The Z-buffer algorithm is used for hidden surface removal of objects. The…
2012
The Z-buffer algorithm is used for hidden surface removal of objects. The maximum number of objects that can be handled by this algorithm shall
Answer: B. be arbitrary no. of objects — ConceptThe Z-buffer (depth-buffer) method is an image-space visibility algorithm. Alongside the frame buffer, which holds one colour per pixel, it maintains a…
- A.
Depend on the application
- B.
be arbitrary no. of objects
- C.
Depend on the memory availability
- D.
Depend on the processor
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Correct answer: B
Concept
The Z-buffer (depth-buffer) method is an image-space visibility algorithm. Alongside the frame buffer, which holds one colour per pixel, it maintains a depth buffer holding one depth value per pixel, initialised to the far plane.
Its visibility working storage is therefore (colour bits + depth bits) × width × height — a quantity fixed by the raster resolution alone. Nothing in this Z-buffer working-state expression refers to the scene, so this buffer footprint does not grow with the amount of geometry drawn.
Application
Initialise every pixel: its depth entry is set to the far plane (maximum depth) and its colour entry to the background colour.
Take one surface at a time and scan-convert it; the algorithm never needs to hold two surfaces simultaneously, and the surfaces need no particular order.
For each pixel the surface covers, compute the fragment depth z and compare it with the depth already stored at that pixel.
If z is nearer to the viewer, overwrite that pixel’s depth entry with z and its colour entry with the surface’s shade; otherwise discard the fragment.
Once the surface is finished, no separate per-object or per-surface record is retained; its currently visible fragments remain represented through the one depth value and one colour held for each pixel.
Submitting one more surface therefore adds scan-conversion work but does not enlarge the Z-buffer’s per-pixel allocation, so the Z-buffer method itself imposes no object-count cap.
Cross-check
Quantity | What it actually governs |
|---|---|
Raster resolution | The size of the depth and frame buffers, fixed when they are allocated |
Number of objects | Z-buffer work increases with submitted fragments; its per-pixel buffer size is unchanged |
Processor speed | How fast a frame is rasterised, not what can be stored |
Application domain | Which geometry is submitted, not the per-pixel depth test itself |
Contrast this with object-space methods. Depth sorting (the painter’s algorithm) must hold and sort the entire surface list, costing O(n log n) time plus per-object storage, so its working set really does scale with n. The Z-buffer trades that for a fixed-size, resolution-determined buffer, which is exactly why it is the visibility method built into hardware rasterisers.
Practical hardware can still be limited by memory for geometry and model data, draw-call overhead, and rendering time. The conclusion is narrower: the Z-buffer’s own per-pixel allocation contains no object-count-dependent term.
Hence the number of objects the Z-buffer algorithm can handle is arbitrary.