Class ClothoidList¶

Defined in File ClothoidList.m

Inheritance Relationships¶

Base Type¶

public CurveBase (Class CurveBase)

Class Documentation¶

class ClothoidList : public CurveBase ¶

Public Functions

function ClothoidList()¶

Create a new C++ class instance for the clothoid list object

Usage:

ref = ClothoidCurve()

On output:

ref: reference handle to the object instance

function is_type( ignoredArg)¶

function reserve( self, N)¶

Reserve memory for N segments

Usage:

ref.reserve( N );

function save( self, fname)¶: Save the clothoid list to a file

function load( self, varargin)¶

Load the clothoid list from a file (check consistency of the readed segments)

Usage:

ref.load( filename );
ref.load( filename, tol );

filename : file name to be read tol : tolerance used to check consistency

function push_back( self, varargin)¶

Append a curve to the clothoid list

Usage:

ref.push_back( obj ); % mode 1
ref.push_back( kappa0, dkappa, L ); % mode 2
ref.push_back( x0, y0, theta0, kappa0, dkappa, L ); % mode 3

Mode 1

obj : curve to be appended can be one of
- LineSegment
- BiArc
- BiarcList
- CircleArc
- ClothoidCurve
- ClothoidList
- PolyLine

Mode 2

kappa0 : initial curvature of the appended clothoid
dkappa : derivative of the curvature of the appended clothoid
L : length of the the appended clothoid

Mode 3

x0, y0 : initial position of the appended clothoid, the builded clothoid will be translated to the and of the actual clothoid list
theta0 : initial curvature of the appended clothoid
kappa0 : initial curvature of the appended clothoid
dkappa : derivative of the curvature of the appended clothoid
L : length of the the appended clothoid

function push_back_G1( self, varargin)¶

Append a curve to the clothoid list

Usage:

ref.push_back( x1,y1,theta1 ); % mode 1
ref.push_back( x0,y0,theta0,x1,y1,theta1); % mode 2

Mode 1

Build a clothoid arc using final point and angle of the clothoid list and

x1, y1 : final point
theta1 : final angle

the builded clothoid is appended to the list

Mode 2

Build a clothoid arc using the data

x0, y0 : initial point
theta0 : initial angle
x1, y1 : final point
theta1 : final angle

the builded clothoid is appended to the list

function get( self, k)¶

Get the clothoid at position k. The biarc is returned as a clothoid object or the data defining the clothoid.

[ x0, y0, theta0, kappa0, dkappa, L ] = ref.get(k);
C = ref.get(k);

function append( self, lst)¶

Append a curve to a clothoid list.

C = LineSegment( ... );
...
C = Biarc( ... );
...
C = CircleArc( ... );
% ....
ref.append(C); % append biarc

function getSTK( self)¶

Return curvilinear coordinates, angle and curvature at node point for the clothoid list

[ s, theta, kappa ] = ref.getSTK();

s curvilinear coordinates nodes
theta angles at nodes
kappa curvature at nodes

function getXY( self)¶

Return xy-coordinates at node points for the clothoid list

[ x, y ] = ref.getXY();

x x-coordinates at nodes
y y-coordinates at nodes

function numSegments( self)¶

function build_3arcG2( self, x0, y0, theta0, kappa0, )¶

function build_3arcG2fixed( self, s0, x0, y0, theta0, kappa0, )¶

function build_2arcG2( self, x0, y0, theta0, kappa0, )¶

function build_CLC( self, x0, y0, theta0, kappa0, )¶

function build_G1( self, x, y, varargin)¶

Given a list of xy-coordinates at node points build a clothoid list. If third argument (angle) is not present angles are estimated internally.

ref.build_G1( x, y );
ref.build_G1( x, y, theta );

x x-coordinates at nodes
y y-coordinates at nodes
theta angle at nodes

function build( self, x0, y0, theta0, s, kappa)¶

Given a list of curvilinear coordinated and curvatures at nodes build a G2 clothoid list. Initial position and angle must be set to determine a unique clothoid list.

ref.build( x0, y0, theta0, s, kappa );

x0 initial x-coordinates
y0 initial y-coordinates at nodes
theta0 initial angle
s list of curvilinear coordinates
kappa list of curvatures at nodes

function build_theta( self, x, y)¶

Given a list of xy-coordinates at node points build a guess of angles for the clothoid list.

theta = ref.build_theta( x, y );

x x-coordinates at nodes
y y-coordinates at nodes

function build_raw( self, x, y, abscissa, theta, kappa)¶

function make_closed( self)¶

function make_open( self)¶

function is_closed( self)¶

function deltaTheta( self)¶

function deltaKappa( self)¶

function closestPointBySample( self, qx, qy, ds)¶

function distanceBySample( self, qx, qy, ds)¶

function closestSegment( self, qx, qy)¶

function closestPointInRange( self, qx, qy, ibegin, iend, varargin)¶

function closestPointInSRange( self, qx, qy, s_begin, s_end, varargin)¶

Find closest point of a Clothoid list given a s-range

[ icurve, x, y, s, t, iflag, dst ] = ...
   ref.closestPointInSRange( qx, qy, s_begin, s_end, varargin );

[ icurve, x, y, s, t, iflag, dst ] = ...
   ref.closestPointInSRange( qx, qy, s_begin, s_end, varargin, 'ISO' );

[ icurve, x, y, s, t, iflag, dst ] = ...
   ref.closestPointInSRange( qx, qy, s_begin, s_end, varargin, 'SAE' );

res = ref.closestPointInSRange( qx, qy, s_begin, s_end, varargin );
res = ref.closestPointInSRange( qx, qy, s_begin, s_end, varargin, 'ISO' );
res = ref.closestPointInSRange( qx, qy, s_begin, s_end, varargin, 'SAE' );

%
% res is a struct with field
%
% res.icurve = number of the segment with the projected point
% res.x      = projected x
% res.y      = projected y
% res.s      = curvilinear coordinate of the projection
% res.t      = normal curvilinear coordinate ('ISO' or 'SAE' convenction)
% res.iflag  = 1 OK -1 projection failed
% res.dst    = point curve distance
%

function s_to_index( self, s)¶

function export_table( self, filename)¶

function export_ruby( self, filename)¶

function info( self)¶

function find_coord1( self, x, y, varargin)¶

function plot( self, varargin)¶

Plot the clothoid list

Usage:

ref.plot();
ref.plot( npts );

fmt1 = {'Color','blue','Linewidth',2}; % first arc of the biarc
fmt2 = {'Color','red','Linewidth',2};  % second arc of the biarc
ref.plot( npts, fmt1, fmt2 );

npts: number of sampling points for plotting
fmt1: format of the odd clothoids
fmt2: format of the even clothoids

function plot_offs( self, offs, npts, varargin)¶

Plot the clothoid list with offset

Usage:

ref.plot_offs( offs, npts );

fmt1 = {'Color','blue','Linewidth',2}; % first arc of the biarc
fmt2 = {'Color','red','Linewidth',2};  % second arc of the biarc
ref.plot_offs( offs, npts, fmt1, fmt2 );

npts: number of sampling points for plotting
fmt1: format of the first arc
fmt2: format of the second arc
offs: offset used in the plotting

function plotCurvature( self, npts, varargin)¶

Plot the curvature of the clothoid list

Usage:

ref.plotCurvature( npts );

fmt1 = {'Color','blue','Linewidth',2};
fmt2 = {'Color','red','Linewidth',2};
ref.plotCurvature( npts, fmt1, fmt2 );

npts: number of sampling points for plotting
fmt1: format of the first arc
fmt2: format of the second arc

function plotAngle( self, npts, varargin)¶

Plot the angle of the clothoid list

Usage:

ref.plotAngle( npts );

fmt1 = {'Color','blue','Linewidth',2};
fmt2 = {'Color','red','Linewidth',2};
ref.plotAngle( npts, fmt1, fmt2 );

npts: number of sampling points for plotting
fmt1: format of the first arc
fmt2: format of the second arc

function plotNormal( self, step, len)¶

Plot the normal of the clothoid list

Usage:

ref.plotNormal( step, len );

step: number of sampling normals
len: length of the plotted normal

function saveSampled( self, filename, ds)¶

Save the clothoid list sampled on a file

Usage:

ref.saveSampled( filename, ds );

filename: file name
ds: sample point every ds

the file is of the form

X Y THETA
0 0 1.2
...
...

function saveClothoids( self, filename)¶

Save the clothoid list on a file as a list of segments

Usage:

ref.saveClothoids( filename, ds );

filename: file name
ds: sample point every ds

the file is of the form

x0 y0 theta0 kappa0 dk  L
0  0  1.2    0.0    0.1 2
...
...

function obj_handle( self)¶

Return the pointer of the interbal stored c++ object

Usage

obj = ref.obj_handle();

function copy( self, C)¶

Make of copy of a curve object

Usage

ref.copy( C );

where C id the curve object to be copied.

function bbox( self, varargin)¶

Return the bounding box of the curve object

Usage

[ xmin, ymin, xmax, ymax ] = ref.bbox( C );
[ xmin, ymin, xmax, ymax ] = ref.bbox( C, offs );
[ xmin, ymin, xmax, ymax ] = ref.bbox( C, offs, 'ISO' );
[ xmin, ymin, xmax, ymax ] = ref.bbox( C, offs, 'SAE' );

xmin: x minimum coordinate of the bounding box
ymin: y minimum coordinate of the bounding box
xmax: x maximum coordinate of the bounding box
ymax: y maximum coordinate of the bounding box

Optional Arguments

offs: offset of the curve used in the bbox computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for offset computation

function translate( self, tx, ty)¶

Translate the curve by (tx,ty)

Usage

ref.translate( tx, ty );

function trim( self, smin, smax)¶

Cut the curve at the curvilinear parameter smin up to smax

Usage

ref.trim( smin, smax );

function rotate( self, angle, cx, cy)¶

Rotate the curve by angle angle around point (cx, cy)

Usage

ref.rotate( angle, cx, cy );

function reverse( self)¶

Reverse the direction of travel of the curve.

Usage

ref.reverse();

function scale( self, sc)¶

Scale the curve by factor sc

Usage

ref.scale( sc );

function changeOrigin( self, newX0, newY0)¶

Translate the curve in such a way the origin is at (newX0,newY0.

Usage

ref.changeOrigin( newX0, newY0 );

function evaluate( self, s, varargin)¶

Evaluate the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

[ x, y, theta, kappa ] = ref.evaluate( s );
[ x, y, theta, kappa ] = ref.evaluate( s, offs );
[ x, y, theta, kappa ] = ref.evaluate( s, offs, 'ISO' );
[ x, y, theta, kappa ] = ref.evaluate( s, offs, 'SAE' );

Optional Arguments

offs: offset of the curve used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for offset computation

function eval( self, varargin)¶

Evaluate the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

XY = ref.eval( s );
XY = ref.eval( s, offs );
XY = ref.eval( s, offs, 'ISO' );
XY = ref.eval( s, offs, 'SAE' );

[X,Y] = ref.eval( s );
[X,Y] = ref.eval( s, offs );
[X,Y] = ref.eval( s, offs, 'ISO' );
[X,Y] = ref.eval( s, offs, 'SAE' );

Optional Arguments

offs: offset of the curve used compiutation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for offset computation

Output

XY: matrix 2 x n of the evaluated points
X: vector of the x-coordinates of the evaluated points
Y: vector of the y-coordinates of the evaluated points

function eval_D( self, varargin)¶

Evaluate the first derivatives of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

XY = ref.eval_D( s );
XY = ref.eval_D( s, offs );
XY = ref.eval_D( s, offs, 'ISO' );
XY = ref.eval_D( s, offs, 'SAE' );

[X,Y] = ref.eval_D( s );
[X,Y] = ref.eval_D( s, offs );
[X,Y] = ref.eval_D( s, offs, 'ISO' );
[X,Y] = ref.eval_D( s, offs, 'SAE' );

Optional Arguments

offs: offset of the curve used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for offset computation

Output

XY: matrix 2 x n of the evaluated points
X: vector of the x-coordinates of the evaluated point derivatives
Y: vector of the y-coordinates of the evaluated point derivatives

function eval_DD( self, varargin)¶

Evaluate the second derivatives of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

XY = ref.eval_DD( s );
XY = ref.eval_DD( s, offs );
XY = ref.eval_DD( s, offs, 'ISO' );
XY = ref.eval_DD( s, offs, 'SAE' );

[X,Y] = ref.eval_DD( s );
[X,Y] = ref.eval_DD( s, offs );
[X,Y] = ref.eval_DD( s, offs, 'ISO' );
[X,Y] = ref.eval_DD( s, offs, 'SAE' );

Optional Arguments

offs: offset of the curve used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for offset computation

Output

XY: matrix 2 x n of the evaluated points
X: vector of the x-coordinates of the evaluated point derivatives
Y: vector of the y-coordinates of the evaluated point derivatives

function eval_DDD( self, varargin)¶

Evaluate the third derivatives of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

XY = ref.eval_DDD( s );
XY = ref.eval_DDD( s, offs );
XY = ref.eval_DDD( s, offs, 'ISO' );
XY = ref.eval_DDD( s, offs, 'SAE' );

[X,Y] = ref.eval_DDD( s );
[X,Y] = ref.eval_DDD( s, offs );
[X,Y] = ref.eval_DDD( s, offs, 'ISO' );
[X,Y] = ref.eval_DDD( s, offs, 'SAE' );

Optional Arguments

offs: offset of the curve used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for offset computation

Output

XY: matrix 2 x n of the evaluated points
X: vector of the x-coordinates of the evaluated point derivatives
Y: vector of the y-coordinates of the evaluated point derivatives

function theta( self, s)¶

Evaluate the angle of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

theta = ref.theta( s );

function theta_D( self, s)¶

Evaluate the angle derivatives (curvature) of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

theta = ref.theta_D( s );

function theta_DD( self, s)¶

Evaluate the angle second derivatuve of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

theta = ref.theta_DD( s );

function theta_DDD( self, s)¶

Evaluate the angle third derivative of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

theta = ref.theta_DDD( s );

function kappa( self, s)¶

Evaluate the curvature of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

theta = ref.kappa( s );

function kappa_D( self, s)¶

Evaluate the curvature derivative of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

theta = ref.kappa_D( s );

function kappa_DD( self, s)¶

Evaluate the curvature second derivative of the curve at curvilinear coordinate s. Argument s may be a vector for multiple evaluations.

Usage

theta = ref.kappa_DD( s );

function xyBegin( self)¶

Evaluate initial point of the curve.

Usage

[ x0, y0 ] = ref.xyBegin();

function xyEnd( self)¶

Evaluate final point of the curve.

Usage

[ x1, y1 ] = ref.xyEnd();

function xBegin( self)¶

Evaluate initial x-coordinate of the curve.

Usage

x0 = ref.xBegin();

function xEnd( self)¶

Evaluate final x-coordinate of the curve.

Usage

x1 = ref.xEnd();

function yBegin( self)¶

Evaluate initial y-coordinate of the curve.

Usage

y0 = ref.yBegin();

function yEnd( self)¶

Evaluate final y-coordinate of the curve.

Usage

y1 = ref.yEnd();

function thetaBegin( self)¶

Evaluate initial angle of the curve.

Usage

theta = ref.thetaBegin();

function thetaEnd( self)¶

Evaluate final angle of the curve.

Usage

theta = ref.thetaEnd();

function kappaBegin( self)¶

Evaluate initial curvature of the curve.

Usage

kappa0 = ref.kappaBegin();

function kappaEnd( self)¶

Evaluate final curvature of the curve.

Usage

kappa1 = ref.kappaEnd();

function length( self, varargin)¶

Return the length of the curve.

Usage

length = ref.length();

function points( self)¶

function bbTriangles( self, varargin)¶

Evaluate the bounding box triangles of curve.

Usage

[P1,P2,P3] = ref.bbTriangles();
[P1,P2,P3] = ref.bbTriangles(max_angle,max_size);
[P1,P2,P3] = ref.bbTriangles(max_angle,max_size,offs);
[P1,P2,P3] = ref.bbTriangles(max_angle,max_size,offs,'ISO');
[P1,P2,P3] = ref.bbTriangles(max_angle,max_size,offs,'SAE');

Optional Arguments

max_angle: maximum curve angle variation admitted in a triangle
max_size: maximum triangles size
offs: offset of the curve used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for the offset

Output

P1: 2 x n matrix with the first points of the triangles
P2: 2 x n matrix with the second points of the triangles
P3: 2 x n matrix with the third points of the triangles

function closestPoint( self, qx, qy, varargin)¶

Evaluate the point at minimum distance of another point on the curve. qx and qy may be vectors so that the return values are vectors too.

Usage

[ x, y, s, t, iflag, dst ] = ref.closestPoint( qx, qy );
[ x, y, s, t, iflag, dst ] = ref.closestPoint( qx, qy, offs );
[ x, y, s, t, iflag, dst ] = ref.closestPoint( qx, qy, offs, 'ISO' );
[ x, y, s, t, iflag, dst ] = ref.closestPoint( qx, qy, offs, 'SAE' );

Optional Arguments

offs: offset of the curve used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for the offset

Output

x, y: Point at minimum distance from (qx,qy) on the curve.
s, t: Curvilinear coordinates of the point (qx,qy).
iflag: iflag < 0 some error in computation, iflag >0 is the numer of segment containing the point at minimum distance.
dst: point curve distance.

function distance( self, qx, qy, varargin)¶

Evaluate the distance of a point (qx,qy) to the curve. qx and qy may be vectors so that the return values are vectors too.

Usage

dst = ref.distance( qx, qy );
dst = ref.distance( qx, qy, offs );
dst = ref.distance( qx, qy, offs, 'ISO' );
dst = ref.distance( qx, qy, offs, 'SAE' );

Optional Arguments

offs: offset of the curve used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for the offset

function collision( self, OBJ, varargin)¶

Check if two curve collide.

Usage

ok = ref.collision( obj );
ok = ref.collision( obj, offs, offs1 );
ok = ref.collision( obj, offs, offs1, 'ISO' );
ok = ref.collision( obj, offs, offs1, 'SAE' );

Optional Arguments

offs, offs1: offset of the curves used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for the offsets

function intersect( self, OBJ, varargin)¶

Intersect two curves.

Usage

[s1,s2] = ref.intersect( obj );
[s1,s2] = ref.intersect( obj, offs, offs1 );
[s1,s2] = ref.intersect( obj, offs, offs1, 'ISO' );
[s1,s2] = ref.intersect( obj, offs, offs1, 'SAE' );

s1: curvilinear coordinates of the intersections on the first curve
s2: curvilinear coordinates of the intersections on the second curve

Optional Argument

offs, offs1: offset of the curves used in computation
’ISO’/’SAE’: use ISO or SAE orientation of the normal for the offsets

function find_coord( self, x, y)¶

Get the curvilinear coordinates of the point (x,y)

Usage:

[s,t] = ref.find_coord( x, y );

s: curvilinear coordinate along the curve
t: curvilinear coordinate along the normal of the curve

function yesAABBtree( self)¶: Activate the use of AABB three in intersection/collision computations

function noAABBtree( self)¶: Deactivate the use of AABB three in intersection/collision computations

function plotTBox( self, P1, P2, P3, varargin)¶

Plot a triangle BBOX

Usage:

ref.plotTBox( P1, P2, P3 );
ref.plotTBox( P1, P2, P3, 'Color', 'red' );

function plotBBox( self, varargin)¶

Plot the bounding box of the curve

Usage:

ref.plotBBox();
ref.plotBBox('Color', 'red' );

function plotTriangles( self, varargin)¶

Plot the covering triangles of the curve

Usage:

ref.plotTriangles()
ref.plotTriangles('red','FaceAlpha', 0.5);