How can I draw/display a character based on Bezier equations? I have the plot equations:
x(t)=3t-3t^2
y(t)=2-3t^2+2t^3
x(t)=3t-3t^2
y(t)=1-3t^2+2t^3
and the plot should look like a character '3' like the following:
My problem is how to plot the equations in order to get '3'? What should I plug where? In the book examples they have 0<=t<=1 but I do not know still how to plot those equations. Any help is appreciated!
Convert the curves to Bézier form (i.e. calculate the control points). Suppose one of your curves has control points $A,B,C,D$. You have probably been taught that the curve starts at the point $A$, and is tangent to the line $AB$. Similarly, it ends at the point $D$, and is tangent to the line $CD$. Also, the curve is contained inside the quadrilateral $ABCD$. That should give you enough information to sketch it, roughly.
The point of this exercise (I suppose) is that the control points tell you something about the geometry of the curve, but the coefficients in the given equations do not.
Also, note that your second curve is just a copy of the first one, but shifted downwards one unit in the $y$-direction. So, once you have sketched the first curve, it's easy to sketch the second one.