AP_Math: add Vector2f::circle_segment_intersection

libraries/AP_Math/vector2.cpp

@@ -173,6 +173,70 @@ bool Vector2<T>::segment_intersection(const Vector2<T>& seg1_start, const Vector
     }
 }
 
+// find the intersection between a line segment and a circle
+// returns true if they intersect and intersection argument is updated with intersection closest to seg_start
+// solution adapted from http://stackoverflow.com/questions/1073336/circle-line-segment-collision-detection-algorithm
+template <typename T>
+bool Vector2<T>::circle_segment_intersection(const Vector2<T>& seg_start, const Vector2<T>& seg_end, const Vector2<T>& circle_center, float radius, Vector2<T>& intersection)
+{
+    // calculate segment start and end as offsets from circle's center
+    const Vector2f seg_start_local = seg_start - circle_center;
+
+    // calculate vector from start to end
+    const Vector2f seg_end_minus_start = seg_end - seg_start;
+
+    const float a = sq(seg_end_minus_start.x) + sq(seg_end_minus_start.y);
+    const float b = 2 * ((seg_end_minus_start.x * seg_start_local.x) + (seg_end_minus_start.y * seg_start_local.y));
+    const float c = sq(seg_start_local.x) + sq(seg_start_local.y) - sq(radius);
+    const float delta = sq(b) - (4.0f * a * c);
+
+    // check for invalid data
+    if (fabsf(a) < FLT_EPSILON) {
+        return false;
+    }
+    if (isnan(a) || isnan(b) || isnan(c) || isnan(delta)) {
+       return false;
+    }
+
+    // check for invalid delta (i.e. discriminant)
+    if (delta < 0.0f) {
+        return false;
+    }
+
+    const float delta_sqrt = safe_sqrt(delta);
+    const float t1 = (-b + delta_sqrt) / (2.0f * a);
+    const float t2 = (-b - delta_sqrt) / (2.0f * a);
+
+    // Three hit cases:
+    //          -o->             --|-->  |            |  --|->
+    // Impale(t1 hit,t2 hit), Poke(t1 hit,t2>1), ExitWound(t1<0, t2 hit),
+
+    // Three miss cases:
+    //       ->  o                     o ->              | -> |
+    // FallShort (t1>1,t2>1), Past (t1<0,t2<0), CompletelyInside(t1<0, t2>1)
+
+    // intersection = new Vector3(E.x + t1 * d.x, secondPoint.y, E.y + t1 * d.y);
+    //   intersection.x = seg_start.x + t1 * seg_end_minus_start.x;
+    //   intersection.y = seg_start.y + t1 * seg_end_minus_start.y;
+
+    if ((t1 >= 0.0f) && (t1 <= 1.0f)) {
+        // t1 is the intersection, and it is closer than t2 (since t1 uses -b - discriminant)
+        // Impale, Poke
+        intersection = seg_start + (seg_end_minus_start * t1);
+        return true;
+    }
+
+    // here t1 did not intersect so we are either started inside the sphere or completely past it
+    if ((t2 >= 0.0f) && (t2 <= 1.0f)) {
+        // ExitWound
+        intersection = seg_start + (seg_end_minus_start * t2);
+        return true;
+    }
+
+    // no intersection: FallShort, Past or CompletelyInside
+    return false;
+}
+
 // only define for float
 template float Vector2<float>::length(void) const;
 template float Vector2<float>::operator *(const Vector2<float> &v) const;
@@ -192,6 +256,7 @@ template bool Vector2<float>::is_nan(void) const;
 template bool Vector2<float>::is_inf(void) const;
 template float Vector2<float>::angle(const Vector2<float> &v) const;
 template bool Vector2<float>::segment_intersection(const Vector2<float>& seg1_start, const Vector2<float>& seg1_end, const Vector2<float>& seg2_start, const Vector2<float>& seg2_end, Vector2<float>& intersection);
+template bool Vector2<float>::circle_segment_intersection(const Vector2<float>& seg_start, const Vector2<float>& seg_end, const Vector2<float>& circle_center, float radius, Vector2<float>& intersection);
 
 template bool Vector2<long>::operator ==(const Vector2<long> &v) const;
 

libraries/AP_Math/vector2.h

@@ -226,6 +226,10 @@ struct Vector2
     // the point of intersection is returned in the intersection argument
     static bool segment_intersection(const Vector2<T>& seg1_start, const Vector2<T>& seg1_end, const Vector2<T>& seg2_start, const Vector2<T>& seg2_end, Vector2<T>& intersection);
 
+    // find the intersection between a line segment and a circle
+    // returns true if they intersect and intersection argument is updated with intersection closest to seg_start
+    static bool circle_segment_intersection(const Vector2<T>& seg_start, const Vector2<T>& seg_end, const Vector2<T>& circle_center, float radius, Vector2<T>& intersection);
+
 };
 
 typedef Vector2<int16_t>        Vector2i;