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>

 

logo7.mw      Explanation will be done in class. 

>	restart: with(plots):

 

>	DP:= densityplot(1, x=0..2, y=0..4): DP:

 

Defining the quadratic and cubic Bezier curves, p and q respectively. 

>	p[0]:=t^2: p[1]:=2*t*(1-t): p[2]:= (1-t)^2:

 

>	q[0]:=t^3: q[1]:=3*t^2*(1-t): q[2]:=3*t*(1-t)^2: q[3]:= (1-t)^3:

 

Points defined by trial and error plus a bit of planning. 

>	a[0]:= [0,4]: a[1]:=[1.0, 4.1]: a[2]:=[2,4]:

 

>	b[0]:= [0.1,0]: b[1]:= [0.2,0.4]: b[2]:= [0.4, 0.9]:

 

>	c[0]:= b[2]: c[1]:= c[0]+ 1.2*(b[2]-b[1]); #see explanation done in class

 

(1)

 

>	c[2]:= [1.6,3.5]: c[3]:= a[2]:

 

Defining the curves controlled by the corresponding 'polygons' 

>	bz[1]:= sum(p[k]*a[k],k=0..2):

 

>	bz[2]:= sum(p[k]*b[k],k=0..2):

 

>	bz[3]:= sum(q[k]*c[k],k=0..3):

 

bz[ ] [1],  bz[ ][2]  represent the x and y components of the Bezier curve. 

>	B1:= plot([bz[1][1],bz[1][2], t=0..1], scaling=constrained):

 

>	B2:= plot([bz[2][1],bz[2][2],t=0..1], scaling=constrained):

 

>	B3:= plot([bz[3][1], bz[3][2], t=0..1], scaling=constrained):

 

Defining the sets of controlled points to be plotted with the graph. 

>	ptc:= plot({seq(c[j],j=0..3)}, style=point, symbol=box, color=blue):

 

>	ptb:= plot({seq(b[k],k=0..2)},style=point, symbol=circle, color = green):

 

>

 

>	display({B1,B2,B3, ptb, ptc}, axes=boxed);

 

Adjusting the 'foot' of 7. 

>	bb[0]:=b[0]: bb[1]:=[0.12,0.3]:

 

>	bb[2]:=b[1]: bb[3]:=b[2]:

 

>	bbz[2]:= sum(bb[k]*q[k],k=0..3):

 

>	BB2:= plot([bbz[2][1], bbz[2][2], t=0..1], scaling=constrained):

 

>

BB2;

 

>