Samet Türkmen-030060143-4th week

        Bezier curve:
  
        B ezier developed a reformulation of Ferguson curves in terms of Bernstein polynomials for the UNISURF System at Renault in France in 1970. 


         Degree elevation: The degree elevation algorithm permits us to increase the degree and control points of a B ezier curve from n to n+1 without changing the shape of the curve.
          
         Variation diminishing property
A polygon can be created by the segments connecting the ordered vertices of a B ezier
curve.
In 2D: The number of intersections of a straight line with a planar B ezier curve is
no greater than the number of intersections of the line with the control polygon. A line
intersecting the convex hull of a planar B ezier curve may intersect the curve, be tangent to
the curve, or not intersect the curve at all. It may not, however, intersect the curve more
times than it intersects the control polygon. 
In 3D: The same relation holds true for a plane.
Results : (a rough interpretation)
      A B ezier curve oscillates less than its polygon.
     The polygon's segments exaggerate the oscillation of the curve.
This property is important in intersection algorithms and in detecting the \fairness" of
B ezier curves.

(N. M. Patrikalakis, Massachusetts Institute of Technology  Cambridge, MA 02139-4307, USA, lecture 4 and 5, p.7)

      B spline:


  
The formulation of uniform B-splines can be generalized to accomplish certain objectives.
These include
-Non-uniform parameterization.
- Greater general flexibility.
- Change of one polygon vertex in a B ezier curve or of one data point in a cardinal (or
interpolatory) spline curve changes entire curve (global schemes).
- Remove necessity to increase degree of B ezier curves or construct composite B ezier curves
using previous schemes in order to increase degrees of freedom.
- Obtain a \local" approximation scheme.
The development extends the B ezier curve formulation to a piecewise polynomial curve with
easy continuity control.






(N. M. Patrikalakis, Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA, lecture 6 , p.2)




      Phase change materials:

          There are two methods that can hold irregular shaped or curved workpieces in a medium other than hard tooling.In the first and older method.a low melting point metal is used as as the clamping medium.For example,an irregular shaped workpiee is dipped into molten lead and allowed to set.After setting, the solidified lead block is champed in a simple fixture.The possibly adverse effect of such materials as lead on the workpiece to be champed must be considered


          In the second method, the supportingmedium is magnetorheological or electrorheological fluid .In the MR application, the particles are ferromagnetic or paramagnetic micrometerin size as well as using nanoparticles, and in a nonmagnetic fluid.






(Kalpakjian S., Schmid S.R., Manufacturing engineering and technology, 5th Edition,p.1177)





      Photopolymerization:


          
         Stereolithography process was used to polymerize SU-8 spun on the slides.This technology enables the fabrication of many complex shapes. The spectra physics model 2020 argon ion laser was used for irradiations. An exposure of 300mJ/cm^2 was required to properly manufacture quite vertical 30 micrometer height patterns. Matrix of regular polymeric wells was obtained by succesive duplications of an empty disc pattern inside a full polymer square,in the four directions. to get compact cross- linking, hatch pattern was performed every 100 micrometers and in the two ortogonal directions.

(Paulo Jorge Bártolo, Virtual and Rapid Manufacturing , p.348)