offs) const¶: Initial x-coordinate with offset (SAE standard).

inline real_type yBegin_SAE(real_type offs) const¶: Initial y-coordinate with offset (SAE standard).

inline real_type xEnd_SAE(real_type offs) const¶: Final y-coordinate with offset (SAE standard).

inline real_type yEnd_SAE(real_type offs) const¶: Final y-coordinate with offset (ISO standard).

inline real_type nx_Begin_SAE() const¶: Intial normal x-coordinate (SAE).

inline real_type ny_Begin_SAE() const¶: Intial normal y-coordinate (SAE).

inline real_type nx_End_SAE() const¶: Final normal x-coordinate (SAE).

inline real_type ny_End_SAE() const¶: Intial normal y-coordinate (SAE).

inline real_type kappa(real_type s) const¶: Ccurvature at curvilinear coodinate s.

inline real_type kappa_D(real_type s) const¶: Curvature derivative at curvilinear coodinate s.

inline real_type kappa_DD(real_type s) const¶: Curvature second derivative at curvilinear coodinate s.

inline real_type nx_ISO(real_type s) const¶: Normal x-coordinate at curvilinear coodinate s (ISO).

inline real_type nx_ISO_D(real_type s) const¶: Normal derivative x-coordinate at curvilinear coodinate s (ISO).

inline real_type nx_ISO_DD(real_type s) const¶: Normal second derivative x-coordinate at curvilinear coodinate s (ISO).

inline real_type nx_ISO_DDD(real_type s) const¶: Normal third derivative x-coordinate at curvilinear coodinate s (ISO).

inline real_type ny_ISO(real_type s) const¶: Normal y-coordinate at curvilinear coodinate s (ISO).

inline real_type ny_ISO_D(real_type s) const¶: Normal derivative y-coordinate at curvilinear coodinate s (ISO).

inline real_type ny_ISO_DD(real_type s) const¶: Normal second derivative y-coordinate at curvilinear coodinate s (ISO).

inline real_type ny_ISO_DDD(real_type s) const¶: Normal third derivative y-coordinate at curvilinear coodinate s (ISO).

inline real_type nx_SAE(real_type s) const¶: Normal x-coordinate at curvilinear coodinate s (SAE).

inline real_type nx_SAE_D(real_type s) const¶: Normal derivative x-coordinate at curvilinear coodinate s (SAE).

inline real_type nx_SAE_DD(real_type s) const¶: Normal second derivative x-coordinate at curvilinear coodinate s (SAE).

inline real_type nx_SAE_DDD(real_type s) const¶: Normal third derivative x-coordinate at curvilinear coodinate s (SAE).

inline real_type ny_SAE(real_type s) const¶: Normal y-coordinate at curvilinear coodinate s (ISO)

inline real_type ny_SAE_D(real_type s) const¶: Normal derivative y-coordinate at curvilinear coodinate s (SAE).

inline real_type ny_SAE_DD(real_type s) const¶: Normal second derivative x-coordinate at curvilinear coodinate s (SAE).

inline real_type ny_SAE_DDD(real_type s) const¶: Normal third derivative y-coordinate at curvilinear coodinate s (SAE).

inline void nor_ISO(real_type s, real_type &nx, real_type &ny) const¶: Normal at curvilinear coodinate s (ISO).

inline void nor_ISO_D(real_type s, real_type &nx_D, real_type &ny_D) const¶: Normal derivative at curvilinear coodinate s (ISO).

inline void nor_ISO_DD(real_type s, real_type &nx_DD, real_type &ny_DD) const¶: Normal second derivative at curvilinear coodinate s (ISO).

inline void nor_ISO_DDD(real_type s, real_type &nx_DDD, real_type &ny_DDD) const¶: Normal third derivative at curvilinear coodinate s (ISO).

inline void nor_SAE(real_type s, real_type &nx, real_type &ny) const¶: Normal at curvilinear coodinate s (SAE).

inline void nor_SAE_D(real_type s, real_type &nx_D, real_type &ny_D) const¶: Normal derivative at curvilinear coodinate s (SAE).

inline void nor_SAE_DD(real_type s, real_type &nx_DD, real_type &ny_DD) const¶: Normal second derivative at curvilinear coodinate s (SAE).

inline void nor_SAE_DDD(real_type s, real_type &nx_DDD, real_type &ny_DDD) const¶: Normal third at curvilinear coodinate s (SAE).

inline virtual void evaluate_SAE(real_type s, real_type offs, real_type &th, real_type &k, real_type &x, real_type &y) const¶

Evaluate curve with offset at curvilinear coordinate s (SAE).

Parameters

s – [in] curvilinear coordinate
offs – [in] offset
th – [out] angle
k – [out] curvature
x – [out] x-coordinate
y – [out] y-coordinate

inline real_type X_SAE(real_type s, real_type offs) const¶: x-coordinate at curvilinear coordinate s with offset offs (SAE).

inline real_type Y_SAE(real_type s, real_type offs) const¶: y-coordinate at curvilinear coordinate s with offset offs (SAE).

inline real_type X_SAE_D(real_type s, real_type offs) const¶: x-coordinate derivative at curvilinear coordinate s with offset offs (SAE).

inline real_type Y_SAE_D(real_type s, real_type offs) const¶: y-coordinate derivative at curvilinear coordinate s with offset offs (SAE).

inline real_type X_SAE_DD(real_type s, real_type offs) const¶: x-coordinate second derivative at curvilinear coordinate s with offset offs (SAE).

inline real_type Y_SAE_DD(real_type s, real_type offs) const¶: y-coordinate second derivative at curvilinear coordinate s with offset offs (SAE).

inline real_type X_SAE_DDD(real_type s, real_type offs) const¶: x-coordinate third derivative at curvilinear coordinate s with offset offs (SAE).

inline real_type Y_SAE_DDD(real_type s, real_type offs) const¶: y-coordinate third derivative at curvilinear coordinate s with offset offs (SAE).

inline void eval_SAE(real_type s, real_type offs, real_type &x, real_type &y) const¶

Compute curve at position s with offset offs (SAE).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x – [out] coordinate
y – [out] coordinate

inline void eval_SAE_D(real_type s, real_type offs, real_type &x_D, real_type &y_D) const¶

Compute derivative curve at position s with offset offs (SAE).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x_D – [out] x-coordinate first derivative
y_D – [out] y-coordinate first derivative

inline void eval_SAE_DD(real_type s, real_type offs, real_type &x_DD, real_type &y_DD) const¶

Compute second derivative curve at position s with offset offs (SAE).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x_DD – [out] x-coordinate second derivative
y_DD – [out] y-coordinate second derivative

inline void eval_SAE_DDD(real_type s, real_type offs, real_type &x_DDD, real_type &y_DDD) const¶

Compute third derivative curve at position s with offset offs (SAE).

Parameters

s – [in] parameter on the curve
offs – [in] offset of the curve
x_DDD – [out] x-coordinate third derivative
y_DDD – [out] y-coordinate third derivative

inline bool collision(BaseCurve const &C) const¶: Check collision with another curve.

inline bool collision_ISO(real_type offs, BaseCurve const &C, real_type offs_C) const¶

Check collision with another curve with offset (ISO).

Parameters

offs – [in] curve offset
C – [in] second curve to check collision
offs_C – [in] curve offset of the second curve

Returns

true if collision is detected

inline bool collision_SAE(real_type offs, BaseCurve const &C, real_type offs_C) const¶

Check collision with another curve with offset (SAE).

Parameters

offs – [in] curve offset
C – [in] second curve to check collision
offs_C – [in] curve offset of the second curve

Returns

true if collision is detected

inline void intersect(BaseCurve const &C, IntersectList &ilist, bool swap_s_vals) const¶

Intersect the curve with another curve.

Parameters

C – [in] second curve intersect
ilist – [out] list of the intersection (as parameter on the curves)
swap_s_vals – [in] if true store (s2,s1) instead of (s1,s2) for each intersection

inline void intersect_ISO(real_type offs, BaseCurve const &C, real_type offs_C, IntersectList &ilist, bool swap_s_vals) const¶

Intersect the curve with another curve with offset (ISO)

Parameters

offs – [in] offset first curve
C – [in] second curve intersect
offs_C – [in] offset second curve
ilist – [out] list of the intersection (as parameter on the curves)
swap_s_vals – [in] if true store (s2,s1) instead of (s1,s2) for each intersection

inline void intersect_SAE(real_type offs, BaseCurve const &C, real_type offs_C, IntersectList &ilist, bool swap_s_vals) const¶

Intersect the curve with another curve with offset (SAE).

Parameters

offs – [in] offset first curve
C – [in] second curve intersect
offs_C – [in] offset second curve
ilist – [out] list of the intersection (as parameter on the curves)
swap_s_vals – [in] if true store (s2,s1) instead of (s1,s2) for each intersection

inline int_type closestPoint_SAE(real_type qx, real_type qy, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const¶

Given a point find closest point on the curve.

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
x – x-coordinate of the projected point on the curve
y – y-coordinate of the projected point on the curve
s – parameter on the curve of the projection
t – curvilinear coordinate of the point x,y (if orthogonal projection)
dst – distance point projected point

Returns

1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

inline int_type closestPoint_SAE(real_type qx, real_type qy, real_type offs, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const¶

Given a point find closest point on the curve.

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
offs – offset of the curve
x – x-coordinate of the projected point on the curve
y – y-coordinate of the projected point on the curve
s – parameter on the curve of the projection
t – curvilinear coordinate of the point x,y (if orthogonal projection)
dst – distance point projected point

Returns

1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

inline virtual real_type distance(real_type qx, real_type qy) const¶

Compute the distance between a point \( q=(q_x,q_y) \) and the curve.

Parameters

qx – [in] component \( q_x \)
qy – [in] component \( q_y \)

Returns

the computed distance

inline real_type distance_ISO(real_type qx, real_type qy, real_type offs) const¶

Compute the distance between a point \( q=(q_x,q_y) \) and the curve with offset (ISO).

Parameters

qx – [in] component \( q_x \)
qy – [in] component \( q_y \)
offs – [in] offset of the curve

Returns

the computed distance

inline real_type distance_SAE(real_type qx, real_type qy, real_type offs) const¶

Compute the distance between a point \( q=(q_x,q_y) \) and the curve with offset (SAE).

Parameters

qx – [in] component \( q_x \)
qy – [in] component \( q_y \)
offs – [in] offset of the curve

Returns

the computed distance

inline bool findST_ISO(real_type x, real_type y, real_type &s, real_type &t) const¶

Find the curvilinear coordinate of point \( P=(x,y) \) respect to the curve (ISO), i.e.

\[ P = C(s)+N(s)t \]

where \( C(s) \) is the curve position respect to the curvilinear coordinates and \( C(s) \) is the normal at the point \( C(s) \).

Parameters

x – [in] component \( x \)
y – [in] component \( y \)
s – [out] curvilinear coordinate
t – [out] offset respect to the curve of \( (x,y) \)

Returns

true if the coordinate are found

inline bool findST_SAE(real_type x, real_type y, real_type &s, real_type &t) const¶

Find the curvilinear coordinate of point \( (x,y) \) respect to the curve (SAE), i.e.

\[ P = C(s)+N(s)t \]

where \( C(s) \) is the curve position respect to the curvilinear coordinates and \( C(s) \) is the normal at the point \( C(s) \).

Parameters

x – [in] component \( x \)
y – [in] component \( y \)
s – [out] curvilinear coordinate
t – [out] offset respect to the curve of \( (x,y) \)

Returns

true if the coordinate are found

Friends

friend ostream_type &operator<<(ostream_type &stream, BiarcList const &CL)¶: pretty print the biarc list