Function for computing distance of line segment and point.

src/Math/Geometry/Distance.h

@@ -54,6 +54,64 @@ class Distance {
         template<class T> static T linePointSquared(const Vector3<T>& a, const Vector3<T>& b, const Vector3<T>& point) {
             return Vector3<T>::cross(point - a, point - b).lengthSquared()/(b - a).lengthSquared();
         }
+
+        /**
+         * @brief %Dístance of point from line segment
+         * @param a         Starting point of the line
+         * @param b         Ending point of the line
+         * @param point     Point
+         *
+         * Returns distance of point from line segment or from its
+         * starting/ending point, depending on where the point lies.
+         *
+         * Determining whether the point lies next to line segment or outside
+         * is done using Pythagorean theorem. If the following equation
+         * applies, the point **p** lies outside line segment closer to **a**:
+         * @f[
+         *      |\boldsymbol p - \boldsymbol b|^2 > |\boldsymbol b - \boldsymbol a|^2 + |\boldsymbol p - \boldsymbol a|^2
+         * @f]
+         * On the other hand, if the following equation applies, the point
+         * lies outside line segment closer to **b**:
+         * @f[
+         *      |\boldsymbol p - \boldsymbol a|^2 > |\boldsymbol b - \boldsymbol a|^2 + |\boldsymbol p - \boldsymbol b|^2
+         * @f]
+         * The last alternative is when the following equation applies. The
+         * point then lies between **a** and **b** and the distance is
+         * computed the same way as in linePoint().
+         * @f[
+         *      |\boldsymbol b - \boldsymbol a|^2 > |\boldsymbol p - \boldsymbol a|^2 + |\boldsymbol p - \boldsymbol b|^2
+         * @f]
+         *
+         * @see lineSegmentPointSquared()
+         */
+        template<class T> inline static T lineSegmentPoint(const Vector3<T>& a, const Vector3<T>& b, const Vector3<T>& point) {
+            return sqrt(lineSegmentPointSquared(a, b, point));
+        }
+
+        /**
+         * @brief %Distance of point from line segment, squared
+         *
+         * More efficient than lineSegmentPoint() for comparing distance with
+         * other values, because it doesn't compute the square root.
+         */
+        template<class T> static T lineSegmentPointSquared(const Vector3<T>& a, const Vector3<T>& b, const Vector3<T>& point) {
+            Vector3<T> pointMinusA = point - a;
+            Vector3<T> pointMinusB = point - b;
+            T pointDistanceA = pointMinusA.lengthSquared();
+            T pointDistanceB = pointMinusB.lengthSquared();
+            T bDistanceA = (b - a).lengthSquared();
+
+            /* Point is before A */
+            if(pointDistanceB > bDistanceA + pointDistanceA)
+                return pointDistanceA;
+
+            /* Point is after B */
+            if(pointDistanceA > bDistanceA + pointDistanceB)
+                return pointDistanceB;
+
+            /* Between A and B */
+            return Vector3<T>::cross(pointMinusA, pointMinusB).lengthSquared()/bDistanceA;
+        }
 };
 
 }}}

src/Math/Geometry/Test/DistanceTest.cpp

@@ -43,4 +43,28 @@ void DistanceTest::linePoint() {
         Constants<float>::Sqrt2/Constants<float>::Sqrt3);
 }
 
+void DistanceTest::lineSegmentPoint() {
+    Vector3 a(0.0f);
+    Vector3 b(1.0f);
+
+    /* Point on the line segment */
+    QCOMPARE((Distance::lineSegmentPoint(a, b, Vector3(0.25f))), 0.0f);
+
+    /* Point on the line, outside the segment, closer to A */
+    QCOMPARE((Distance::lineSegmentPoint(a, b, Vector3(-1.0f))), +Constants<float>::Sqrt3);
+
+    /* Point on the line, outside the segment, closer to B */
+    QCOMPARE((Distance::lineSegmentPoint(a, b, Vector3(1.0f+1.0f/Constants<float>::Sqrt3))), 1.0f);
+
+    /* Point next to the line segment */
+    QCOMPARE((Distance::lineSegmentPoint(a, b, Vector3(1.0f, 0.0f, 1.0f))),
+        Constants<float>::Sqrt2/Constants<float>::Sqrt3);
+
+    /* Point outside the line segment, closer to A */
+    QCOMPARE((Distance::lineSegmentPoint(a, b, Vector3(1.0f, 0.0f, 1.0f)-Vector3(1.0f))), 1.0f);
+
+    /* Point outside the line segment, closer to B */
+    QCOMPARE((Distance::lineSegmentPoint(a, b, Vector3(1.0f, 0.0f, 1.0f)+Vector3(1.0f))), +Constants<float>::Sqrt2);
+}
+
 }}}}

src/Math/Geometry/Test/DistanceTest.h

@@ -24,6 +24,7 @@ class DistanceTest: public QObject {
 
     private slots:
         void linePoint();
+        void lineSegmentPoint();
 };
 
 }}}}