Program Listing for File Biarc.m¶
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classdef Biarc < CurveBase
%> MATLAB class wrapper for the underlying C++ class
methods
%> Create a new C++ class instance for the Biarc object
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> self = Biarc();
%> self = Biarc( x0, y0, theta0, x1, y1, theta1 );
%>
%> \endrst
%>
%> **Optinal Arguments:**
%>
%> - `x0`, `y0`: coordinate of initial point
%> - `theta0` : orientation of the clothoid at initial point
%> - `x1`, `y1`: coordinate of final point
%> - `theta1` : orientation of the clothoid at final point
%>
%> **On output:**
%>
%> - self: reference handle to the object instance
%>
function self = Biarc( varargin )
self@CurveBase( 'BiarcMexWrapper' );
self.objectHandle = BiarcMexWrapper( 'new' );
if nargin > 0
ok = BiarcMexWrapper( 'build_G1', self.objectHandle, varargin{:} );
if ~ok
error('Biarc constructor failed');
end
end
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Build the interpolating G1 biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> ref.build_G1( x0, y0, theta0, x1, y1, theta1 );
%>
%> \endrst
%>
%> **On input:**
%>
%> - `x0`, `y0`: coordinate of initial point
%> - `theta0` : orientation of the clothoid at initial point
%> - `x1`, `y1`: coordinate of final point
%> - `theta1` : orientation of the clothoid at final point
%>
function ok = build( self, x0, y0, theta0, x1, y1, theta1 )
ok = BiarcMexWrapper( 'build_G1', self.objectHandle, ...
x0, y0, theta0, x1, y1, theta1 );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
function str = is_type( ~ )
str = 'BiArc';
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Build the interpolating biarc by 3 points
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> ref.build_3P( x0, y0, x1, y1, x2, y2 );
%> ref.build_3P( [x0, y0], [x1, y1], [x2, y2] );
%>
%> \endrst
%>
%> **On input:**
%>
%> - `x0`, `y0`: coordinate of initial point
%> - `x1`, `y1`: coordinate of middle point
%> - `x2`, `y2`: coordinate of final point
%>
%> alternative
%>
%> p0: coordinate of initial point
%> p1: coordinate of middle point
%> p2: coordinate of final point
%>
function ok = build_3P( self, varargin )
ok = BiarcMexWrapper( 'build_3P', self.objectHandle, varargin{:} );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get junction point of the biarc x-coordinate
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> x = ref.xMiddle();
%>
%> \endrst
%>
function res = xMiddle( self )
res = BiarcMexWrapper( 'xMiddle', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get junction point of the biarc y-coordinate
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> x = ref.yMiddle();
%>
%> \endrst
%>
function res = yMiddle( self )
res = BiarcMexWrapper( 'yMiddle', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get junction point angle of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> theta = ref.thetaMiddle();
%>
%> \endrst
%>
function res = thetaMiddle( self )
res = BiarcMexWrapper( 'thetaMiddle', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get curvature of the first arc of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> kappa0 = ref.kappa0();
%>
%> \endrst
%>
function res = kappa0( self )
res = BiarcMexWrapper( 'kappa0', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get curvature of the second arc of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> kappa1 = ref.kappa1();
%>
%> \endrst
%>
function res = kappa1( self )
res = BiarcMexWrapper( 'kappa1', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get length of the first arc of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> length0 = ref.length0();
%>
%> \endrst
%>
function res = length0( self )
res = BiarcMexWrapper( 'length0', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get length of the second arc of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> length1 = ref.length1();
%>
%> \endrst
%>
function res = length1( self )
res = BiarcMexWrapper( 'length1', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get the biarc G1 data
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> [x0,y0,theta0,x1,y1,theta1] = ref.getData();
%>
%> \endrst
%>
%> - `x0`, `y0`: initial point of the biarc
%> - `theta0` : initial angle of the biarc
%> - `x1`, `y1`: final point of the biarc
%> - `theta1` : final angle of the biarc
%>
function [ x0,y0,theta0,x1,y1,theta1] = getData( self )
x0 = self.xBegin();
y0 = self.yBegin();
theta0 = self.thetaBegin();
x1 = self.xEnd();
y1 = self.yEnd();
theta1 = self.thetaEnd();
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get the two circle arc composing a biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> [C0,C1] = ref.getCircles();
%>
%> \endrst
%>
function [ C0, C1 ] = getCircles( self )
x0 = self.xBegin();
y0 = self.yBegin();
theta0 = self.thetaBegin();
kappa0 = self.kappa0();
L = self.length0();
C0 = CircleArc( x0, y0, theta0, kappa0, L );
x0 = self.xMiddle();
y0 = self.yMiddle();
theta0 = self.thetaMiddle();
kappa0 = self.kappa1();
L = self.length1();
C1 = CircleArc( x0, y0, theta0, kappa0, L );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Return the nurbs represantation of the two arc composing the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> [arc0,arc1] = ref.to_nurbs();
%>
%> \endrst
%>
%> - `arc0`: the nurbs of the first arc
%> - `arc1`: the nurbs of the second arc
%>
function [ arc0, arc1 ] = to_nurbs( self )
[ arc0, arc1 ] = BiarcMexWrapper( 'to_nurbs', self.objectHandle );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Get the curvilinear coordinates of the point `(x,y)`
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> [s,t] = ref.find_coord( x, y );
%>
%> \endrst
%>
%> - `s`: curvilinear coordinate along the curve
%> - `t`: curvilinear coordinate along the normal of the curve
%>
function [ s, t ] = find_coord( self, x, y )
[ s, t ] = BiarcMexWrapper( 'findST', self.objectHandle, x, y );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Plot the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> ref.plot( npts );
%>
%> fmt1 = {'Color','blue','Linewidth',2};
%> fmt2 = {'Color','red','Linewidth',2};
%> ref.plot( npts, fmt1, fmt2 );
%>
%> \endrst
%>
%> - `npts`: number of sampling points for plotting
%> - `fmt1`: format of the first arc
%> - `fmt2`: format of the second arc
%>
function plot( self, npts, varargin )
if nargin<2
npts = 64;
end
if nargin>2
fmt1 = varargin{1};
else
fmt1 = {'Color','blue','Linewidth',2};
end
if nargin>3
fmt2 = varargin{2};
else
fmt2 = {'Color','red','Linewidth',2};
end
[C0,C1] = self.getCircles();
C0.plot(npts,fmt1);
hold on;
C1.plot(npts,fmt2);
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Plot the curvature of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> ref.plotCurvature( npts );
%>
%> fmt1 = {'Color','blue','Linewidth',2};
%> fmt2 = {'Color','red','Linewidth',2};
%> ref.plotCurvature( npts, fmt1, fmt2 );
%>
%> \endrst
%>
%> - `npts`: number of sampling points for plotting
%> - `fmt1`: format of the first arc
%> - `fmt2`: format of the second arc
%>
function plotCurvature( self, npts, varargin )
if nargin < 2
npts = 1000;
end
L = BiarcMexWrapper( 'length', self.objectHandle );
S = 0:L/npts:L;
[ ~, ~, ~, kappa ] = BiarcMexWrapper( 'evaluate', self.objectHandle, S );
plot( S, kappa, varargin{:} );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Plot the angle of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> ref.plotAngle( npts );
%>
%> fmt1 = {'Color','blue','Linewidth',2};
%> fmt2 = {'Color','red','Linewidth',2};
%> ref.plotAngle( npts, fmt1, fmt2 );
%>
%> \endrst
%>
%> - `npts`: number of sampling points for plotting
%> - `fmt1`: format of the first arc
%> - `fmt2`: format of the second arc
%>
function plotAngle( self, npts, varargin )
if nargin < 2
npts = 1000;
end
L = BiarcMexWrapper( 'length', self.objectHandle );
S = 0:L/npts:L;
[ ~, ~, theta, ~ ] = BiarcMexWrapper( 'evaluate', self.objectHandle, S );
plot( S, theta, varargin{:} );
end
% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
%> Plot the normal of the biarc
%>
%> **Usage:**
%>
%> \rst
%> .. code-block:: matlab
%>
%> ref.plotNormal( step, len );
%>
%> \endrst
%>
%> - `step`: number of sampling normals
%> - `len`: length of the plotted normal
%>
function plotNormal( self, step, len )
for s=0:step:self.length()
[ x, y, theta, ~ ] = self.evaluate(s);
n = [sin(theta),-cos(theta)];
A = [x,x+len*n(1)];
B = [y,y+len*n(2)];
plot(A,B);
end
end
end
end
