How can contour map data be used to determine volume?

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Discussion Overview

The discussion centers on the methods for calculating the volume of a hill using contour map data. It explores theoretical approaches and mathematical formulas relevant to this application.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant suggests calculating the volume by determining the area of each contour line and multiplying by the distance between the lines.
  • Another participant mentions a specific formula for calculating the area of a polygon given its vertex coordinates, emphasizing that it applies regardless of the polygon's shape as long as the sides do not cross.
  • There is a request for clarification on the notation used in the area formula, specifically regarding the coordinates of the polygon's vertices.
  • A clarification is provided about the meaning of the vertex coordinates, indicating that they represent the corners of the polygon.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the best method for calculating volume from contour maps, and there are varying levels of understanding regarding the mathematical details involved.

Contextual Notes

Some assumptions about the nature of the contour lines and the specific characteristics of the polygons are not fully explored, and there may be limitations related to the types of polygons that can be used in the area calculations.

brandy
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if you are given a contour map how could you calculate the volume of the hill.
 
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Roughly you would work out the area of each contour line and multiply by the distance between lines.
There is an interesting law for the area of any polygon if you are given the contours as line segments.
 
they'r ellipses but id still like to hear it
 
If you have the x,y coordinates of each vertex of a polygon then
Area = (x0y1 + x1y2 + ... + xn-1y0 - y0x1 - y1x2 - ... - yn-1x0) / 2

It doesn't matter what shape it is (doesn't have to be convex) as long as the sides don't
cross each other.
 
what exactly do u mean by x0 and x1 and y0 and etc
 
The coordinates of each vertex of the polygon, ie x0,y0 is the first corner, x1,y1 is the second etc..
The nice thing is that you don't have to calculate any lengths or angles.
 

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