ST_3DIntersects / ST_3DDistance solid aware in LWGEOM

[komzpa]

From ​https://github.com/postgis/postgis/pull/351#issuecomment-449620811

To implement solid-aware ST_Distance and ST_Intersects we seem to need to add a not super large bit of logic:

distance = mindist_as_it_is(geom1, geom2);
if (box1 &&& box2 and distance > 0)
{ /* check if we are completely inside */
geom1, box1, geom2, box2 = swap_so_that_box1_is_inside_box2();
if (not ST_IsSold(geom2)) 
    return distance;
pt1 = take_any_point_in(geom1);
if (raycast_count_hits_to_infinity_from_point(pt1, geom2) is odd) 
    return 0
else 
    return distance;
}

This way we can avoid the semantic change altogether.

[komzpa]

A dead simple way to perform raycast is to make three calls to lwgeom_clip_to_ordinate_range and count number of geometries in result. Need to teach it not to drop ones that lost their dimensionality.

[hmercier]

@komzpa could you detail ? I do not understand how lwgeom_clip_to_ordinate_range helps here ...

A ray casting in 3D means to me testing intersection between a ray and each face of the mesh.

[komzpa]

Ray from point to infinity can be expressed as a box (Xmin=X[-eps], Xmax=X[+eps], Ymin=Y[-eps], Ymax=Y[+eps], Zmin=Z, Zmax = infinity). You can intersect such box with any dimension geometry by feeding the ranges into lwgeom_clip_to_ordinate_range.

Afterwards you get a bunch of super tiny polygons with 2D area=0, area = eps^{2. Count ones with area>0, that will get you a good approximation of number of hits. If you find a hit with area of 0 < area < eps}2, it's on the edge, mark it with a TODO:FIXME and emit a warning.

[komzpa]

In 17247:

[format] Tidy up measures3d.

References #4278

[komzpa]

In 17260:

Make lwgeom_mindist3d solid aware. Add TIN support.

Thanks Hugo Mercier for suggesting test cases.

Closes #4278
Closes ​https://github.com/postgis/postgis/pull/373