main.m

% SABIR ILYASS
% Curves and surfaces : differential geometry in practice

clc; clear; close all;

%% 1 Differential geometry of curves and surfaces
% 1.1 Planar curves
% 1.1.1 Study of an ellipse

% question 1,2,3  and 4:
X = ellipse(25,25,20);
% afficher_courbe(X);
tracer_frenet(X);

% 1.1.2 Study of a manually entered curve
% Question 5:
X2 = saisir_courbe;
n = size(X2,2);
Y = zeros(2, n + 2);
Y(:,1:n) = X2;
Y(:,n+1) = X2(:,1); X2(:,n+2) = X2(:,2);
tracer_frenet(Y);


% 1.2 An example of a surface : the digital terrain model
% Question 6:
im = double(imread("saltlake.png"));
% imshow(im,[]);
image_2_3D(im, 1);

% question 7:
Gaussian_mean_curvature(im,0.4,"gaussian");

% % 2 Modeling of curves and surfaces0
% % 2.1 Curve/surface reconstruction from a point cloud
% % Question 8:
X3 = saisir_courbe();
Crust(X3);

% 2.2 Modeling of smooth curves
% Question 9:
% Enter a set of points manually with the mouse
X = saisir_courbe();

% Get the number of points
n = size(X,2);

% initialization of the Bezier curve
% we take 100 * n points to draw more 
% points of the beziers curve and to show more its curvature
Bezier_points = zeros(2,n * 100);

for i = 1: 100 * n
    [Cu_1, Cu_2] = bezier(X, (i - 1) / (100 * n));
    Bezier_points(1,i) = Cu_1;
    Bezier_points(2,i) = Cu_2;
end

% plot segments between the points of the point cloud X
for i = 1:(n - 1)
    plot([X(1,i) X(1, i + 1)],[X(2,i) X(2, i + 1)]);
end

% plot the Bezier curve
for i = 1:(100 * n - 1)    
    plot([Bezier_points(1,i) Bezier_points(1, i + 1)],[Bezier_points(2,i) Bezier_points(2, i + 1)]);
end