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copied!<h2>Velocity</h2> <p>If you look at <a href="http://www.kfish.org/boids/pseudocode.html#ref1" rel="nofollow">their pseudocode</a> for vector addition and subtraction, they are explicitly performing these operations on three-dimensional vectors, e.g.</p> <pre><code>PROCEDURE Vector_Add(Vector v1, Vector v2) Vector v v.x = v1.x + v2.x v.y = v1.y + v2.y v.z = v1.z + v2.z RETURN v END PROCEDURE </code></pre> <p>In the <em>Auxiliary Functions</em> section, it also says:</p> <blockquote> <p>... all the additions and subtractions in the above pseudocode are vector operations</p> </blockquote> <p>So we can assume <code>b.velocity = b.velocity + v1 + v2 + v3 + ...</code> is vector addition for 3D vectors.</p> <h2>Vector Magnitude</h2> <p>The subtraction of the two vectors is called the difference between vectors, and produces a new vector. In your case, let <code>diffB = b.position - bJ.position</code>.</p> <p>Now <code>|b.position - bJ.position|</code> is equivalent to <code>|diffB|</code>, and is taking the magnitude of the difference vector <code>diffB</code>, not the absolute value of a <em>"single value"</em> (called a scalar.) Magnitude is also called vector length, or norm.</p> <p>What may be confusing is that the magnitude of a vector is denoted by the same notation as absolute value. So <code>diffB</code> is a difference vector, and <code>|diffB|</code> is the magnitude of that vector. Magnitude is defined for a vector <code>v</code> in Euclidean space by <code>|v| = sqrt(x1^2 + ... + xn^2)</code>.</p> <p>So, for your 3D vector <code>diffB</code>:</p> <pre><code>|diffB| = sqrt(x1^2 + x2^2 + x3^2) = sqrt(x^2 + y^2 + z^2) </code></pre> <p>Since the result of square root is a scalar, it can clearly satisfy <code>< 100</code>. </p> <hr> <p>So yes, I believe velocity is a 3D vector <code>velocity = {x1, x2, x3}</code>, and while I haven't thoroughly reviewed the boid pseudocode, your data structure appears correct.</p>

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