2.6 Bezier curve

Several BEZIER curves (with eventually some line segments)

• Shortcut: Ctrl+B
• We give a name.
• Then a command like [<list of points>]. The list of points can be:

1. A list of three points [A,C,B]. The Bezier curve’s origin is <A> and the other extremity is <B> with a control point C. It’s the curve parametrized with ${\left(1-t\right)}^{2}A+2t\left(1-t\right)C+{t}^{2}B$.
2. A 4 points list (or more): [A1,C1,C2,A2,C3,C4,A3...]: it’s successive Bezier curves with 2 control points, the first one goes from A1 to A2, is controled by C1, C2 (parametrized with: ${\left(1-t\right)}^{3}A1+3{\left(1-t\right)}^{2}tC1+3\left(1-t\right){t}^{2}C2+{t}^{3}A2$), the second one goes from A2 to A3 and the control points are C3,C4 ...etc. One exception though, the control points can be replaced with the jump constant. In that case, we jump directly from A1 to A2 with a line segment.
• The number of points computed (by curve) can be modified in the Attributes (variable NbPoints).
• Corresponding graphical command:Bezier (to be used in a User-defined type element).
• Exemple(s)[-2, -1+i, i, 1, jump, 1-i, jump, -2-i, jump, -2].