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Diffstat (limited to '2d/_collisions/polygon_polygon.html.content')
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1 files changed, 39 insertions, 6 deletions
diff --git a/2d/_collisions/polygon_polygon.html.content b/2d/_collisions/polygon_polygon.html.content index 820fcbc..2d6f6b7 100644 --- a/2d/_collisions/polygon_polygon.html.content +++ b/2d/_collisions/polygon_polygon.html.content @@ -15,8 +15,40 @@ </script> <article> - <h1>Polygon Intersections</h1> + <h1>Separating Axis Theorem</h1> <section> + <p> + The Separating Axis Theorem (SAT) provides a way to find the intersection between any <i>n</i>-sided <a href='https://ianqvist.blogspot.com/2009/09/convex-polygon-based-collision.html'>convex</a> polygon or circle. In this tutorial, I will explain how this theorem works, and how you can use it to both detect and resolve collisions in your simulation. + </p> + </section> + <section> + <h2>Explanation of Separating Axis Theorem</h2> + <p> + SAT makes use of vector projection to figure out whether or not two concave polygons are intersecting. The way to think about it is this: + + <br/> + <br/> + + Given two shapes <b>A</b> and <b>B</b>. + + Imagine we could isolate a single edge of A and shine a light on it. + + + </p> + </section> + <section> + <h2>Algorithm for Finding the Intersection</h2> + <p> + Given two polygons <b>A</b> and <b>B</b>: + <ol> + <li>For each edge on A, get the normal <i>n</i> of that edge.</li> + <li>Project each vertex <i>v</i> of <b>A</b> onto <i>n</i>. Return the minimum and maximum projection of all vertices.</li> + <li>Repeat Step 2 for polygon <b>B</b>.</li> + <li>If the min and max projections found in Steps 2 and 3 do <b>NOT</b> overlap, the polygons are not intersecting. Return false.</li> + <li>If the projections overlap for each edge of both shapes, the shapes are intersecting. Return true.</li> + </ol> + </p> + </section> <section> <h2> @@ -31,10 +63,11 @@ Stop </button> </div> - <footer id="references"> - <h2>References</h2> - <ul> - </ul> - </footer> </section> + <footer id="references"> + <h2>References</h2> + <ul> + <li><a href="https://en.wikipedia.org/wiki/Vector_projection">Vector Projection Wikapedia</a></li> + </ul> + </footer> </article> |