SplineVec Class Reference¶

Splines: SplineVec Class Reference

Splines

Inheritance diagram for SplineVec:

Public Member Functions
function	SplineVec ()

function	setup (in self, in P)

function	knots (in self, in t)

function	get_knots (in self)

function	chordal (in self)

function	centripetal (in self)

function	CatmullRom (in self)

function	eval (in self, in x)

function	eval_D (in self, in x)

function	eval_DD (in self, in x)

function	eval_DDD (in self, in x)

function	curvature (in self, in x)

function	curvature_D (in self, in x)

function	tmin (in self, in x)

function	tmax (in self, in x)

Protected Member Functions
function	copyElement (in self)

Detailed Description

MATLAB class wrapper for the underlying C++ class

The construction of the spline is done as follows

instantiate the spline object

spl = SplineVec();

load the points as a matrix dim x npts where dim is the space dimension and npts is the number of poinst

spl.setup( P ); % P is a dim x npts matrix

build or load the knots

spl.knots( T );   % vector of knots
spl.chordal();    % build knots using chordal distance
spl.centripetal(; % build knots centripetal

build the spline, for the moment only Catmull Rom

spl.CatmullRom();

Constructor & Destructor Documentation

◆ SplineVec()

function SplineVec::SplineVec ( )

Build an empty parametric spline:

spl = SplineVec();

Member Function Documentation

◆ CatmullRom()

function SplineVec::CatmullRom ( in self )

Build the spline using Catmull Rom algorithm

P = [ 0, 0; 1.34, 5; 5, 8.66; 10, 10; 10.6, 10.4; 10.7, 12; ...
      10.7, 28.6; 10.8, 30.2; 11.4, 30.6; 19.6, 30.6; ...
      20.2, 30.2; 20.3, 28.6; 20.3, 12; 20.4, 10.4; ...
      21, 10; 26, 8.66; 29.66, 5; 31, 0 ];
 
S = SplineVec();  % initialize spline
S.setup(P.');     % load points
S.centripetal();  % setup knots
 
% plot interpolation points
hold off;
plot( P(:,1), P(:,2), 'o','Color','red', ...
      'MarkerSize',10,'MarkerFaceColor','blue','MarkerEdgeColor','green');
hold on;
% sample spline for plotting
t  = linspace(S.tmin(),S.tmax(),1000);
PP = S.eval(t);
 
% plot curve
plot( PP(1,:), PP(2,:), '-', 'Color', 'blue', 'Linewidth', 3);

\html_imega{exampleVec.png,width=80%}

◆ centripetal()

function SplineVec::centripetal ( in self )

Build the knots using centripetal parametrization

\begin{eqnarray*} t_0 = 0, \qquad t_k = t_{k-1} + || \mathbf{p}_k - \mathbf{p}_{k-1} ||^{1/2} \end{eqnarray*}

◆ chordal()

function SplineVec::chordal ( in self )

Build the knots using chordal distance

\begin{eqnarray*} t_0 = 0, \qquad t_k = t_{k-1} + || \mathbf{p}_k - \mathbf{p}_{k-1} || \end{eqnarray*}

◆ copyElement()

function SplineVec::copyElement ( in self )

protected

Make a deep copy of a curve object

Usage

B = A.copy();

where A is the curve object to be copied.

◆ curvature()

function SplineVec::curvature	(	in	self,
		in	x )

Evaluate spline curvature at x

kappa = obj.curvature( x );

◆ curvature_D()

function SplineVec::curvature_D	(	in	self,
		in	x )

Evaluate spline curvature derivative at x

kappa = obj.curvature_D( x );

◆ eval()

function SplineVec::eval	(	in	self,
		in	x )

Evaluate spline at x

p = obj.eval( x );

◆ eval_D()

function SplineVec::eval_D	(	in	self,
		in	x )

Evaluate spline derivative at x

p_D = obj.eval_D( x );

◆ eval_DD()

function SplineVec::eval_DD	(	in	self,
		in	x )

Evaluate spline second derivative at x

p_DD = obj.eval_DD( x );

◆ eval_DDD()

function SplineVec::eval_DDD	(	in	self,
		in	x )

Evaluate spline third derivative at x

p_DDD = obj.eval_DDD( x );

◆ get_knots()

function SplineVec::get_knots ( in self )

Get the knots of the spline

t = spl.get_knots();

◆ knots()

function SplineVec::knots	(	in	self,
		in	t )

Setup the knots of the spline

spl.knots( t );

◆ setup()

function SplineVec::setup	(	in	self,
		in	P )

Setup the point of the spline

spl.setup( P );

◆ tmax()

function SplineVec::tmax	(	in	self,
		in	x )

Return initial t-coordinate of the spline

t = obj.tmax();

◆ tmin()

function SplineVec::tmin	(	in	self,
		in	x )