From 4878f0fc6a039d220dd7adecb18d19c688ae50b0 Mon Sep 17 00:00:00 2001
From: Matthew Kosarek <mattkae@protonmail.com>
Date: Thu, 1 Jul 2021 19:46:08 -0400
Subject: (mkosarek) Decent SAT description for now

---
 2d/_collisions/polygon_polygon/snippet2.cpp | 117 ++++++++++++++++++++++++++++
 1 file changed, 117 insertions(+)
 create mode 100644 2d/_collisions/polygon_polygon/snippet2.cpp

(limited to '2d/_collisions/polygon_polygon')

diff --git a/2d/_collisions/polygon_polygon/snippet2.cpp b/2d/_collisions/polygon_polygon/snippet2.cpp
new file mode 100644
index 0000000..8cbdcbe
--- /dev/null
+++ b/2d/_collisions/polygon_polygon/snippet2.cpp
@@ -0,0 +1,117 @@
+struct IntersectionResult {
+    bool intersect = false;
+    Vector2 collisionNormal;
+    Vector2 relativeVelocity;
+    Vector2 firstPointOfApplication;
+    Vector2 secondPointOfApplication;
+};
+
+struct Edge {
+	Vector2 normal;
+	Vector2 start;
+	Vector2 end;
+};
+
+struct SATResult {
+    Edge* minOverlapEdge = NULL;        // Edge that caused the intersection (on the 'first' shape)
+    Vector2 overlapPoint;               // Point that caused the intersection (on the 'second' shape)
+    float32 minOverlap = FLT_MAX;       // Smallest projection overlap
+};
+
+struct ProjectionResult {
+    Vector2 minVertex;
+    Vector2 maxVertex;
+    Vector2 projection;
+};
+
+// Given the vertices in the shape, we find the min and max vertices that project
+// onto the axis. We also save which vertices were which so that we can resolve
+// the collision later.
+ProjectionResult getProjection(Vector2* vertices, int numVertices, Vector2 axis) {
+    ProjectionResult pr;
+    float32 min = axis.dot(vertices[0]);
+    float32 max = min;
+
+    for (int v = 1; v < numVertices; v++) {
+        float32 d = axis.dot(vertices[v]);
+
+        if (d < min) {
+            pr.minVertex = vertices[v];
+            min = d;
+        } else if (d > max) {
+            pr.maxVertex = vertices[v];
+            max = d;
+        }
+    }
+    
+    pr.projection = Vector2 { min, max };
+    return pr;
+}
+
+bool projectionsOverlap(Vector2 first, Vector2 second) {
+    return first.x <= second.y && second.x <= first.y;
+}
+
+float32 getProjectionOverlap(Vector2 first, Vector2 second) {
+    float32 e = MIN(first.y, second.y);
+    float32 f = MAX(first.x, second.x);
+    return e - f;
+}
+
+bool runSatForShapesEdges(SATResult* result, ConvexPolygon* first, ConvexPolygon* second) {
+    for (int i = 0; i < first->numVertices; i++) {
+        Vector2 normal = first->edges[i].normal;
+
+        ProjectionResult firstProj = getProjection(first->transformedVertices, first->numVertices, normal);
+        ProjectionResult secondProj = getProjection(second->transformedVertices, second->numVertices, normal);
+
+        if (!projectionsOverlap(firstProj.projection, secondProj.projection)) {
+            return false;
+        }
+
+        float32 overlap = getProjectionOverlap(firstProj.projection, secondProj.projection);
+        if (overlap < result->minOverlap) {
+            result->minOverlap = overlap;
+            result->minOverlapEdge = &first->edges[i];
+            
+            // The overlapPoint will be the point on the other shape that penetrated the edge.
+            // If we caught the intersection reasonably early, it should be the point on 'second'
+            // that is nearest to the points on 'first'.
+            float32 min1min2 = (firstProj.minVertex - secondProj.minVertex).length();
+            float32 min1max2 = (firstProj.minVertex - secondProj.maxVertex).length();
+            float32 max1max2 = (firstProj.maxVertex - secondProj.maxVertex).length();
+            float32 max1min2 = (firstProj.maxVertex - secondProj.minVertex).length();
+            
+            float32 closest = MIN(min1min2, MIN(min1max2, MIN(max1max2, max1min2)));
+            if (closest == min1min2 || closest == max1min2) {
+                result->overlapPoint = secondProj.minVertex;
+            } else {
+                result->overlapPoint = secondProj.maxVertex;
+            }
+        }
+    }
+
+    return true;
+}
+
+const float32 EPSILON = 1.f;
+IntersectionResult getIntersection(ConvexPolygon* first, ConvexPolygon* second) {
+    IntersectionResult ir;
+    SATResult sat;
+    
+    if (!runSatForShapesEdges(&sat, first, second)) {
+        return ir;
+    }
+
+    if (!runSatForShapesEdges(&sat, second, first)) {
+        return ir;
+    }
+
+	ir.intersect = true;
+	ir.relativeVelocity = first->body.velocity - second->body.velocity;
+	ir.collisionNormal = sat.minOverlapEdge->normal;
+    ir.firstPointOfApplication = sat.overlapPoint - first->body.position;
+    ir.secondPointOfApplication = sat.overlapPoint - second->body.position;;
+
+	return ir;
+}
-- 
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