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    <p>It's fairly straightforward to do this for regular polygon.</p> <p>The area of an n-sided regular polygon, with a circumscribed circle of radius R is</p> <p><code>A = 1/2 nR^2 * sin((2pi)/n)</code></p> <p>Therefore, knowing n and A you can easily find R</p> <p><code>R = sqrt((2*A)/(n*sin((2pi)/n))</code></p> <p>So, you can pick the center, go at distance R and generate n points at <code>2pi/n</code> angle increments.</p> <p>In R:</p> <pre><code>regular.poly &lt;- function(nSides, area) { # Find the radius of the circumscribed circle radius &lt;- sqrt((2*area)/(nSides*sin((2*pi)/nSides))) # I assume the center is at (0;0) and the first point lies at (0; radius) points &lt;- list(x=NULL, y=NULL) angles &lt;- (2*pi)/nSides * 1:nSides points$x &lt;- cos(angles) * radius points$y &lt;- sin(angles) * radius return (points); } # Some examples par(mfrow=c(3,3)) for (i in 3:11) { p &lt;- regular.poly(i, 100) plot(0, 0, "n", xlim=c(-10, 10), ylim=c(-10, 10), xlab="", ylab="", main=paste("n=", i)) polygon(p) } </code></pre> <p>We can extrapolate to a generic convex polygon.</p> <p>The area of a convex polygon can be found as: <code>A = 1/2 * [(x1*y2 + x2*y3 + ... + xn*y1) - (y1*x2 + y2*x3 + ... + yn*x1)]</code></p> <p>We generate the polygon as above, but deviate angles and radii from those of the regular polygon.</p> <p>We then scale the points to get the desired area. </p> <pre><code>convex.poly &lt;- function(nSides, area) { # Find the radius of the circumscribed circle, and the angle of each point if this was a regular polygon radius &lt;- sqrt((2*area)/(nSides*sin((2*pi)/nSides))) angle &lt;- (2*pi)/nSides # Randomize the radii/angles radii &lt;- rnorm(nSides, radius, radius/10) angles &lt;- rnorm(nSides, angle, angle/10) * 1:nSides angles &lt;- sort(angles) points &lt;- list(x=NULL, y=NULL) points$x &lt;- cos(angles) * radii points$y &lt;- sin(angles) * radii # Find the area of the polygon m &lt;- matrix(unlist(points), ncol=2) m &lt;- rbind(m, m[1,]) current.area &lt;- 0.5 * (sum(m[1:nSides,1]*m[2:(nSides+1),2]) - sum(m[1:nSides,2]*m[2:(nSides+1),1])) points$x &lt;- points$x * sqrt(area/current.area) points$y &lt;- points$y * sqrt(area/current.area) return (points) } </code></pre>
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    1. POHow to generate random shapes given a specified area.(R language).?
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    1. COI edited the code, so it is a bit cleaner. If I have time I'll post a solution for a generic (non regular) convex shape later.
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