Math: cleaned up plane/line intersection.

The function now accepts starting point and direction of the line (not
starting and ending point). Also improved the documentation and test a
bit.

src/Math/Geometry/Intersection.h

@@ -41,34 +41,30 @@ class Intersection {
          * @brief %Intersection of a plane and line
          * @param planePosition Plane position
          * @param planeNormal   Plane normal
-         * @param a             Starting point of the line
-         * @param b             Ending point of the line
-         * @return %Intersection point position, NaN if the line lies on the
-         * plane or infinity if the intersection doesn't exist. %Intersection
-         * point can be computed from the position with `a+intersection(...)*b`.
-         * If returned value is in range @f$ [ 0 ; 1 ] @f$, the intersection
-         * is inside the line segment defined by `a` and `b`.
+         * @param p             Starting point of the line
+         * @param r             Direction of the line
+         * @return %Intersection point position `t` on the line, NaN if the
+         *      line lies on the plane or infinity if the intersection doesn't
+         *      exist. %Intersection point can be then computed from with
+         *      `p + t*r`. If returned value is in range @f$ [ 0 ; 1 ] @f$, the
+         *      intersection is inside the line segment defined by `p` and `r`.
          *
          * First the parameter *f* of parametric equation of the plane
          * is computed from plane normal **n** and plane position: @f[
          *      \begin{pmatrix} n_0 \\ n_1 \\ n_2 \end{pmatrix} \cdot
          *      \begin{pmatrix} x \\ y \\ z \end{pmatrix} - f = 0
          * @f]
-         * Using plane normal **n**, parameter *f* and points **a** and **b**,
-         * value of *t* is computed and returned. @f[
+         * Using plane normal **n**, parameter *f* and line defined by **p**
+         * and **r**, value of *t* is computed and returned. @f[
          *      \begin{array}{rcl}
-         *          \Delta \boldsymbol b & = & \boldsymbol b - \boldsymbol a \\
-         *          f & = & \boldsymbol n \cdot (\boldsymbol a + \Delta \boldsymbol b \cdot t) \\
-         *          \Rightarrow t & = & \cfrac{f - \boldsymbol n \cdot \boldsymbol a}{\boldsymbol n \cdot \Delta \boldsymbol b}
+         *          f & = & \boldsymbol n \cdot (\boldsymbol p + t \boldsymbol r) \\
+         *          \Rightarrow t & = & \cfrac{f - \boldsymbol n \cdot \boldsymbol p}{\boldsymbol n \cdot \boldsymbol r}
          *      \end{array}
          * @f]
          */
-        template<class T> static T planeLine(const Vector3<T>& planePosition, const Vector3<T>& planeNormal, const Vector3<T>& a, const Vector3<T>& b) {
-            /* Compute f from normal and plane position */
-            T f = Vector3<T>::dot(planePosition, planeNormal);
-
-            /* Compute t */
-            return (f-Vector3<T>::dot(planeNormal, a))/Vector3<T>::dot(planeNormal, b-a);
+        template<class T> static T planeLine(const Vector3<T>& planePosition, const Vector3<T>& planeNormal, const Vector3<T>& p, const Vector3<T>& r) {
+            const T f = Vector3<T>::dot(planePosition, planeNormal);
+            return (f-Vector3<T>::dot(planeNormal, p))/Vector3<T>::dot(planeNormal, r);
         }
 };
 

src/Math/Geometry/Test/CMakeLists.txt

@@ -23,5 +23,5 @@
 #
 
 corrade_add_test(MathGeometryDistanceTest DistanceTest.cpp)
-corrade_add_test(MathGeometryIntersectionTest IntersectionTest.cpp)
+corrade_add_test(MathGeometryIntersectionTest IntersectionTest.cpp LIBRARIES MagnumMathTestLib)
 corrade_add_test(MathGeometryRectangleTest RectangleTest.cpp LIBRARIES MagnumMathTestLib)

src/Math/Geometry/Test/IntersectionTest.cpp

@@ -48,19 +48,19 @@ void IntersectionTest::planeLine() {
 
     /* Inside line segment */
     CORRADE_COMPARE((Intersection::planeLine(planePosition, planeNormal,
-        Vector3(0.0f, 0.0f, -1.0f), Vector3(0.0f, 0.0f, 1.0f))), 0.75f);
+        Vector3(0.0f, 0.0f, -1.0f), Vector3(0.0f, 0.0f, 2.0f))), 0.75f);
 
     /* Outside line segment */
     CORRADE_COMPARE((Intersection::planeLine(planePosition, planeNormal,
-        Vector3(0.0f, 0.0f, 1.0f), Vector3(0.0f, 0.0f, 2.0f))), -0.5f);
+        Vector3(0.0f, 0.0f, 1.0f), Vector3(0.0f, 0.0f, 1.0f))), -0.5f);
 
     /* Line lies on the plane */
     CORRADE_COMPARE(Intersection::planeLine(planePosition, planeNormal,
-        Vector3(1.0f, 0.5f, 0.5f), Vector3(0.0f, 1.0f, 0.5f)), std::numeric_limits<Float>::quiet_NaN());
+        Vector3(1.0f, 0.5f, 0.5f), Vector3(-1.0f, 0.5f, 0.0f)), std::numeric_limits<Float>::quiet_NaN());
 
     /* Line is parallell to the plane */
     CORRADE_COMPARE((Intersection::planeLine(planePosition, planeNormal,
-        Vector3(1.0f, 0.0f, 1.0f), Vector3(0.0f, 0.0f, 1.0f))), -std::numeric_limits<Float>::infinity());
+        Vector3(1.0f, 0.0f, 1.0f), Vector3(-1.0f, 0.0f, 0.0f))), -std::numeric_limits<Float>::infinity());
 }
 
 }}}}

src/Physics/Plane.cpp

@@ -49,12 +49,12 @@ bool Plane::collides(const AbstractShape<3>* other) const {
 }
 
 bool Plane::operator%(const Line3D& other) const {
-    Float t = Intersection::planeLine(transformedPosition(), transformedNormal(), other.transformedA(), other.transformedB());
+    Float t = Intersection::planeLine(transformedPosition(), transformedNormal(), other.transformedA(), other.transformedB()-other.transformedA());
     return t != t || (t != std::numeric_limits<Float>::infinity() && t != -std::numeric_limits<Float>::infinity());
 }
 
 bool Plane::operator%(const LineSegment3D& other) const {
-    Float t = Intersection::planeLine(transformedPosition(), transformedNormal(), other.transformedA(), other.transformedB());
+    Float t = Intersection::planeLine(transformedPosition(), transformedNormal(), other.transformedA(), other.transformedB()-other.transformedA());
     return t > 0.0f && t < 1.0f;
 }