next up previous notation contents
Next: 4.2.8 Sequential Rendering Up: 4.2 Basic Rendering Previous: 4.2.6 Continuity-Based Testing

4.2.7 Linear Interval Arithmetic

Let tex2html_wrap_inline31473 denote a two-dimensional linear interval arithmetic, such as tex2html_wrap_inline33001 or tex2html_wrap_inline38047 . We will not ensure that R represents tex2html_wrap_inline37549 directly; we will instead work with tex2html_wrap_inline38053 . The interval specification tex2html_wrap_inline37715 is computed by evaluating the specification S using the interval arithmetic tex2html_wrap_inline31473 . The interval inclusion property assures us that

math26627

Let tex2html_wrap_inline37721 describe tex2html_wrap_inline37563 , using an element of tex2html_wrap_inline31441 :

math25241

We may then determine tex2html_wrap_inline37727 by considering

math26638

for tex2html_wrap_inline38069 . The remaining sections detail how tex2html_wrap_inline37727 may be determined. We account for the domain of S as before.

Other linear interval arithmetics may be used, such as tex2html_wrap_inline38075 or tex2html_wrap_inline38077 , given an appropriate tex2html_wrap_inline38079 . Better renderings may be obtained by taking S into account when choosing tex2html_wrap_inline31473 and tex2html_wrap_inline38079 .


next up previous notation contents
Next: 4.2.8 Sequential Rendering Up: 4.2 Basic Rendering Previous: 4.2.6 Continuity-Based Testing
Jeff TupperMarch 1996