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    <p>Ok, I have classical solution that work in any dimensions. </p> <p>First of all, you got sphere and a line, and you need to have good model of them. Sphere is easy you just have a Vector <code>.center</code> and <code>.diameter</code>.</p> <pre><code>class Sphere: def __init__( sphere, center, diameter ): sphere.center=Vector(center) sphere.diameter=float(diameter) </code></pre> <p>Line could be more problematic for beginners because it could be defined in many ways. The most useful comes from parametric equation, you have a direction in Vector <code>.direction</code> and some staring point <code>.center</code>. We assume that <code>.direction</code> is unit length, and <code>.center</code> is the nearest point on line from (0,0). In most cases we need to create a line, having to points Vectors:</p> <pre><code>def line_on_two_points( A, B ): return Line( direction= Vector(B)-A, center=A ) </code></pre> <p>So we have to fix the <code>direction</code> and <code>center</code> in the constructor. <code>.direction</code> is easy to fix wee need just to make it unit length. To find <code>.center</code>, we need <a href="http://en.wikipedia.org/wiki/Scalar_projection" rel="nofollow noreferrer">scalar projection</a>. Here is as vector to D: <img src="https://i.stack.imgur.com/vrA4j.png" alt="The nearest point on line from (0,0)"></p> <p>Having <code>.direction</code> as unit length A to B and <code>center</code> as from C to A, we could init our line as:</p> <pre><code>class Line: def __init__( line, direction, center ): line.direction= Vector(direction) / length(direction) line.center= center - line.direction*dot(center,line.direction) </code></pre> <p>If we don't have a line, just two points we could just do:</p> <pre><code>#class Sphere: def colide_line_on_two_points( sphere, A, B ): line=line_on_two_points( A-sphere.center, B-sphere.center) return length(line.center) &lt; sphere.diameter </code></pre> <p>But when we have a line we try to optimize it as:</p> <pre><code>#class Sphere: def colide_line( sphere, line ): return line.distance_to(sphere.center) &lt; sphere.diameter </code></pre> <p>The <code>.distance_to()</code> function is a bit tricky:</p> <p><img src="https://i.stack.imgur.com/CB2e7.png" alt="Vector from line to point"></p> <pre><code>#class Line: def vector_to( line, P ): return line.center + line.direction * dot(line.direction,P) - P def distance_to( line, P ): return length( line.center + line.direction * dot(line.direction,P) - P ) def move_to( line, P ): line.center += line.direction * dot(line.direction,P) - P </code></pre> <p>The last but not least is the <code>Vector</code> type, I try numpy, but it's rather slow for 2D,3D:</p> <pre><code>from numpy import array as Vector from numpy import dot from numpy.linalg import norm as length </code></pre>
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