3D graphics eBook - Course Materials Repository

Polygon 111
Polygon
Polygons are used in computer graphics to compose images that are three-dimensional in appearance. Usually (but
not always) triangular, polygons arise when an object's surface is modeled, vertices are selected, and the object is
rendered in a wire frame model. This is quicker to display than a shaded model; thus the polygons are a stage in
computer animation. The polygon count refers to the number of polygons being rendered per frame.
Competing methods for rendering polygons that avoid seams
• Point
• Floating Point
• Fixed-Point
• Polygon
• because of rounding, every scanline has its own direction in space and may show its front or back side to the
viewer.
• Fraction (mathematics)
• Bresenham's line algorithm
• Polygons have to be split into triangles
• The whole triangle shows the same side to the viewer
• The point numbers from the Transform and lighting stage have to converted to Fraction (mathematics)
• Barycentric coordinates (mathematics)
• Used in raytracing
Potentially visible set
Potentially Visible Sets are used to accelerate the rendering of 3D environments. This is a form of occlusion culling,
whereby a candidate set of potentially visible polygons are pre-computed, then indexed at run-time in order to
quickly obtain an estimate of the visible geometry. The term PVS is sometimes used to refer to any occlusion culling
algorithm (since in effect, this is what all occlusion algorithms compute), although in almost all the literature, it is
used to refer specifically to occlusion culling algorithms that pre-compute visible sets and associate these sets with
regions in space. In order to make this association, the camera view-space (the set of points from which the camera
can render an image) is typically subdivided into (usually convex) regions and a PVS is computed for each region.
Benefits vs. Cost
The benefit of offloading visibility as a pre-process are:
• The application just has to look up the pre-computed set given its view position. This set may be further reduced
via frustum culling. Computationally, this is far cheaper than computing occlusion based visibility every frame.
• Within a frame, time is limited. Only 1/60th of a second (assuming a 60 Hz frame-rate) is available for visibility
determination, rendering preparation (assuming graphics hardware), AI, physics, or whatever other app specific
code is required. In contrast, the offline pre-processing of a potentially visible set can take as long as required in
order to compute accurate visibility.
The disadvantages are:
• There are additional storage requirements for the PVS data.
• Preprocessing times may be long or inconvenient.