Contour: Constructing a Contour Map from h(x,y) = x^2 + y

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In summary, the conversation discusses creating a contour map from a given height field in a specific domain and making east-western cross sections at different points in the domain. There is a brief discussion about the values for the northern, middle, and southern parts of the cross section, and it is determined to be at y = 9, 4.5, and 0 respectively.
  • #1
hexa
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Hello,

I have a sum:
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make a contour map from a height field h(x,y) = x^2 + y on the domain: [-3<_ x <_3 ; 0<_ y <_9]. Make an east-western cross section (paralell to x-axis) through the field h in the northern, middle and southern part of the domain and draw all three height profiles into a figure.
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Well, the first part is not really a problem, but what would be the northern, middle and southern part of such cross section? I can only imagine a negative and positive value for y and zero for the middle?

hexa
 
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  • #2
y can't be negative based on the domain you supplied. Therefore, the height is always non-negative. Making a cross section I would think means make a cross section at y = 9, another at y = 4.5, and another at y = 0. In other words, set z = x^2 + y, and draw the height (z) at y = 9, 4.5, and 0.
 
  • #3
you're right, daveb, didn't think of the domain. But still that's more or less what I thought. Thanks a lot for confirming.
 

1. What is a contour map?

A contour map is a type of map that shows the shape and elevation of a surface. It uses contour lines to represent points of equal elevation on the surface.

2. How is a contour map constructed?

A contour map is constructed by plotting the points of equal elevation from the given function onto a grid. The contour lines are then drawn to connect these points and create a visual representation of the shape and elevation of the surface.

3. What does the function h(x,y) = x^2 + y represent?

The function h(x,y) = x^2 + y represents a surface with a parabolic shape. The values of x and y determine the elevation of the surface at a specific point.

4. How do you determine the contour interval for a contour map?

The contour interval is determined by the range of values in the function. The interval should be small enough to accurately represent the changes in elevation, but not too small that it makes the map cluttered and difficult to read.

5. Can contour maps be used for any type of surface?

Contour maps can be used for any type of surface, as long as the function accurately represents the elevation at each point. However, they are most commonly used for topographic maps of land surfaces.

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