Texas Instruments TI89TITANIUM User Manual - Page 945

Contour Levels and Implicit Plot Algorithm Contours are calculated and plotted by the following method. An implicit plot is the same as a contour, except that an implicit plot is for the z=0 contour only. Algorithm Based on your x and y Window variables, the distance between xmin and xmax and between ymin and ymax is divided into a number of grid lines specified by xgrid and ygrid. These grid lines intersect to form a series of rectangles. For each rectangle, the equation is evaluated at each of the four corners (also called vertices or grid points) and an average value (E) is calculated: E = z---1-----+-----z--2-----+4-----z--3-----+-----z--4-- The E value is treated as the value of the equation at the center of the rectangle. For each specified contour value (Ci) • At each of the five points shown to the right, the difference between the point's z value and the contour value is calculated. • A sign change between any two adjacent points implies that a contour crosses the line that joins those two points. Linear interpolation is used to approximate where the zero crosses the line. • Within the rectangle, any zero crossings are connected with straight lines. • This process is repeated for each contour value. Each rectangle in the grid is treated similarly. Runge-Kutta Method For Runge-Kutta integrations of ordinary differential equations, the TI-89 Titanium / Voyage™ 200 uses the Bogacki-Shampine 3(2) formula as found in the journal Applied Math Letters, 2 (1989), pp. 1-9. Appendix B: Technical Reference 946