# Class BiarcList

- Defined in File BiarcList.m

## Inheritance Relationships

### Base Type

- `public CurveBase` (Class CurveBase)

## Class Documentation

class BiarcList : public CurveBase

  Public Functions

  function BiarcList()

    Create a new C++ class instance for the list of biarc object

    Usage:

        self = BiarcList();

    On output:

    - self: reference handle to the object instance

  function is_type( ignoredArg)

    Return the string `"BiarcList"`with the name of the object class

  function reserve( self, N)

    Reserve memory for `N` biarc

    Usage:

        ref.reserve(N);

  function push_back( self, varargin)

    Append to the BiarcList another biarc. The biarc is obtained setting the final postion and angle while the initial position and angle are taken from the last biarc on the biarc list. Another possibility is to push a biarc is obtained by passing initial and final positions, initial and final angles.

    Usage:

        ref.push_back(x1,y1,theta1);
        ref.push_back(x0,y0,theta0,x1,y1,theta1);

    - `x0`, `y0`: initial position of the biarc to be appended

    - `theta0` : initial angle of the biarc to be appended

    - `x1`, `y1`: final position of the biarc to be appended

    - `theta1` : final angle of the biarc to be appended

  function get( self, k)

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

        BA = ref.get(k); % get the biarc object
        [ x0, y0, theta0, x1, y1, theta1 ] = ref.get(k); % get the biarc data

  function append( self, lst)

    Append a biarc or a biarc list.

        ba = Biarc( ... );
        % ....
        ref.append(ba); % append biarc

        blist = BiarcList();
        % ...
        ref.append(blist); % append biarc list

  function getXY( self)

    Return the list of points (initial and final) of the biarcs

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

  function numSegments( self)

    Return number of biarc in the list

        nseg = ref.numSegments();

  function build_G1( self, varargin)

    Build a biarc list given a set of points and if available the angles at the points. If the angles are missing the angle at a node is computed by building the circle passing by 3 consecutive points. The node is the middle point.

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

    - `x`, `y`: vectors of `x` and `y` coordinates of the nodes

    - `thetas`: angles at the nodes

  function build_theta( self, x, y)

    Build the angles a the list of nodes. The angle at a node is computed by building the circle passing by 3 consecutive points. The node is the middle point.

        thetas = ref.build_theta(x,y);

    - `x`, `y`: vectors of `x` and `y` coordinates of the nodes

  function info( self)
  function find_coord1( self, x, y)

    Find curvilinear coordinates of inputs points

        [ s, t, ipos ] = ref.find_coord1(x,y);

    Input:

    - `x`, `y`: vectors of `x` and `y` coordinates of the poinst

    Output:

    - `s`, `t` : curvilinar coordinates of the points

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

  function plot( self, varargin)

    Plot the biarc 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 first arc

    - `fmt2`: format of the second arc

  function plot_offs( self, offs, npts, varargin)

    Plot the biarc 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 biarc 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 biarc 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 biarc list

    Usage:

        ref.plotNormal( step, len );

    - `step`: number of sampling normals

    - `len`: length of the plotted normal

  function save( self, filename, ds)

    Save the biarc list sampled on a file

    Usage:

        ref.save( filename, ds );

    - `filename`: file name

    - `ds`: sample point every `ds`

    the file is of the form

        X Y THETA
        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);