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diff --git a/2d/_collisions/polygon_polygon.html b/2d/_collisions/polygon_polygon.html index 5d360af..4c4698a 100644 --- a/2d/_collisions/polygon_polygon.html +++ b/2d/_collisions/polygon_polygon.html @@ -4,7 +4,7 @@ <meta charset="utf-8"> <link rel="stylesheet" href="/index.css"> <title>Physics for Games</title> - <link rel="shortcut icon" href="favicon/favicon.ico" type="image/x-icon"> + <link rel="shortcut icon" href="/favicon/favicon.ico" type="image/x-icon"> <meta name="description" content="A place to learn all about real-time physics simulations through descriptions, code snippets, and example programs all written in C++ and OpenGL."> <meta name="og:description" content="A place to learn all about real-time physics simulations through descriptions, code snippets, and example programs all written in C++ and OpenGL."> </head> @@ -159,13 +159,65 @@ <li>If the projections overlap for each edge of both shapes, the shapes are intersecting. Return true.</li> </ol> - And that is all there is to <i>finding</i> the intersection between two convex polygons. - </p> + And that is all there is to <i>finding</i> the intersection between two convex polygons. Here is the code snippet that does this if you are interested: + + <pre><code><span class="code_keyword">Vector2</span> getProjection(Vector2* vertices, <span class="code_keyword">int</span> numVertices, <span class="code_keyword">Vector2</span> axis) { + <span class="code_comment">// Find the min and max vertex projections</span> + <span class="code_keyword">float32</span> min = axis.dot(vertices[0]); + <span class="code_keyword">float32</span> max = min; + + for (int v = 1; v < numVertices; v++) { + <span class="code_keyword">float32</span> d = axis.dot(vertices[v]); + + if (d < min) { + min = d; + } else if (d > max) { + max = d; + } + } + + <span class="code_keyword">return</span> <span class="code_keyword">Vector2</span> { min, max }; +} + +<span class="code_keyword">bool</span> projectionsOverlap(Vector2 first, <span class="code_keyword">Vector2</span> second) { + <span class="code_keyword">return</span> first.x <= second.y && second.x <= first.y; +} + +<span class="code_keyword">bool</span> doIntersect(ConvexPolygon* first, ConvexPolygon* second) { + IntersectionResult ir; + + <span class="code_comment">// Check agaisnt the edges of the first polygon</span> + for (int i = 0; i < first->numVertices; i++) { + <span class="code_keyword">Vector2</span> normal = first->edges[i].normal; + + <span class="code_keyword">Vector2</span> firstProj = getProjection(first->transformedVertices, first->numVertices, normal); + <span class="code_keyword">Vector2</span> secondProj = getProjection(second->transformedVertices, second->numVertices, normal); + + if (!projectionsOverlap(firstProj, secondProj)) { + <span class="code_keyword">return</span> false; + } + } + + <span class="code_comment">// Check against the edges of the second polygon</span> + for (int i = 0; i < second->numVertices; i++) { + <span class="code_keyword">Vector2</span> normal = second->edges[i].normal; + + <span class="code_keyword">Vector2</span> firstProj = getProjection(first->transformedVertices, first->numVertices, normal); + <span class="code_keyword">Vector2</span> secondProj = getProjection(second->transformedVertices, second->numVertices, normal); + + if (!projectionsOverlap(firstProj, secondProj)) { + <span class="code_keyword">return</span> false; + } + } + + <span class="code_keyword">return</span> true; +} +</code></pre> </p> </section> <section> <h2>SAT Collision Resolution</h2> <p> - Now that we know our objects have intersecting, we want to be able to send them tumbling away from each other to simulate a collision. To do this, we will need to find the following things: + Now that we know our objects have intersected, we want to be able to send them tumbling away from each other to simulate a collision. To do this, we will need to find the following things: <ul> <li><b>Collision Normal</b>: in what direction, point towards object <b>A</b>, did the polygons intersect</li> <li><b>Point of Application</b>: at what point on each object did the objects first intersect</li> |