Implement vector _projection_ functions.

simgear/math/SGVec3.hxx

@@ -352,12 +352,16 @@ perpendicular(const SGVec3<T>& v)
   }
 }
 
-/// The euclidean norm of the vector, that is what most people call length
+/// Construct a unit vector in the given direction.
+/// or the zero vector if the input vector is zero.
 template<typename T>
 inline
 SGVec3<T>
 normalize(const SGVec3<T>& v)
-{ return (1/norm(v))*v; }
+{ T normv = norm(v);
+  if (normv > 0.0) return (1/norm(v))*v;
+  else return v;
+}
 
 /// Return true if exactly the same
 template<typename T>
@@ -476,6 +480,15 @@ SGVec3d
 toVec3d(const SGVec3f& v)
 { return SGVec3d(v(0), v(1), v(2)); }
 
+// calculate the projection of u along the direction of d.
+template<typename T>
+inline SGVec3<T> SGProjection(const SGVec3<T>& u, const SGVec3<T>& d)
+{
+  T denom = dot(d, d);
+  if (denom == 0.) return u;
+  else return  d * (dot(u,d) / denom);
+}
+
 #ifndef NO_OPENSCENEGRAPH_INTERFACE
 inline
 SGVec3d

simgear/math/vector.cxx

@@ -29,6 +29,20 @@
 #include "vector.hxx"
 
 
+// calculate the projection, p, of u along the direction of d.
+void sgProjection(sgVec3 p, const sgVec3 u, const sgVec3 d){
+    double denom = sgScalarProductVec3(d,d);
+    if (denom == 0.) sgCopyVec3(p, u);
+    else sgScaleVec3(p, d, sgScalarProductVec3(u,d) / denom);
+}
+
+// Same thing, except using double precision
+void sgProjection(sgdVec3 p, const sgdVec3 u, const sgdVec3 d){
+    double denom = sgdScalarProductVec3(d,d);
+    if (denom == 0.) sgdCopyVec3(p, u);
+    else sgdScaleVec3(p, d, sgdScalarProductVec3(u,d) / denom);
+}
+
 // Given a point p, and a line through p0 with direction vector d,
 // find the closest point (p1) on the line
 void sgClosestPointToLine( sgVec3 p1, const sgVec3 p, const sgVec3 p0,
@@ -40,8 +54,7 @@ void sgClosestPointToLine( sgVec3 p1, const sgVec3 p, const sgVec3 p0,
     sgSubVec3(u, p, p0);
 
     // calculate the projection, u1, of u along d.
-    // u1 = ( dot_prod(u, d) / dot_prod(d, d) ) * d;
-    sgScaleVec3( u1, d, sgScalarProductVec3(u,d) / sgScalarProductVec3(d,d) );
+    sgProjection(u1, u, d);
 
     // calculate the point p1 along the line that is closest to p
     // p0 = p1 + u1
@@ -60,12 +73,7 @@ void sgdClosestPointToLine( sgdVec3 p1, const sgdVec3 p, const sgdVec3 p0,
     sgdSubVec3(u, p, p0);
 
     // calculate the projection, u1, of u along d.
-    // u1 = ( dot_prod(u, d) / dot_prod(d, d) ) * d;
-    double ud = sgdScalarProductVec3(u, d);
-    double dd = sgdScalarProductVec3(d, d);
-    double tmp = ud / dd;
-
-    sgdScaleVec3(u1, d, tmp);;
+    sgProjection(u1, u, d);
 
     // calculate the point p1 along the line that is closest to p
     // p0 = p1 + u1
@@ -84,8 +92,7 @@ double sgClosestPointToLineDistSquared( const sgVec3 p, const sgVec3 p0,
     sgSubVec3(u, p, p0);
 
     // calculate the projection, u1, of u along d.
-    // u1 = ( dot_prod(u, d) / dot_prod(d, d) ) * d;
-    sgScaleVec3( u1, d, sgScalarProductVec3(u,d) / sgScalarProductVec3(d,d) );
+    sgProjection(u1, u, d);
 
     // v = u - u1 = vector from closest point on line, p1, to the
     // original point, p.
@@ -106,12 +113,7 @@ double sgdClosestPointToLineDistSquared( const sgdVec3 p, const sgdVec3 p0,
     sgdSubVec3(u, p, p0);
 
     // calculate the projection, u1, of u along d.
-    // u1 = ( dot_prod(u, d) / dot_prod(d, d) ) * d;
-    double ud = sgdScalarProductVec3(u, d);
-    double dd = sgdScalarProductVec3(d, d);
-    double tmp = ud / dd;
-
-    sgdScaleVec3(u1, d, tmp);;
+    sgProjection(u1, u, d);
 
     // v = u - u1 = vector from closest point on line, p1, to the
     // original point, p.

simgear/math/vector.hxx

@@ -38,7 +38,17 @@
 
 
 /**
- * Map a vector onto a plane.
+ * calculate the projection, p, of u along the direction of d.
+ * @param p (out) the projection
+ * @param u (in) the vector to be projected
+ * @param d (in) the direction onto which we project
+ */
+void sgProjection(sgVec3 p, const sgVec3 u, const sgVec3 d);
+void sgProjection(sgdVec3 p, const sgdVec3 u, const sgdVec3 d);
+
+
+/**
+ * Map i.e. project a vector onto a plane.
  * @param normal (in) normal vector for the plane
  * @param v0 (in) a point on the plane
  * @param vec (in) the vector to map onto the plane