Texas Instruments TI-92 Owners Manual - Page 589

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 z1 =f(x1 ,y1 ) z3 =f(x2 ,y1 ) evaluated at each of the four E corners (also called vertices or grid points) and an average value (E) is calculated: z1 + z2 + z3 + z4 E = 4 z2 =f(x1 ,y2 ) z4 =f(x2 ,y2 ) 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. z1 ìCi EìCi z3 ìCi z2 ìCi z4 ìCi ¦ 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. 572 Appendix B: Reference Information