Class CircleArc

Inheritance Relationships

Base Type

Class Documentation

class CircleArc : public CurveBase

Public Functions

function CircleArc( varargin)

Create a new C++ class instance for the circle arc object

Usage:

ref = CircleArc() % create empty circle
ref = CircleArc( x0, y0, theta0, k0, L ) % circle passing from (x0,y0) 
                                         % at angle theta0 with curvature k0
                                         % and length L

On input:

  • x0, y0: coordinate of initial point

  • theta0: orientation of the circle at initial point

  • k0: curvature of the circle at initial point

  • L: length of curve from initial to final point

On output:

  • ref: reference handle to the object instance

function is_type( ignoredArg)
function build( self, x0, y0, theta0, k0, L)

Build the circle from known parameters

Usage:

ref.build( x0, y0, theta0, k0, L )

build a circle passing from (x0,y0) at angle theta0 with curvature and length

On input:

  • x0, y0: coordinate of initial point

  • theta0: orientation of the circle at initial point

  • k0: curvature of the circle at initial point

  • L: length of curve from initial to final point

function build_G1( self, varargin)

Build the circle from known parameters

Usage:

ref.build( x0, y0, theta0, x1, y1 ); % circle passing to [x0,y0] and [x1,y1]
                                     % with angle theta0 at [x0,y0]
ref.build( p0, theta0, p1 ); % circle passing to p0 and p1 with angle theta0 at p0

On input:

  • x0, y0: coordinate of initial point

  • theta0: orientation of the circle at initial point

  • k0: curvature of the circle at initial point

  • L: length of curve from initial to final point

  • p0: 2D point

  • p1: 2D point

function build_3P( self, varargin)

Build the circle arc given 3 points. The point can be alingned in this case a degenerate straight arc if build.

Usage:

ref.build_3P( x0, y0, x1, y1, x2, y2 )
ref.build_3P( p0, p1, p2 )
function scale( self, sc)

Scale circle by sc factor

Usage:

ref.scale( sc );
function changeCurvilinearOrigin( self, s0, L)

Change the origin of the circle curve to s0 and set arc lenght to L

Usage:

ref.changeCurvilinearOrigin( s0, L );
function to_nurbs( self)

return a nurbs representation of the circle arc

function plot( self, npts, fmt)

Plot the arc

Usage:

ref.plot( npts );

fmt = {'Color','blue','Linewidth',2};
ref.plot( npts, fmt );

  • npts: number of sampling points for plotting

  • fmt : format of the arc

function plotPolygon( self, varargin)

Plot the polygon of the NURBS for the arc

Usage:

ref.plotPolygon();
ref.plotPolygon( 'Color','blue','Linewidth',2 );

  • fmt : format of the arc

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 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 info( self)

Print on the console some information on the stored curve.

Usage

ref.info();
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);