M367    letterD.mws 

>

restart;

 

>	with(plots): with(plottools):

 

Example in Cubic Bezier Curve Construction 

>	b:= j-> binomial(3,j)*x^j*(1-x)^(3-j);

 

(1)

 

Plotting the letter D 

>	d1x:= [-0.2,0,0.7,1.0]: d1y:= [2,2,2,2]: #top flat part

 

>	d2x:= [1.0,1.3,2,2]: d2y:= [2,2,1.8,1]: #top right arch

 

>	d4x:= [-0.2, -0.1, 0, 0]: d4y:=[2,2,1.8,1.7]:#top left arch

 

>	d6x:= [0,0,0,0]: d6y:= [1.7,1.2, 0.8, 0.3]: #outer vert line

 

>	d8x:= [0.2,0.2,0.2,0.2]: d8y:= [0.3,0.7,1.2,1.7]: #inner vert line

 

>	d9x:= [0.2,0.3, 0.5,0.8]: d9y:=[1.7,1.8,1.85,1.85]:#inner top arch

 

>	d10x:=[0.8,1.1,1.6,1.6]: d10y:=[1.85,1.85, 1.5,1]:#inner right arch

 

>

 

>	T1:= seq([d1x[k],d1y[k]], k=1..4):

 

>	T2:= seq([d2x[k],d2y[k]], k=1..4):

 

>	T4:= seq([d4x[k],d4y[k]], k=1..4):

 

>	T6:= seq([d6x[k],d6y[k]], k=1..4):

 

>	T8:= seq([d8x[k],d8y[k]], k=1..4):

 

>	T9:= seq([d9x[k],d9y[k]], k=1..4):

 

>	T10:= seq([d10x[k],d10y[k]], k=1..4);

 

(2)

 

>	pts:= plot([T1, T2, T4, T6, T8, T9, T10], style=point, symbol = box, scaling = constrained, color = blue):

 

>	BT1:= evalm(sum(b(k-1)*T1[k], k=1..4)):

 

>	BT2:= evalm(sum(b(k-1)*T2[k], k=1..4)):

 

>	BT4:= evalm(sum(b(k-1)*T4[k], k=1..4)):

 

>	BT6:= evalm(sum(b(k-1)*T6[k], k=1..4)):

 

>	BT8:= evalm(sum(b(k-1)*T8[k], k=1..4)):

 

>	BT9:= evalm(sum(b(k-1)*T9[k], k=1..4)):

 

>	BT10:= evalm(sum(b(k-1)*T10[k], k=1..4)):

 

>

 

>	CT1:= plot([BT1[1], BT1[2], x=0..1], color=orange):

 

>	CT2:= plot([BT2[1], BT2[2], x=0..1], color= cyan):

 

>	CT3:= plot([BT2[1], 2-BT2[2], x=0..1], color= cyan):#reflect of C2

 

>	CT4:= plot([BT4[1], BT4[2], x=0..1], color= brown):

 

>	CT5:= plot([BT4[1], 2-BT4[2], x=0..1], color= brown):#reflec. of C4

 

>	CT6:= plot([BT6[1], BT6[2], x=0..1]):

 

>	CT7:= plot([BT1[1], 2-BT1[2], x=0..1], color=orange):#reflect of C1

 

>	CT8:= plot([BT8[1], BT8[2], x=0..1], color=red):

 

>	CT9:= plot([BT9[1], BT9[2], x=0..1], color= blue):

 

>	CT10:= plot([BT10[1], BT10[2], x=0..1], color=green):

 

>	CT11:=plot([BT10[1], 2-BT10[2],x=0..1],color=green):#reflect of C10

 

>	CT12:= plot([BT9[1], 2-BT9[2], x=0..1], color= blue):#relect of C9

 

>	display({CT1,CT2,CT3,CT4,CT5,CT6,CT7,CT8,CT9,CT10,CT11,CT12, pts}, scaling=constrained, axes=none);

 

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