Bezierkurver

Bezierkurver.

Figuren viser kurve med parameterfremstilling:

(1-t)³ a₀ + 3 (1-t)² t a₁ + 3 (1-t) t² a₂ + t³ a₃; for 0 < t < 1.

Bezier-kurven er opfundet af den franske ingeniør Pierre Étienne Bézier (1910-1999) – i første omgang for at kunne give en simpel beskrivelse af en bils kurvede former. (Han arbejdede for Renault). Bezier-kurver har mange andre anvendelser fx til beskrivelse af skifttegn. Du kan flytte de fire styrepunkter og se, hvordan kurven påvirkes.

Figure figure = Position [0,0] Size[x,y] Origin[x/2,y/2] Unit x/5 Color "white"; //Axes axes = Color "black"; Grid grid = Color "blue"; //Units units = Color "black"; Point a0 = [-1,0] Free Size 2.5 Color "red"; Point a1 = [0,0] Free Size 2.5 Color "red"; Point a2 = [0,1] Free Size 2.5 Color "red"; Point a3 = [1,1] Free Size 2.5 Color "red"; Label a0lab = "a₀" At a0 Offset [10,-10] Color "black" Style "font-weight:bold;"; Label a1lab = "a₁" At a1 Offset [10,-10] Color "black" Style "font-weight:bold;"; Label a2lab = "a₂" At a2 Offset [10,-10] Color "black" Style "font-weight:bold;"; Label a3lab = "a₃" At a3 Offset [10,-10] Color "black" Style "font-weight:bold;"; Line a01 = Start a0 Dir a1-a0 Size 1.5 Color "blue"; Line a23 = Start a2 Dir a3-a2 Size 1.5 Color "blue"; ParametricCurve bezier = a0*(1-t)^3 + a1*3*(1-t)^2*t + a2*3*(1-t)*t^2 + a3*t^3 From 0 To 1 Size 1.5 Color "blue";