New class Math::GeometryUtils.

GeometryUtils::intersection() computes intersection of a plane and a
line.

src/Math/GeometryUtils.h

@@ -0,0 +1,81 @@
+#ifndef Magnum_Math_GeometryUtils_h
+#define Magnum_Math_GeometryUtils_h
+/*
+    Copyright © 2010, 2011 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::GeometryUtils
+ */
+
+#include "Matrix3.h"
+
+namespace Magnum { namespace Math {
+
+/**
+@brief Geometry utils
+*/
+template<class T> class GeometryUtils {
+    public:
+        /**
+         * @brief Intersection of a plane and line
+         * @param plane     Plane defined by three points
+         * @param a         Starting point of the line
+         * @param b         Ending point of the line
+         * @return Value, NaN if the line lies on the plane or infinity if the
+         * intersection doesn't exist. Intersection point can be then computed
+         * with <tt>a+intersection(...)*b</tt>. If returned value is in range
+         * @f$ [ 0 ; 1 ] @f$, the intersection is inside the line segment
+         * defined by @c a and @c b.
+         *
+         * First the parametric equation of the plane is computed,
+         * @f$ cx + dy + ez = f @f$. Parameters @f$ (c, d, e) @f$ are cross
+         * product of two vectors defining the plane, parameter @f$ f @f$ is
+         * computed using @f$ (c, d, e) @f$ and one of points defining the
+         * plane.
+         * @f[
+         *     \begin{array}{lcl}
+         *         (g, h, i) & = & plane                                    \\
+         *         (c, d, e) & = & (h - g) \times (i - g)                   \\
+         *         f & = & (c, d, e) \cdot g
+         *     \end{array}
+         * @f]
+         *
+         * Using parametric equation and points @f$ a @f$ and @f$ b @f$, value
+         * of @f$ t @f$ is computed and returned.
+         * @f[
+         *     \begin{array}{lcl}
+         *         \Delta b & = & b - a                                     \\
+         *         f & = & (c, d, e) \cdot (a + \Delta b \cdot t)           \\
+         *         t & = & \frac{f - (c, d, e) \cdot a}
+         *                 {(c, d, e) \cdot \Delta b}
+         *      \end{array}
+         * @f]
+         */
+        static T intersection(const Matrix3<T>& plane, const Vector3<T>& a, const Vector3<T>& b) {
+            /* Cross product of two vectors defining the plane */
+            Vector3<T> crossProduct = Vector3<T>::cross(plane.at(1)-plane.at(0), plane.at(2)-plane.at(0));
+
+            /* Compute f with cross product and one of the points defining the
+               plane */
+            T f = crossProduct*plane.at(0);
+
+            /* Compute t */
+            return (f-crossProduct*a)/(crossProduct*(b-a));
+        }
+};
+
+}}
+
+#endif

src/Math/Test/CMakeLists.txt

@@ -4,3 +4,5 @@ magnum_add_test(Vector4Test Vector4Test.h Vector4Test.cpp)
 
 magnum_add_test(MatrixTest MatrixTest.h MatrixTest.cpp)
 magnum_add_test(Matrix4Test Matrix4Test.h Matrix4Test.cpp)
+
+magnum_add_test(GeometryUtilsTest GeometryUtilsTest.h GeometryUtilsTest.cpp)

src/Math/Test/GeometryUtilsTest.cpp

@@ -0,0 +1,71 @@
+/*
+    Copyright © 2010, 2011 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 "GeometryUtilsTest.h"
+
+#include <limits>
+#include <QtTest/QTest>
+
+#include "Matrix3.h"
+#include "GeometryUtils.h"
+
+QTEST_APPLESS_MAIN(Magnum::Math::Test::GeometryUtilsTest)
+
+typedef Magnum::Math::Matrix3<float> Matrix3;
+typedef Magnum::Math::Vector3<float> Vector3;
+
+Q_DECLARE_METATYPE(Matrix3)
+Q_DECLARE_METATYPE(Vector3)
+
+using namespace std;
+
+namespace Magnum { namespace Math { namespace Test {
+
+using ::Matrix3;
+using ::Vector3;
+
+void GeometryUtilsTest::intersection_data() {
+    QTest::addColumn<Matrix3>("plane");
+    QTest::addColumn<Vector3>("a");
+    QTest::addColumn<Vector3>("b");
+    QTest::addColumn<float>("expected");
+
+    float plane[] = {
+        0, 0, 0,
+        1, 0, 0,
+        0, 1, 0
+    };
+    QTest::newRow("inside") << Matrix3(plane) << Vector3(0, 0, -1) << Vector3(0, 0, 1) << 0.5f;
+    QTest::newRow("outside") << Matrix3(plane) << Vector3(0, 0, 1) << Vector3(0, 0, 2) << -1.0f;
+    QTest::newRow("NaN") << Matrix3(plane) << Vector3(1, 0, 0) << Vector3(0, 1, 0) << numeric_limits<float>::quiet_NaN();
+    QTest::newRow("inf") << Matrix3(plane) << Vector3(1, 0, 1) << Vector3(0, 0, 1) << numeric_limits<float>::infinity();
+}
+
+void GeometryUtilsTest::intersection() {
+    QFETCH(Matrix3, plane);
+    QFETCH(Vector3, a);
+    QFETCH(Vector3, b);
+    QFETCH(float, expected);
+
+    /* Handling also NaN, which cannot be fuzzy compared */
+    float actual = GeometryUtils<float>::intersection(plane, a, b);
+
+    /* All possible workarounds for comparing to inf and NaN */
+    if(expected > numeric_limits<float>::max()) QCOMPARE(actual, expected);
+    else if(expected != expected) QVERIFY(actual != actual);
+    else QVERIFY(actual == expected);
+}
+
+}}}

src/Math/Test/GeometryUtilsTest.h

@@ -0,0 +1,32 @@
+#ifndef Magnum_Math_Test_GeometryUtilsTest_h
+#define Magnum_Math_Test_GeometryUtilsTest_h
+/*
+    Copyright © 2010, 2011 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 Test {
+
+class GeometryUtilsTest: public QObject {
+    Q_OBJECT
+
+    private slots:
+        void intersection_data();
+        void intersection();
+};
+
+}}}
+
+#endif