Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations TeX Export

@article{citeulike:6043921, abstract = {Conventional plotting programs adopt techniques such as adaptive sampling to approximate, but not to guarantee, correctness and completeness in graphing functions. Moreover, implicitly defined mathematical relations can impose an even greater challenge as they either cannot be plotted directly, or otherwise are likely to be misrepresented. In this paper, we address these problems by investigating interval constraint plotting as an alternative approach that plots a hull of the specified curve. We present some empirical evidence that this hull property can be achieved by a \$\$\mathcal{O}(n)\$\$ algorithm. Practical experience shows that the hull obtained is the narrowest possible whenever the precision of the underlying floating-point arithmetic is adequate. We describe IASolver, a Java applet (http://www.cs.brandeis.edu/\~{}tim) that serves as testbed for this idea.}, author = {Hickey, Timothy J. and Qju, Zhe and Van Emden, Maarten H.}, citeulike-article-id = {6043921}, citeulike-linkout-0 = {http://dx.doi.org/10.1023/A:1009950630139}, citeulike-linkout-1 = {http://www.springerlink.com/content/w8w9rr7l4m714415}, day = {1}, doi = {10.1023/A:1009950630139}, journal = {Reliable Computing}, keywords = {article, graphing, interval\_arithmetic, interval\_methods, plotting, polynomial, visualization}, month = {February}, number = {1}, pages = {81--92}, posted-at = {2009-10-30 18:54:17}, priority = {2}, title = {Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations}, url = {http://dx.doi.org/10.1023/A:1009950630139}, volume = {6}, year = {2000} }

TY - JOUR ID - citeulike:6043921 L3 - citeulike-article-id:6043921 N2 - Conventional plotting programs adopt techniques such as adaptive sampling to approximate, but not to guarantee, correctness and completeness in graphing functions. Moreover, implicitly defined mathematical relations can impose an even greater challenge as they either cannot be plotted directly, or otherwise are likely to be misrepresented. In this paper, we address these problems by investigating interval constraint plotting as an alternative approach that plots a hull of the specified curve. We present some empirical evidence that this hull property can be achieved by a $$\mathcal{O}(n)$$ algorithm. Practical experience shows that the hull obtained is the narrowest possible whenever the precision of the underlying floating-point arithmetic is adequate. We describe IASolver, a Java applet (http://www.cs.brandeis.edu/~tim) that serves as testbed for this idea. IS - 1 JF - Reliable Computing EP - 92 TI - Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations VL - 6 SP - 81 KW - article KW - graphing KW - interval_arithmetic KW - interval_methods KW - plotting KW - polynomial KW - visualization AU - Hickey, Timothy AU - Qju, Zhe AU - Van Emden, Maarten PY - 2000/02/01/ UR - http://dx.doi.org/10.1023/A:1009950630139 ER -