point_set_random_simplify : function to random simplify a point set.

Author and support : nicolas.douillet (at) free.fr, 2019.

% Syntax

V_out = point_set_random_simplify(V_in);
V_out = point_set_random_simplify(V_in, smpf_coeff);
[V_out, idx_vect] = point_set_random_simplify(V_in, smpf_coeff);

% Description

V_out = point_set_random_simplify(V_in) randomly samples V_in point set
at the default rate of 0.5 (50% of the points are kept) and stores it in
V_out.

V_out = point_set_random_simplify(V_in, smpf_coeff) randomly samples
V_in point set at the rate given by smpf_coeff.

[V_out, idx_vect] = point_set_random_simplify(V_in, smpf_coeff) also
provides the index vector of the points kept, such that
V_out = V_in(idx_vect,:).

% See also : RAND,RANDI,COLON

% Input arguments

| | |
- V_in = [Vx Vy Vz] : numeric double matrix, size(V_in) = [nb_vertices_in, 3].
| | |

- smpf_coeff : numeric double scalar, 0 <= smpf_coeff <= 1. Default value
is smpf_coeff = 0.5.

% Output arguments

| | |
- V_out = [Vx Vy Vz] : numeric double matrix, size(V_out) = [numel(idx_vect), 3].
| | |

- idx_vect : numeric vector of integers > 0.

% Example
N = 20000;
X = 2*(rand(N,1)-0.5);
Y = 2*(rand(N,1)-0.5);
Z = 2*(rand(N,1)-0.5);

Rho = X.^2 + Y.^2 + Z.^2;
f = Rho <= 1;
X = X(f);
Y = Y(f);
Z = Z(f);

M = [X, Y, Z];

figure;
subplot(121);
plot3(X,Y,Z,'.','Color',[0 0 1],'Linewidth',2), hold on;
axis equal;

N = point_set_random_simplify(M);
subplot(122);
plot3(N(:,1), N(:,2), N(:,3),'.','Color',[0 0 1],'Linewidth',2), hold on;
axis equal;