I have one curve. I want to create another curve offset to that one at right angle.

%initial conditions%
t = 0:0.01:1;
b0 = (1-t).^2;
b1 = 2.*t.*(1-t);
b2 = t.^2;

%point conditions%
p0 = [5,12];
p1 = [9,8];
p2 = [5,1];

P = [p0;p1;p2];

x = p0(1).*b0 + p1(1).*b1 + p2(1).*b2;
y = p0(2).*b0 + p1(2).*b1 + p2(2).*b2;

%c = (x(t),y(t))

%offset curve
%for 1st curve
Offx1= x + 1;
Offy1= y + 1;
plot(x,y)
hold on
%plot Bezier Curve offset
plot(Offx1,Offy1)
axis equal
hold off
grid on;

Answer 1

[Bruno Luong]

%initial conditions%
t = 0:0.01:1;
b0 = (1-t).^2;
b1 = 2.*t.*(1-t);
b2 = t.^2;
B = [b0; b1; b2];

% derivative
b0p = -2*(1-t);
b1p = 2*(1-t) - 2*t;
b2p = 2*t;
Bp = [b0p; b1p; b2p];

%point conditions%
p0 = [5,12];
p1 = [9,8];
p2 = [5,1];

P = [p0; p1; p2];
xy = P'*B;

% rotate unit-tangent vector by 90 deg to find normal
xyp = P'*Bp;
xyp = xyp./sqrt(sum(xyp.^2,1));
normal = [0 -1; 
          1 0]*xyp;

% move points in the normal direction     
step = sqrt(2); 
xy1 = xy + step*normal;

Offx1 = xy1(1,:);
Offy1 = xy1(2,:);

x = xy(1,:);
y = xy(2,:);

plot(x,y)
hold on
%plot Bezier Curve offset
plot(Offx1,Offy1)
axis equal
hold off
grid on;

[Bruno Luong]

Be careful: such curve can cross it-self for large curvature and/or move with with large step.

Answer 2

[Image Analyst]

Just don't add the offset to the y vector and it will be to the right and not to the right and up:

%initial conditions%
t = 0:0.01:1;
b0 = (1-t).^2;
b1 = 2.*t.*(1-t);
b2 = t.^2;

%point conditions%
p0 = [5,12];
p1 = [9,8];
p2 = [5,1];

P = [p0;p1;p2];

x = p0(1).*b0 + p1(1).*b1 + p2(1).*b2;
y = p0(2).*b0 + p1(2).*b1 + p2(2).*b2;

%c = (x(t),y(t))

%offset curve
%for 1st curve
Offx1= x + 1;
plot(x, y, 'b-', 'LineWidth', 2)
hold on
%plot Bezier Curve offset
plot(Offx1, y, 'r-', 'LineWidth', 2)
axis equal
hold off
grid on;

Answer 3

[Prashant Dhabaliya]

Thank you Matt. I would like to create the curve attached to this file. I request you to see this one.

Answer 4

[Prashant Dhabaliya]

Thank you Bruno Luong and Image analyst for your support.