%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-06-06 14:26:46
 % @LastEditTime: 2021-06-06 15:55:17
%--------------------------

x0 = 0; 
x1 = 1; 
x01 = 0.5;
x10 = 0.5;
n = 100;
dx = (x1-x0) / n;

y0 = 1;
y1 = -1;
y01 = 3;
y10 = -3; 
Q = [x0, 0, x01, 0, x10, 0, x1, 0;
    0, y0, 0, y01, 0, y10, 0, y1]';

y = zeros(n+1, 2);
for i = 0:n
    t = i*dx;
    B = Bezier_matrix(t);
    y(i+1, :) = diag(B * Q);
end

figure; 
plot(y(:,1), y(:,2), 'k','linewidth',2); 
hold on; plot([x0,x0],[0,y0],':','Color', 'k','linewidth',2); plot([x1,x1],[0,y1],':','Color', 'k','linewidth',2);
plot([x0-0.1, x1+0.1], [0,0], 'k','linewidth',1);
plot([x0,x01],[y0,y01],':','Color', 'k','linewidth',2); plot([x10,x1],[y10,y1],':','Color', 'k','linewidth',2);
scatter([x0,x01,x10,x1],[y0,y01,y1,y1], 'MarkerEdgeColor','k', 'MarkerFaceColor',[1,1,1], 'LineWidth',2);
xlabel('X','Color','k','FontSize',16);
% ylabel('Y','Color','k','FontSize',16);
ylim([-2.5,2.5]);

figure; plot([x0,0.2,0.8,x1], [y0,1.414,-1.414,y1], 'k','linewidth',2);
hold on; plot([x0,x0],[0,y0],':','Color', 'k','linewidth',2); plot([x1,x1],[0,y1],':','Color', 'k','linewidth',2);
plot([x0-0.1, x1+0.1], [0,0], 'k','linewidth',1);
scatter([x0,0.2,0.8,x1], [y0,1.414,-1.414,y1], 'MarkerEdgeColor','k', 'MarkerFaceColor',[1,1,1], 'LineWidth',2);
xlabel('X','Color','k','FontSize',16);
% ylabel('Y','Color','k','FontSize',16);
ylim([-2.5,2.5])

figure; plot([x0,x1], [y0,y1], 'k','linewidth',2);
hold on; plot([x0,x0],[0,y0],':','Color', 'k','linewidth',2); plot([x1,x1],[0,y1],':','Color', 'k','linewidth',2);
plot([x0-0.1, x1+0.1], [0,0], 'k','linewidth',1);
scatter([x0,x1],[y0,y1], 'MarkerEdgeColor','k', 'MarkerFaceColor',[1,1,1], 'LineWidth',2);
xlabel('X','Color','k','FontSize',16);
ylabel('Y','Color','k','FontSize',16);
ylim([-2.5,2.5])

function B = Bezier_matrix(t)
    B = [1, t, t^2, t^3] * [1, 0,0,0;
                            -3,3,0,0;
                            3,-6,3,0;
                            -1,3,-3,1]; % 1,4
    I = eye(2, 2);
    B = kron(B, I); % 2,8
end