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4.2.6 Continuity-Based Testing

Subpixel sample testing rarely verifies one-dimensional elements of graphs. Consider a graph G[g = 0], with tex2html_wrap_inline37997 . Consider tex2html_wrap_inline37999 , tex2html_wrap_inline38001 . If

math26421

then we set tex2html_wrap_inline37727 to tex2html_wrap_inline32719 , since

figure26429

so

math26440

The corners of tex2html_wrap_inline37563 are common initial choices for tex2html_wrap_inline33497 and tex2html_wrap_inline38011 . Continuity-based testing is often used in place of subpixel sample testing where = occurs in a specification.

Compare the following two tex2html_wrap_inline35053 renderings of tex2html_wrap_inline37957 , produced using, and not using, continuity-based testing:

figure26446

  tex2html_wrap_inline38023 denotes a rendering produced using continuity-based testing. With sample testing, a sample must be chosen which lies within a graph; with continuity-based testing, a pair of samples must be chosen such that the graph lies between the two samples. If each sample is a point within tex2html_wrap_inline38025 , and the samples are chosen uniformly and independently, the outer pixels of each step have a 25% chance of being verified as tex2html_wrap_inline32719 , while the inner pixel of each step has a 50% chance of being verified as tex2html_wrap_inline32719 . With subpixel sample testing, each pixel has a 0% chance of being verified as tex2html_wrap_inline32719 .

Consider the following two renderings, both of which employ continuity-based testing:

figure26554

Continuity-based testing fares poorly with tex2html_wrap_inline38037 , as tex2html_wrap_inline38039 is non-negative for all (x,y).


next up previous notation contents
Next: 4.2.7 Linear Interval Arithmetic Up: 4.2 Basic Rendering Previous: 4.2.5 Exhaustive Subpixel Testing
Jeff TupperMarch 1996