Example 3.  Find the Bézier curve which has the starting at the point [Graphics:Images/BezierCurveMod_gr_82.gif] and destination point [Graphics:Images/BezierCurveMod_gr_83.gif] which has the control points [Graphics:Images/BezierCurveMod_gr_84.gif] and [Graphics:Images/BezierCurveMod_gr_85.gif], respectively.  Use the parametric equations to form the  Bézier curve.

Solution 3.

[Graphics:../Images/BezierCurveMod_gr_86.gif]


[Graphics:../Images/BezierCurveMod_gr_87.gif]

Replace the values in  [Graphics:../Images/BezierCurveMod_gr_88.gif] and call it  [Graphics:../Images/BezierCurveMod_gr_89.gif].  

[Graphics:../Images/BezierCurveMod_gr_90.gif]


[Graphics:../Images/BezierCurveMod_gr_91.gif]

Graph the curve  [Graphics:../Images/BezierCurveMod_gr_92.gif],  remember that the interval for this parametric curve is  for  [Graphics:../Images/BezierCurveMod_gr_93.gif].   

[Graphics:../Images/BezierCurveMod_gr_94.gif]


[Graphics:../Images/BezierCurveMod_gr_95.gif]

[Graphics:../Images/BezierCurveMod_gr_96.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004