# Geometry Puzzler

## Jun 27, 09

For the love of puzzlers, try your hand at the following math problem:

You are given four 2-dimensional co-ordinates in a random order. What is the simplest method to draw the enclosing polygon created by joining the points?

Answers should be written in C-like syntax or pseudo code, without library dependencies, and should not include any visual methods. You can simply return an array of co-ordinates that, when followed in order, will draw the proper polygon.

For example:

function polygon(p1, p2, p3, p4) {

polygon( [x

The winning entry will be used in a 3D game released for amoebaOS, and will be credited within the game for their contribution!

Good luck and have fun!

You are given four 2-dimensional co-ordinates in a random order. What is the simplest method to draw the enclosing polygon created by joining the points?

Answers should be written in C-like syntax or pseudo code, without library dependencies, and should not include any visual methods. You can simply return an array of co-ordinates that, when followed in order, will draw the proper polygon.

For example:

function polygon(p1, p2, p3, p4) {

// code

return [ p3, p2, p4, p1];

}return [ p3, p2, p4, p1];

polygon( [x

_{1},y_{1}] , [x_{2},y_{2}] , [x_{3},y_{3}] , [x_{4},y_{4}] );The winning entry will be used in a 3D game released for amoebaOS, and will be credited within the game for their contribution!

Good luck and have fun!

{

// Make the list of points into an array:

p = [a,b,c,d];

// Find the midpoint

mp = [0,0];

for(i=0; i<4; i++)

{

mp[0] += p[i][0];

mp[1] += p[i][1];

}

mp[0] = mp[0] / 4; // Dividing the total x's and y's by 4

mp[1] = mp[1] / 4; // results in the mid-point

// Now that we have the mid-point, get the angle between

// each point and the mid-point

angles = [0,0,0,0];

for(i=0;i<4;i++)

{

angle = atan2(p[i][0]-mp[0], p[i][1]-mp[1]);

angles[i] = angle;

}

// Sort the points by increasing angle

p.sortBy(increasingAngle); // I can't really think of a very language independent way to do this.

return p; // Return the array

}

Unfortunately, this technique uses atan2(), so it's something that you would only want to do once and not every single frame.

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