Contour Levels And Implicit Plot Algorithm - Texas Instruments TI-89 Titanium User Manual

Contour Levels and Implicit Plot Algorithm

Algorithm
Appendix B: Technical Reference
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.
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:
z + z + z + z
1 2 3 4
E =
4
The E value is treated as the value of the equation at the center of the
rectangle.
For each specified contour value (C
¦
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.
z =f(x ,y )
1 1 1
E
z =f(x ,y )
2 1 2
):
i
ìC
z
1 i
EìC
ìC
z
2 i
z =f(x ,y )
3 2 1
z =f(x ,y )
4 2 2
ìC
z
3 i
i
ìC
z
4 i
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