Algorithms for Parallel Polygon Rendering by Theoharis Theoharis

By Theoharis Theoharis

This e-book is the results of the examine within the implementation of polygon-based snap shots operations on convinced normal goal parallel processors; the purpose is to supply a speed-up over sequential implementations of the photographs operations involved, and the ensuing software program might be considered as a subset of the appliance suites of the appropriate parallel machines. A literature evaluate and a quick description of the architectures thought of supply an advent into the sphere. such a lot algorithms are regularly awarded in an informally outlined extension of the Occam language inclusive of unmarried guideline a number of facts move (SIMD) facts kinds and operations on them. unique tools for polygon rendering - together with the operations of filling, hidden floor removal and tender shading - are offered 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 offered within the publication and the invaluable literature survey, the reader may also anticipate to achieve an perception into the programming of the correct parallel machines.

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5 broadcasts. Thus the latter The cost of a planar multiplication is 2 . 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~ ).

Under will add the constant planar integer [ai*2 k] under N/2 The masks for the evaluation of aix are shown in The value of the constant planar integer that is added to the sum each mask is indicated underneath the mask. Three masks are required since three planar additions are performed (1og28=3). 00110011 O0110011 00110011 00110011 00110011 00il 10011 00110011 O011001:1 010101 010101 010101 o11 0 1 0 1 0 1 0 liO 1 0 1 010101 01 010101 O1 010101 Ol o1 01 °i', [ai x~20] O0 O0 oo O0 O0 O0 O0 O0 [ai x 21] 0 0 li 1 1 1 !

The space perspective transformation is chosen so [Newm79]. 2) which can be expressed as a linear function of x and y when solved for z: Z(x,y) where A = - a l e , = Ax + By and C = - d l e . 3) produces the depth (z) of the polygon's plane at that pixel. 1) for filling. A planar integer D with the values of function (3,3) within the first window intersected by the polygon is calculated at a cost of 21og2N planar additions. The planar integers D for subsequent relevant windows are computed incrementally at a cost of l planar addition each.

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