Function for computing distance of line and point.

src/Math/Geometry/Distance.h

@@ -0,0 +1,61 @@
+#ifndef Magnum_Math_Geometry_Distance_h
+#define Magnum_Math_Geometry_Distance_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+/** @file
+ * @brief Class Magnum::Math::Geometry::Distance
+ */
+
+#include "Math/Vector3.h"
+
+namespace Magnum { namespace Math { namespace Geometry {
+
+/** @brief Functions for computing distances */
+class Distance {
+    public:
+        /**
+         * @brief %Distance of line and point
+         * @param a         First point of the line
+         * @param b         Second point of the line
+         * @param point     Point
+         *
+         * The distance *d* is computed from point **p** and line defined by **a**
+         * and **b** using @ref Vector3::cross() "cross product":
+         * @f[
+         *      d = \frac{|(\boldsymbol p - \boldsymbol a) \times (\boldsymbol p - \boldsymbol b)|}
+         *      {|\boldsymbol b - \boldsymbol a|}
+         * @f]
+         *
+         * @see linePointSquared()
+         */
+        template<class T> inline static T linePoint(const Vector3<T>& a, const Vector3<T>& b, const Vector3<T>& point) {
+            return sqrt(linePointSquared(a, b, point));
+        }
+
+        /**
+         * @brief %Distance of line and point, squared
+         *
+         * More efficient than linePoint() for comparing distance with other
+         * values, because it doesn't compute the square root.
+         */
+        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();
+        }
+};
+
+}}}
+
+#endif

src/Math/Geometry/Test/CMakeLists.txt

@@ -1 +1,2 @@
+corrade_add_test(MathGeometryDistanceTest DistanceTest.h DistanceTest.cpp)
 corrade_add_test(MathGeometryIntersectionTest IntersectionTest.h IntersectionTest.cpp)

src/Math/Geometry/Test/DistanceTest.cpp

@@ -0,0 +1,46 @@
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+#include "DistanceTest.h"
+
+#include <limits>
+#include <QtTest/QTest>
+
+#include "Math.h"
+#include "Distance.h"
+
+QTEST_APPLESS_MAIN(Magnum::Math::Geometry::Test::DistanceTest)
+
+using namespace std;
+
+namespace Magnum { namespace Math { namespace Geometry { namespace Test {
+
+typedef Magnum::Math::Vector3<float> Vector3;
+
+void DistanceTest::linePoint() {
+    Vector3 a(0.0f);
+    Vector3 b(1.0f);
+
+    /* Point on the line */
+    QCOMPARE((Distance::linePoint(a, b, Vector3(0.25f))), 0.0f);
+
+    /* The distance should be the same for all equidistant points */
+    QCOMPARE((Distance::linePoint(a, b, Vector3(1.0f, 0.0f, 1.0f))),
+        Constants<float>::Sqrt2/Constants<float>::Sqrt3);
+    QCOMPARE((Distance::linePoint(a, b, Vector3(1.0f, 0.0f, 1.0f)+Vector3(100.0f))),
+        Constants<float>::Sqrt2/Constants<float>::Sqrt3);
+}
+
+}}}}

src/Math/Geometry/Test/DistanceTest.h

@@ -0,0 +1,31 @@
+#ifndef Magnum_Math_Geometry_Test_DistanceTest_h
+#define Magnum_Math_Geometry_Test_DistanceTest_h
+/*
+    Copyright © 2010, 2011, 2012 Vladimír Vondruš <mosra@centrum.cz>
+
+    This file is part of Magnum.
+
+    Magnum is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License version 3
+    only, as published by the Free Software Foundation.
+
+    Magnum is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU Lesser General Public License version 3 for more details.
+*/
+
+#include <QtCore/QObject>
+
+namespace Magnum { namespace Math { namespace Geometry { namespace Test {
+
+class DistanceTest: public QObject {
+    Q_OBJECT
+
+    private slots:
+        void linePoint();
+};
+
+}}}}
+
+#endif