Fix scale-dependent ulp bounds in RoundLineIntersector

[dongclin]

Summary

Fixes a scale-invariance bug in kernels/geometry/roundline_intersector.h (RTC_GEOMETRY_TYPE_ROUND_LINEAR_CURVE) where three ulp epsilon bounds in ConeGeometry::isInsideCappedCone and ConeGeometryIntersector::intersectCone were not scaled by the squared tangent slant length g = dPdP - drdr.

Root Cause

Unlike Cone (kernels/geometry/cone.h) and Cylinder (kernels/geometry/cylinder.h), which normalize the segment axis by rl = rcp_length(p1 - p0) so that axial projections are O(L) and unitless parameters lie in [0, 1], ConeGeometry in roundline_intersector.h avoids the square root by scaling the axial parameter domain by g = ||p1 - p0||^2 - (r1 - r0)^2 (O(L^2)):

• The cone segment spans unnormalized axial coordinate y in [0, g], with normalized curve parameter u = clamp(y / g, 0.0f, 1.0f).
• Lines 338 & 342 (ConeGeometryIntersector::intersectCone):
  • lower = select((y_cone_front > -(float)ulp) & (y_cone_front <= g) & (g > 0.0f), ...)
  • upper = select((y_cone_back > -(float)ulp) & (y_cone_back <= g) & (g > 0.0f), ...)
    Because y_cone_front and y_cone_back have units of g (O(L^2)), testing > -(float)ulp admits phantom cylinder/cone hits behind p0 over physical distance ulp / L (u in [-ulp / g, 0)). Furthermore, because t_first = select(valid_lower, t_cone_sphere_lower, t_cone_sphere_upper), an external ray hits the back wall t_cone_upper if t_cone_lower is rejected—so both front and back bounds must be scaled by g.
• Line 203 (ConeGeometry::isInsideCappedCone):
  • cap0 = -r0dr + vfloat<M>(ulp)
  • cap1 = -r1*dr + dPdP = -r0dr + g
    Because cap1 - (-r0dr) = g, comparing against an unscaled ulp (1.1920929e-7f) causes cap0 >= cap1 whenever g <= ulp (segment length L <= sqrt(ulp) ~= 3.45e-4), collapsing (cap0, cap1) to the empty set so neighbor-cone clipping (coneL.isInsideCappedCone / coneR.isInsideCappedCone) unconditionally returns false.

Before vs. After Fix (rtcIntersect1 on L-Shaped 2-Segment Curve (-L,0,0) -> (0,0,0) -> (0,L,0), r = 0.35*L)

1. Reference (L = 1.0)	2. Before Fix (L = 1e-4)	3. After Fix (L = 1e-4, ulp * g)

At L = 1e-4 (g = 1e-8 < ulp), both segments grow a ulp / L = 11.92 * L phantom cylinder backward past their start vertices (Seg 0 extends 11.92 * L to the left of (-L,0,0), and Seg 1 extends 11.92 * L downward through the (0,0,0) corner), while isInsideCappedCone fails to clip internal overlap at the (0,0,0) joint. Scaling ulp by g in all three places restores exact scale invariance.

At L = 1e-4 (g = 1e-8 < ulp), both segments grow a ulp / L = 11.92 * L phantom cylinder backward past their start vertices (Seg 0 extends 11.92 * L to the left of (-L,0,0), and Seg 1 extends 11.92 * L downward through the (0,0,0) corner), while isInsideCappedCone fails to clip internal overlap at the (0,0,0) joint. Scaling ulp by g in all three places restores exact scale invariance.

Reproduce with embree_viewer and RoundLineSegments XML
l_curve_1.xml (L = 1.0):

<?xml version="1.0"?>
<scene>
  <Group>
    <RoundLineSegments>
      <positions>
        -1.0 0.0 0.0 0.35
         0.0 0.0 0.0 0.35
         0.0 1.0 0.0 0.35
      </positions>
      <indices>
        0 1
      </indices>
      <material>
        <code>"OBJ"</code>
        <parameters>
          <float3 name="Kd">1 1 1</float3>
        </parameters>
      </material>
    </RoundLineSegments>
  </Group>
</scene>

l_curve_1e-4.xml (L = 1e-4):

<?xml version="1.0"?>
<scene>
  <Group>
    <RoundLineSegments>
      <positions>
        -0.0001 0.0    0.0 0.000035
         0.0    0.0    0.0 0.000035
         0.0    0.0001 0.0 0.000035
      </positions>
      <indices>
        0 1
      </indices>
      <material>
        <code>"OBJ"</code>
        <parameters>
          <float3 name="Kd">1 1 1</float3>
        </parameters>
      </material>
    </RoundLineSegments>
  </Group>
</scene>

Render and compare with embree_viewer:

# 1. Reference (L = 1.0)
./embree_viewer -i l_curve_1.xml \
  --vp -6.0 -5.7 70.0 --vi -6.0 -5.7 0.0 --vu 0 1 0 --fov 12.2 --righthanded \
  --size 360 360 -o l_curve_L_1.png
# 2. Small scale (L = 1e-4)
./embree_viewer -i l_curve_1e-4.xml \
  --vp -0.0006 -0.00057 0.0070 --vi -0.0006 -0.00057 0.0 --vu 0 1 0 --fov 12.2 --righthanded \
  --size 360 360 -o l_curve_L_1e-4.png --compare l_curve_L_1.png