Simplified GeometryUtils::intersection(), updated documentation.

The function now takes only plane normal and position instead of three
points. Also greatly simplified unit test.

src/Math/GeometryUtils.h

@@ -19,60 +19,49 @@
  * @brief Class Magnum::Math::GeometryUtils
  */
 
-#include "Matrix3.h"
+#include "Vector3.h"
 
 namespace Magnum { namespace Math {
 
 /**
 @brief Geometry utils
 */
-template<class T> class GeometryUtils {
+class GeometryUtils {
     public:
         /**
          * @brief Intersection of a plane and line
-         * @param plane     Plane defined by three points
+         * @param planePosition Plane position
-         * @param a         Starting point of the line
+         * @param planeNormal   Plane normal
-         * @param b         Ending point of the line
+         * @param a             Starting point of the line
-         * @return Value, NaN if the line lies on the plane or infinity if the
+         * @param b             Ending point of the line
-         * intersection doesn't exist. Intersection point can be then computed
+         * @return Intersection point position, NaN if the line lies on the
-         * with `a+intersection(...)*b`. If returned value is in range
+         * plane or infinity if the intersection doesn't exist. Intersection
-         * @f$ [ 0 ; 1 ] @f$, the intersection is inside the line segment
+         * point can be computed from the position with `a+intersection(...)*b`.
-         * defined by `a` and `b`.
+         * If returned value is in range @f$ [ 0 ; 1 ] @f$, the intersection
+         * is inside the line segment defined by `a` and `b`.
          *
-         * First the parametric equation of the plane is computed,
+         * First the parameter *f* of parametric equation of the plane
-         * @f$ cx + dy + ez = f @f$. Parameters @f$ (c, d, e) @f$ are cross
+         * is computed from plane normal **n** and plane position:
-         * 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}
+         *      \begin{pmatrix} n_0 \\ n_1 \\ n_2 \end{pmatrix} \cdot
-         *         (g, h, i) & = & plane                                    \\
+         *      \begin{pmatrix} x \\ y \\ z \end{pmatrix} - f = 0
-         *         (c, d, e) & = & (h - g) \times (i - g)                   \\
-         *         f & = & (c, d, e) \cdot g
-         *     \end{array}
          * @f]
-         *
+         * Using plane normal **n**, parameter *f* and points **a** and **b**,
-         * Using parametric equation and points @f$ a @f$ and @f$ b @f$, value
+         * value of *t* is computed and returned.
-         * of @f$ t @f$ is computed and returned.
          * @f[
-         *     \begin{array}{lcl}
+         *      \begin{array}{rcl}
-         *         \Delta b & = & b - a                                     \\
+         *          \Delta \boldsymbol b & = & \boldsymbol b - \boldsymbol a \\
-         *         f & = & (c, d, e) \cdot (a + \Delta b \cdot t)           \\
+         *          f & = & \boldsymbol n \cdot (\boldsymbol a + \Delta \boldsymbol b \cdot t) \\
-         *         t & = & \frac{f - (c, d, e) \cdot a}
+         *          \Rightarrow t & = & \cfrac{f - \boldsymbol n \cdot \boldsymbol a}{\boldsymbol n \cdot \Delta \boldsymbol b}
-         *                 {(c, d, e) \cdot \Delta b}
          *      \end{array}
          * @f]
          */
-        static T intersection(const Matrix3<T>& plane, const Vector3<T>& a, const Vector3<T>& b) {
+        template<class T> static T intersection(const Vector3<T>& planePosition, const Vector3<T>& planeNormal, const Vector3<T>& a, const Vector3<T>& b) {
-            /* Cross product of two vectors defining the plane */
+            /* Compute f from normal and plane position */
-            Vector3<T> crossProduct = Vector3<T>::cross(plane[1]-plane[0], plane[2]-plane[0]);
+            T f = Vector3<T>::dot(planePosition, planeNormal);
-
-            /* Compute f with cross product and one of the points defining the
-               plane */
-            T f = Vector3<T>::dot(crossProduct, plane[0]);
 
             /* Compute t */
-            return (f-Vector3<T>::dot(crossProduct, a)/Vector3<T>::dot(crossProduct, b-a));
+            return (f-Vector3<T>::dot(planeNormal, a)/Vector3<T>::dot(planeNormal, b-a));
         }
 };
 

src/Math/Test/GeometryUtilsTest.cpp

@@ -18,52 +18,36 @@
 #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;
+typedef Magnum::Math::Vector3<float> Vector3;
-using ::Vector3;
-
-void GeometryUtilsTest::intersection_data() {
-    QTest::addColumn<Matrix3>("plane");
-    QTest::addColumn<Vector3>("a");
-    QTest::addColumn<Vector3>("b");
-    QTest::addColumn<float>("expected");
-
-    Matrix3 plane(0.0f, 0.0f, 0.0f,
-                  1.0f, 0.0f, 0.0f,
-                  0.0f, 1.0f, 0.0f);
-    QTest::newRow("inside") << plane << Vector3(0, 0, -1) << Vector3(0, 0, 1) << 0.5f;
-    QTest::newRow("outside") << plane << Vector3(0, 0, 1) << Vector3(0, 0, 2) << -1.0f;
-    QTest::newRow("NaN") << plane << Vector3(1, 0, 0) << Vector3(0, 1, 0) << numeric_limits<float>::quiet_NaN();
-    QTest::newRow("inf") << plane << Vector3(1, 0, 1) << Vector3(0, 0, 1) << numeric_limits<float>::infinity();
-}
 
 void GeometryUtilsTest::intersection() {
-    QFETCH(Matrix3, plane);
+    Vector3 planePosition;
-    QFETCH(Vector3, a);
+    Vector3 planeNormal(0.0f, 0.0f, 1.0f);
-    QFETCH(Vector3, b);
+
-    QFETCH(float, expected);
+    /* Inside line segment */
-
+    QCOMPARE((GeometryUtils::intersection(planePosition, planeNormal,
-    /* Handling also NaN, which cannot be fuzzy compared */
+        Vector3(0, 0, -1), Vector3(0, 0, 1))), 0.5f);
-    float actual = GeometryUtils<float>::intersection(plane, a, b);
+
-
+    /* Outside line segment */
-    /* All possible workarounds for comparing to inf and NaN */
+    QCOMPARE((GeometryUtils::intersection(planePosition, planeNormal,
-    if(expected > numeric_limits<float>::max()) QCOMPARE(actual, expected);
+        Vector3(0, 0, 1), Vector3(0, 0, 2))), -1.0f);
-    else if(expected != expected) QVERIFY(actual != actual);
+
-    else QVERIFY(actual == expected);
+    /* Line lies on the plane */
+    float nan = GeometryUtils::intersection(planePosition, planeNormal,
+        Vector3(1, 0, 0), Vector3(0, 1, 0));
+    QVERIFY(nan != nan);
+
+    /* Line is parallell to the plane */
+    QCOMPARE((GeometryUtils::intersection(planePosition, planeNormal,
+        Vector3(1, 0, 1), Vector3(0, 0, 1))), numeric_limits<float>::infinity());
 }
 
 }}}

src/Math/Test/GeometryUtilsTest.h

@@ -23,7 +23,6 @@ class GeometryUtilsTest: public QObject {
     Q_OBJECT
 
     private slots:
-        void intersection_data();
         void intersection();
 };