## Contents

- Parabola definition
- Compute curvature for a specific position

    %DEMOPARABOLACURVATURE  One-line description here, please.
    %   output = demoParabolaCurvature(input)
    %
    %   Example
    %   demoParabolaCurvature
    %
    %   See also
    %

    % ------
    % Author: David Legland
    % e-mail: david.legland@nantes.inra.fr
    % Created: 2007-02-26
    % Copyright 2007 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas.

## Parabola definition

    % parameters of polynomial curve (here, a parabola)
    c1 = [0 1];
    c2 = [0 0 .5];

    % parametrization for a parabola arc
    t = linspace(-1, 3, 100)';

    % approximation of the curve
    curve = polynomialCurvePoint(t, c1, c2);

    % prepare plot
    figure(1); clf;
    hold on;

    % draw curve
    drawPolyline(curve, 'linewidth', 2);

    % format axis
    axis equal;
    axis([-2 3 0 5]);

## Compute curvature for a specific position

    % the position
    pos = .5;

    % point, derivative and  curvature at chosen point
    point = polynomialCurvePoint(pos, c1, c2);
    deriv = polynomialCurveDerivative(pos, c1, c2);
    kappa = polynomialCurveCurvature(pos, c1, c2);

    % radius is the inverse of the curvature
    radius = 1./kappa;

    % tangent and normal lines
    tangent = [point deriv];
    normal = orthogonalLine(tangent, point);

    % osculating circle
    center = pointOnLine(normal, radius);
    circle = [center radius];

    % display tangent line, normal, and osculating circle
    drawPoint(point, 'color', 'k');
    drawLine(tangent, 'color', 'k');
    drawLine(normal, 'color', 'k');
    drawCircle(circle, 'color', 'k');