#### 8.1.2 (Poly-)Bézier

• Bezier( <point list> ).
• Description: draw BéZIER curves successively (with eventually some segments). There are several possibilities for the point list:
1. a three point list $\left[A,C,B\right]$, then it is a Bézier curve of origin <A> and end <B> with a control point <C>, this is the curve parametrized with:
${\left(1-t\right)}^{2}A+2t\left(1-t\right)C+{t}^{2}B$

2. a 4 or more point list: [A1, C1, C2, A2, C3, C4, A3...]: then it is several Bézier curve with two control points, the first goes from A1 to A2, is controled by C1, C2 (parametrized by ${\left(1-t\right)}^{3}tA1+3{\left(1-t\right)}^{2}tC1\right]+3\left(1-t\right){t}^{2}C2+{t}^{3}A2$), the second goes from A2 to A3 is controlled by C3,C4 ...etc. An exception though, two control points can be replaced with the jump contant. In that case we jump directly from A1 to A2 by drawing a segment.
• The calculated point number (for each curve) is editable in the Attributes (NbPoints variable).

 \begin{texgraph}[name=Bezier,export=pgf]   view(-4,4,-4,5),Marges(0,0,0,0),   size(7.5), Width:=8,   A:=-3+4*i, B:=3+i, C:=3-3*i, D:=-3-3*i,   C1:=4.5*i,C2:=-2*i, C3:=2-i, C4:=-2,   FillStyle:=full, FillColor:=lightblue,Color:=red,   Bezier(A,C1,C2,B,jump,C,C3,C4,D,jump,A),   FillStyle:=none, DotStyle:=cross,   DotScale:=2,Color:=black,   LabelDot(A,"$A$","N",1),   LabelDot(B,"$B$","E",1),   LabelDot(C,"$C$","SE",1),   LabelDot(D,"$D$","SO",1),   LabelDot(C1,"$C_1$","E",1),   LabelDot(C2,"$C_2$","SO",1),   LabelDot(C3,"$C_3$","N",1),   LabelDot(C4,"$C_4$","N",1),   LineStyle:=userdash,   DashPattern:=[5,2,0.5,2], Width:=6,   LineCap:=round,   Ligne([A,C1,C2,B,jump,C,C3,C4,D],0)   \end{texgraph}

Bezier Command