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

Contour Levels and Implicit Plot Algorithm

Algorithm
572 Appendix B: Reference Information
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
and and between
xmax
lines specified by
xgrid
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
( ) is calculated:
E
z + z + z + z
1 2 3 4
E =
4
The value is treated as the value of the equation at the center of the
E
rectangle.
For each specified contour value
( ):
C
i
¦
At each of the five points
shown to the right, the
difference between the point's
value and the contour value
z
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.
Window variables, the distance between
and is divided into a number of grid
ymin ymax
and . These grid lines intersect to form a
ygrid
z =f(x
1
z =f(x
2
z ìC
1
ìC
z
2
xmin
z =f(x ,y
,y )
1 1 3 2
E
z =f(x ,y
,y )
4 2
1 2
ìC
z
i 3 i
EìC
i
z ìC
i 4 i
)
1
)
2