# Plotting contour diagrams? how do i do that?

• starsiege
In summary, if you are looking to plot a function with Contour diagrams, you should first determine what type of function it is and then find the slope and intercept. You can then use these values to find the contour lines.
starsiege
im learning about contour diagrams in my calculus text but I am totally confused as to how one should start drawing those plots?

for example f(x,y) = x+y
then its supposed to go like

x+y = c
y = -x +c

^^i can see that the slope is 1
but how do i plot this graph?..im told that i should give values to c and plot it...but I am totally confused as to how i should do that (the answer is there too but i donno how they drew the graph/which method they used to draw it)

also I am totally confused as to how one can draw a contour diagram from the data given in a table

table of values for f(x,y) = X^2 - Y^2

i have attached the table here too

thank you

#### Attachments

• contour.jpg
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Connect the dots.

well..my main issue is how to find each separate contour line?

if i were to draw one line which dots/values should i use

starsiege said:
well..my main issue is how to find each separate contour line?

if i were to draw one line which dots/values should i use

Well, your curves are easy. Your first example is a straight line so you can use slope and intercept. Your second example looks like a hyperbolic functions so you could find the asymptotes and the point where it crosses the axis.

In general though it is not much different then plotting any function. Pick some x values, find the corresponding y values and plot. If you can find roots, asymptotes and extreme values that can reduce the number of points you need to find. You could use a graphing calculator if you are having trouble.

starsiege said:
well..my main issue is how to find each separate contour line?

if i were to draw one line which dots/values should i use

Here is one procedure to find approximate dots from values in a table: Look along
each row and each column in the table to find the "box" through which the contour
might pass. Then do a linear interpolation to find the coordinates. Then connect the dots.

For example, suppose you look for the contour -1 in your table. Looking along the first
row in your table, this contour would have approximate dots at the
coordinates (-2.8, 3.0) and (2.8,3.0). Now do this for every row and
every column, collect the dots and connect them.

Now, write a computer programme to do this automatically and you will see that it is not as easy as the above instructions seem!

starsiege said:
im learning about contour diagrams in my calculus text but I am totally confused as to how one should start drawing those plots?

for example f(x,y) = x+y
then its supposed to go like

x+y = c
y = -x +c

^^i can see that the slope is 1
I would hope that you could see the slope was -1!

but how do i plot this graph?..im told that i should give values to c and plot it...but I am totally confused as to how i should do that (the answer is there too but i donno how they drew the graph/which method they used to draw it)
Surely, if you are looking at functions of more than 1 variable, you learned long ago that the graph of y= -x+ c is a straight line! You only need two points to determine a straight line. when x= 0, y= c and when y= 0, x= c. Draw the straight line through the intercepts (0, c) and (c, 0). Do that for several different values of c.

also I am totally confused as to how one can draw a contour diagram from the data given in a table

table of values for f(x,y) = X^2 - Y^2

i have attached the table here too

thank you
Why make a table? That's what you do with functions you've never seen before! That's what a calculator does! You are supposed to be smarter than a calculator.

For any c, f(x,y)= c is x2- y2= c. You should recognise immediately that that is a hyperbola. If c is positive, the vertices are at $(\sqrt{c}, 0)$ and $(-\sqrt{c},0)$ and the asymptotes are the lines $y= x+ \sqrt{c}$ and $y= -x+ \sqrt{c}$. If c is negative, the vertices are at $(0, \sqrt{c})$ and $(0, -\sqrt{c})$ and the same asymptotes as above. If c= 0, the asymptotes are the graph. It should take you about 3 minutes to draw several of those contours.

## 1. What is a contour diagram?

A contour diagram is a visual representation of a 3D surface in 2D form. It uses contour lines to show the elevation or value of a variable at different points on the surface.

## 2. How do I create a contour diagram?

To create a contour diagram, you will need to plot data points on a 2D graph and then connect them with contour lines. You can use software such as MATLAB, Python, or Excel to create a contour diagram.

## 3. What is the purpose of a contour diagram?

A contour diagram is used to visualize data and understand the relationship between variables. It can also help identify patterns and trends in the data.

## 4. Can I plot a contour diagram for any type of data?

Yes, contour diagrams can be used for any type of data that can be represented on a 3D surface. This includes data from scientific experiments, geospatial data, and mathematical functions.

## 5. Are there any limitations to using contour diagrams?

Contour diagrams are limited in their ability to accurately represent complex or irregular surfaces. They also require a large amount of data points to create a clear and accurate visualization.

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