# Algorithms for Parallel Polygon Rendering by Theoharis Theoharis

By Theoharis Theoharis

This ebook is the results of the examine within the implementation of polygon-based photographs operations on convinced normal objective parallel processors; the purpose is to supply a speed-up over sequential implementations of the photographs operations involved, and the ensuing software program may be considered as a subset of the appliance suites of the proper parallel machines. A literature overview and a short description of the architectures thought of provide an advent into the sector. such a lot algorithms are regularly offered in an informally outlined extension of the Occam language inclusive of unmarried guideline a number of info flow (SIMD) info forms and operations on them. unique equipment for polygon rendering - together with the operations of filling, hidden floor removing and tender shading - are awarded for SIMD architectures just like the DAP and for a dual-paradigm (SIMD-MIMD) laptop built out of a DAP-like processor array and a transputer community. Polygon clipping algorithms for either transputer and the DAP are defined and contrasted. except the knowledge provided within the publication and the precious literature survey, the reader may also count on to achieve an perception into the programming of the proper parallel machines.

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**Example text**

N - I j = (i+1 if i<(n-1) else 0) n is the number of vertices in the polygon. The d coefficient can be found by using the coordinates of a vertex to solve the plane equation for d. 2. Thus for each relevant window a planar integer S is calculated that contains the interpolated shade for each pixel within the window. Non-planar objects can be shaded by finding the appropriate visible area of the object and evaluating that function. Z If the compute polygon the is not planar subdivided integers S for for the purpose smooth shading of shading, will be then the equivalent time to the taken to cost of evaluating 3 linear functions (one for each of the Red Green and Blue colour components) over the w relevant windows: TSS = 3 )g ($EVAL + (Iv-l)tlt~c).

The network, the difference being that it has access to a special kind of primitive data type: the planar perform data type. The operations on controller can them. Of whose control registers are mapped thus declare variables of planar data course, the planar operations are executed by into the memory of the controller. 6. P l a n a r As Operations mentioned earlier, the Disputer is totally programmable in Occam but the transputer which controls the processor array has access to a special data type, the planar data type.

4 holds true in the case of the DAP (N=32) for pd>_3 bitplanes. 3. A c c u r a c y We shall now of Representation derive the accuracy (depth) of the planar required in order to evaluate a linear function correctly. the coefficients a, b, e of the line passing through arithmetic representation, pd, Given an I x I - p i x e l image space, the image space points (xi, yi) and (Igi+l)Yi+l) are defined as: Since x i , Yi, xi+l and a= (yi -y,÷t) b= (xi÷z-xi) c (xi yi+l xi+l y~ ). 1 can independently range between 0 and I-1, the ranges of a, b and c are: -(I-l) _< a _< ( I - i ) -(I-l) <_ b _< (I-l) -(I-1) 2 _< c _< (I-1) 2.