Example 3.  Find the Bézier curve which has the starting at the point [Graphics:Images/BezierCurveMod_gr_132.gif] and destination point [Graphics:Images/BezierCurveMod_gr_133.gif] which has the control points [Graphics:Images/BezierCurveMod_gr_134.gif] and [Graphics:Images/BezierCurveMod_gr_135.gif], respectively.  Use the parametric equations to form the  Bézier curve.

Solution 3.

[Graphics:../Images/BezierCurveMod_gr_136.gif]
[Graphics:../Images/BezierCurveMod_gr_137.gif]

Replace the values in  [Graphics:../Images/BezierCurveMod_gr_138.gif] and call it  [Graphics:../Images/BezierCurveMod_gr_139.gif].  

[Graphics:../Images/BezierCurveMod_gr_140.gif]
[Graphics:../Images/BezierCurveMod_gr_141.gif]

Graph the curve  [Graphics:../Images/BezierCurveMod_gr_142.gif],  remember that the interval for this parametric curve is  for  [Graphics:../Images/BezierCurveMod_gr_143.gif].   

[Graphics:../Images/BezierCurveMod_gr_144.gif]

[Graphics:../Images/BezierCurveMod_gr_145.gif]

[Graphics:../Images/BezierCurveMod_gr_146.gif]

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003