Continuing work on BaseWindingForPlane() in polylib.c. In fact I'm pursuing

the approach that was committed in r375 (but was then backed out).  I can't
believe my eyes, but I seem to be getting 0.000000% error in some of my
regression tests.  The trick is to scale by a power of 2 and never do a
VectorNormalize().

git-svn-id: svn://svn.icculus.org/gtkradiant/GtkRadiant/trunk@377 8a3a26a2-13c4-0310-b231-cf6edde360e5

diff --git a/libs/mathlib.h b/libs/mathlib.h
index 85afacf29cd84c36b0090d3e32b999dd427bcb8d..44bf01c9bca8e0efd38eaeb51a2e8dec36bab33e 100644 (file)
--- a/libs/mathlib.h
+++ b/libs/mathlib.h
@@ -81,7 +81,6 @@ void VectorMA( const vec3_t va, vec_t scale, const vec3_t vb, vec3_t vc );
 
 void _CrossProduct (vec3_t v1, vec3_t v2, vec3_t cross);
 vec_t VectorNormalize (const vec3_t in, vec3_t out);
-vec_t VectorSetLength (const vec3_t in, vec_t length, vec3_t out);
 vec_t ColorNormalize( const vec3_t in, vec3_t out );
 void VectorInverse (vec3_t v);
 void VectorPolar(vec3_t v, float radius, float theta, float phi);

diff --git a/libs/mathlib/mathlib.c b/libs/mathlib/mathlib.c
index 1234a86f7452bd635affc89d8f9342e0e6defb58..33945cde4ed22436a696c2942e6998c70f954d9c 100644 (file)
--- a/libs/mathlib/mathlib.c
+++ b/libs/mathlib/mathlib.c
@@ -143,21 +143,6 @@ vec_t VectorNormalize( const vec3_t in, vec3_t out ) {
        return length;
 }
 
-vec_t VectorSetLength(const vec3_t in, vec_t length, vec3_t out) {
-       vec_t   origLength;
-
-       origLength = (vec_t) sqrt((in[0] * in[0]) + (in[1] * in[1]) + (in[2] * in[2]));
-       if (origLength == 0)
-       {
-               VectorClear(out);
-               return 0;
-       }
-
-       VectorScale(in, length / origLength, out);
-
-       return origLength;
-}
-
 vec_t ColorNormalize( const vec3_t in, vec3_t out ) {
        float   max, scale;
 

diff --git a/tools/quake3/common/polylib.c b/tools/quake3/common/polylib.c
index 839f7ea5d1ee3071fa7aa26539cb601ceadce9f7..861e782153c1c7d38cae19403ce65fb6f3101871 100644 (file)
--- a/tools/quake3/common/polylib.c
+++ b/tools/quake3/common/polylib.c
@@ -219,10 +219,8 @@ winding_t *BaseWindingForPlane (vec3_t normal, vec_t dist)
        // Once these vectors are calculated, I'm constructing the winding points in exactly the same
        // way as was done in the original function.  Orientation is the same.
 
-       // Note that the 4 points in the returned winding_t may actually not be necessary (3 might
-       // be enough).  However, I want to minimize the chance of ANY bugs popping up due to any
-       // change in behavior of this function.  Therefore, behavior stays exactly the same, except
-       // for precision of math.  Performance might be better in the new function as well.
+       // EDIT: We're also changing the size of the winding polygon; this is a side effect of
+       // eliminating a VectorNormalize() call.  The new winding polygon is actually bigger.
 
        int             x, i;
        vec_t           max, v;
@@ -253,15 +251,42 @@ winding_t *BaseWindingForPlane (vec3_t normal, vec_t dist)
                        vright[2] = normal[1];
                        break;
        }
+       // vright and normal are now perpendicular, you can prove this by taking their
+       // dot product and seeing that it's always exactly 0 (with no error).
+
+       // NOTE: vright is NOT a unit vector at this point.  vright will have length
+       // not exceeding 1.0.  The minimum length that vright can achieve happens when,
+       // for example, the Z and X components of the normal input vector are equal,
+       // and when its Y component is zero.  In that case Z and X of the normal vector
+       // are both approximately 0.70711.  The resulting vright vector in this case
+       // will have a length of 0.70711.
+
+       // We're relying on the fact that MAX_WORLD_COORD is a power of 2 to keep
+       // our calculation precise and relatively free of floating point error.
+       // The code will work if that's not the case, but not as well.
+       VectorScale(vright, MAX_WORLD_COORD * 4, vright);
+
+       // At time time of this writing, MAX_WORLD_COORD was 65536 (2^16).  Therefore
+       // the length of vright at this point is at least 185364.  A corner of the world
+       // at location (65536, 65536, 65536) is distance 113512 away from the origin.
+
        CrossProduct(normal, vright, vup);
 
-       // IMPORTANT NOTE: vright and vup are NOT unit vectors at this point.
-       // However, normal, vup, and vright are pairwise perpendicular.
+       // vup now has length equal to that of vright.
 
-       VectorSetLength(vup, MAX_WORLD_COORD * 2, vup);
-       VectorSetLength(vright, MAX_WORLD_COORD * 2, vright);
        VectorScale(normal, dist, org);
 
+       // org is now a point on the plane defined by normal and dist.  Furthermore,
+       // org, vright, and vup are pairwise perpendicular.  Now, the 4 vectors
+       // (+-)vright + (+-)vup have length that is at least sqrt(185364^2 + 185364^2),
+       // which is about 262144.  That length lies outside the world, since the furthest
+       // point in the world has distance 113512 from the origin as mentioned above.
+       // Also, these 4 vectors are perpendicular to the org vector.  So adding them
+       // to org will only increase their length.  Therefore the 4 points defined below
+       // all lie outside of the world.  Furthermore, it can be easily seen that the
+       // edges connecting these 4 points (in the winding_t below) lie completely outside
+       // the world.  sqrt(262144^2 + 262144^2)/2 = 185363, which is greater than 113512.
+
        w = AllocWinding(4);
 
        VectorSubtract(org, vright, w->p[0]);