From 953c41b0ec054997cdbc77bf6953187a22d9bd12 Mon Sep 17 00:00:00 2001 From: Matthew Kosarek Date: Thu, 24 Jun 2021 09:18:36 -0400 Subject: Updating roadmap, and getting started on SAT collisions --- 2d/_collisions/polygon_polygon.html.content | 45 +++++++++++++++++++++++++---- 1 file changed, 39 insertions(+), 6 deletions(-) (limited to '2d/_collisions/polygon_polygon.html.content') 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 @@
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Polygon Intersections

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Separating Axis Theorem

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+ The Separating Axis Theorem (SAT) provides a way to find the intersection between any n-sided convex 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. +

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Explanation of Separating Axis Theorem

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+ 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: + +
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+ + Given two shapes A and B. + + Imagine we could isolate a single edge of A and shine a light on it. + + +

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Algorithm for Finding the Intersection

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+ Given two polygons A and B: +

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  1. For each edge on A, get the normal n of that edge.
    2. +
  2. Project each vertex v of A onto n. Return the minimum and maximum projection of all vertices.
    3. +
  3. Repeat Step 2 for polygon B.
    4. +
  4. If the min and max projections found in Steps 2 and 3 do NOT overlap, the polygons are not intersecting. Return false.
    5. +
  5. If the projections overlap for each edge of both shapes, the shapes are intersecting. Return true.
    6. +
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References

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