Which of the following statements is/are True regarding the solution to the…

Concept. The visibility (hidden-surface) problem asks which surfaces of a 3-D scene actually reach the viewer, and standard techniques answer it in two different ways. An ordering technique fixes a depth order and rasterises surfaces in that order, relying on the frame buffer keeping the last value written to each pixel. A culling technique instead discards a surface before rasterisation using a purely geometric test on the surface itself, so it never reaches the frame buffer at all.

Application. Test each statement against the definition of the technique it names.

• S1 — an ordering technique. The Painter’s algorithm draws every polygon, so correct occlusion has to come from the drawing order: the polygon that ought to be hidden must be painted first and then be overwritten. It therefore sorts polygons on depth and scan-converts them back-to-front, starting with the farthest polygon, so each nearer polygon paints over whatever lies behind it. S1 gives the opposite painting order — starting with the nearest polygon — which is not how the algorithm works.

• S2 — a culling technique. On a closed, single-sided solid, a face whose outward normal points away from the viewer must lie on the far side of the object and can never be seen, so it is removed before rasterisation. The usual test is the sign of the dot product of the outward face normal with the viewing direction, or equivalently the winding order of the projected vertices. That is precisely what S2 asserts.

Cross-check. Reverse the order in S1 and picture the result: painting front-to-back lets a distant polygon paint over a near one, so a wall behind an object would appear in front of it — visibly wrong occlusion. That thought experiment pins the direction down as farthest-first. Apply the same test to S2: if back faces were kept, a closed opaque solid would rasterise its own interior faces, which is exactly what culling exists to prevent.

Result. Exactly one statement of the pair holds — the backface-culling statement — so the correct choice is “S2 only”.

Caveats worth remembering. The Painter’s algorithm still fails for cyclically overlapping or interpenetrating polygons and needs polygon splitting there. Backface culling is safe wherever the geometry is consistently wound and its back faces are genuinely never meant to be seen, as on a closed opaque solid; it must be switched off for double-sided surfaces such as thin sheets or foliage that have to render from both sides.