Attempting to vis ad_tears drags a few lurking bugs out of
SmallestEnclosingBall_vf: poor calculation of 2-point affine space, poor
handling of duplicate points and dropped support points, poor
calculation of the new center (related to duplicate points), and
insufficient iterations for large point sets. qfvis (modified for
cluster spheres) now loads ad_tears.
As per usual, fp math finds a way to confound any epsilon test. So
rather than relying entirely on test_support_points, check the distance
from the sphere center to the affine point and break out of the loop if
the distance is small enough (< 1% of the current radius). This allows
qfvis to load ad_tears without hacks.
Scaling the checks by 1e-6 was a little too tight for very small
triangles, but 1e-5 seems to work well. This fixes SEB getting stuck for
a ridiculously small (for quake) triangle in ad_tears (probably resulted
from some bad math in qfbsp when generating the portal file from the
bsp).
It seems that i686 code generation is all over the place reguarding sse2
vs fp, with the resulting differences in carried precision. I'm not sure
I'm happy with the situation, but at least it's being tested to a
certain extent. Not sure if this broke basic (no sse) i686 tests.
The calculation fails (produces NaN) if the vectors are anti-parallel,
but works for all other combinations. I came up with this implementation
when I discovered Unity's Quaternion.FromToRotation could did not work
with very small angles. This implementation will produce a usable
quaternion below 0.00255 degrees (though it will be slightly larger than
unit). Unity's failed such that I could see KSP's skybox snap while it
rotated around my test vessel.
When I ported SEB to python, I discovered that I apparently didn't
really understand the paper's description of the end condition and the
usage of the affine and convex sets for center testing. This cleans up
the test and makes SEB more correct for the cases that have less than 4
supporting points (especially when there are less than 4 points total).
The better accuracy is for specific cases (90 degree rotations around a
main axis: the matrix element for that axis is now 1 instead of
0.99999994). The speedup comes from doing fewer additions (multiply
seems to be faster than add for fp, at least in this situation).
After messing with SIMD stuff for a little, I think I now understand why
the industry went with xyzw instead of the mathematical wxyz. Anyway, this
will make for less pain in the future (assuming I got everything).
Now we can get tight (<1e-6 * radius_squared error) bounding spheres. More
importantly (for qfvis, anyway) very quickly: 1.7Mspheres/second for a 5
point cloud on my 2.33GHz Core 2 :)
It "works" for lines, triangles and tetrahedrons. For lines and triangles,
it gives the barycentric coordinates of the perpendicular projection of the
point onto to features. Only tetrahedrons are guaranteed to reproduce the
original point.
And the tests really exercised VectorShear (first attempt had things
messed up when more than one shear value was non-zero). Also,
Mat4Decompose wasn't orthogonalizing the z axis row. Oops. Anyway,
Mat4Decompose is now known to work well, and the usage of its output is
understood :)
I got the idea from blender when I discovered by accident that quat * vect
produces the same result as quat * qvect * quat* and looked up the code to
check what was going on. While matrix/vector multiplication still beats the
pants off quaternion/vector multiplication, QuatMultVec is a slight
optimization over quat * qvect * quat* (17+,24* vs 24+,32*, plus no need to
to generate quat*).
I got rather tired of there being multiple definitions of mostly compatible
plane types (and I need a common type anyway). dplane_t still exists for
now because I want to be careful when messing with the actual bsp format.
functions when told to. also make gcc warn if it can't inline a function.
Explicitly inline several functions (including moving VectorNormalize to
mathlib.h so it /can/ be) resulting in a 5.5% speedup for spam2 (88 to 92
fps)
