with reference to drawing fig1 , a three - dimensional digital object 10 is schematically illustrated . at least an outer surface 12 of digital object 10 is made up of a plurality of polygons 14 , which are illustrated as being triangles having substantially identical dimensions . each polygon 14 of digital object 10 includes at least three vertices 16 , or corners . the numeric data stored for each polygon 14 of digital object 10 represents the positions of each vertex 16 of polygon 14 in the x -, y -, and z - axes . data representative of the positions of the at least three vertices 16 of all of the polygons 14 that make up at least outer surface 12 of digital object 10 are used in various processes , including movement or manipulation of digital object 10 , as well as in rendering an image of digital object 10 . a digital object 10 is rendered to display an image of digital object 10 to a viewer , such as on a computer monitor or on a printed page . once the digital object 10 has been manipulated or moved relative to a reference point , such as the perspective of a viewer , the digital object 10 must be rerendered to indicate movement thereof to the viewer . in rendering an image of a digital object 10 , data regarding the orientation of digital object 10 and of the polygons 14 thereof is evaluated and data representative of the positions of the vertices 16 of each polygon 14 of digital object 10 is used to “ build ” an image of digital object 10 as it is to be shown to a viewer , such as on a computer monitor or on a printed page . the present invention includes methodology for effecting a portion of the rendering process , wherein the vertex 16 data for each polygon 14 of an image of digital object 10 is sorted , then the data for vertices 16 of polygons 14 that will not be visible from the reference point of a viewer ( e . g ., a computer user ) will be culled , or omitted , from the rendering process , thus consuming less random access memory of a computer and speeding up the rendering process . illustrated in drawing fig2 is a flow diagram illustrating the sorting and back face cull decision - making processes of the present invention . illustrated in drawing fig3 is a graphic representation of an analyzed polygon 14 of a digital object 10 ( see fig1 ). as illustrated , polygon 14 is a triangle and includes three vertices 16 a , 16 b , and 16 c . with reference to both drawing fig2 and 3 , prior to rendering an image of digital object 10 , data for each vertex 16 of each polygon 14 of digital object 10 are sent to a portion of a processor under control of a sorting application , as shown at reference character 110 of fig2 . the order in which data for each of vertices 16 a , 16 b , 16 c of polygon 14 are sent to the processor to be sorted may or may not be arbitrary . for example , the positional data for each of the vertices of a polygon may be organized in an order that facilitates a determination of new positions of each vertex following movement of the digital object . while the positional data for each of the three or more vertices of a polygon is “ tied to ,” or associated with , that polygon , in order to conserve memory , the positional data may not be associated with an indicator for a position of a vertex on the polygon relative to other vertices of the polygon ; rather , corresponding x - axis , y - axis , and z - axis data could be associated with a particular vertex based merely on the relative bit locations of these data . data representative of the actual cw or ccw orientation of vertices 16 a , 16 b , 16 c of all of the polygons 14 of digital object 10 may also be sent to the processor , also at reference character 110 of drawing fig2 . as the data for vertices 16 a , 16 b , 16 c may be sent to the processor in an arbitrary order , the data representative of the positions of vertices 16 a , 16 b , 16 c are then sorted , or organized or ordered , as indicated at reference character 112 of drawing fig2 , in a manner that facilitates further processing and use of data representative of the positions of vertices 16 a , 16 b , 16 c and other values based thereon in rendering of an image of digital object 10 . for example , in triangle setup , the coordinates of vertices 16 a , 16 b , 16 c are rasterized so the locations of the lines that define edges 18 a , 18 b , 18 c of each polygon 14 of digital object 10 may be determined and front facing polygons 14 may be rendered . rasterization could proceed in any order ( e . g ., horizontally from top to bottom or from bottom to top , or vertically from left to right or from right to left ). accordingly , the order of the vertices 16 a , 16 b , 16 c is determined based on the order of rasterization . to compute the lines , or polygon edges 18 a , 18 b , 18 c , between vertices 16 a , 16 b , 16 c of polygon 14 , the relative positions of vertices 16 a , 16 b , 16 c must be determined and the order in which positional data representative of each vertex 16 is processed may be changed , depending on the order of rasterization . as an example of the manner in which vertices 16 may be organized , the following series of equations may be used : if (( v2 . y == v0 . y ) and ( v2 . x & lt ; v0 . x )) sort [ 2 ] = 1 else if ( v2 . y & lt ; v0 . y ) sort [ 2 ] = 1 else sort [ 2 ] = 0 if (( v1 . y == v2 . y ) and ( v1 . x & lt ; v2 . x )) sort [ 1 ] = 1 else if ( v1 . y & lt ; v2 . y ) sort [ 1 ] = 1 else sort [ 1 ] = 0 if (( v1 . y == v0 . y ) and ( v1 . x & lt ; v0 . x )) sort [ 0 ] = 1 else if ( v1 . y & lt ; v0 . y ) sort [ 0 ] = 1 else sort [ 0 ] = 0 this series of equations arranges the positional data for vertices 16 of polygon 14 in order of their relative vertical positions . if two vertices 16 have the same vertical orientation , these two vertices 16 are then organized according to the relative horizontal positions . as the cpt for a particular polygon 14 of a digital object 10 or the sign of the cpt may depend on the order in which the positional data for each of vertices 16 a , 16 b , 16 c of polygon 14 is introduced into a processor , sorting of the vertex data may change one or both of the cpt and the sign thereof . as a consequence , a cpt that is calculated before positional data for vertices 16 of polygon 14 is sorted may not be useful in processes that follow a back face culling decision . once sorting has occurred , or concurrently with sorting the vertices 16 of an analyzed polygon 14 of a digital object , as depicted at reference character 114 of drawing fig2 , an orientation decision variable may be computed ( e . g ., by the processor ) to provide information about whether or not the sign of a cpt for an analyzed polygon 14 , which has yet to be calculated until after the positional data for vertices 16 of analyzed polygon 14 has been sorted , will accurately indicate the orientation of vertices 16 of analyzed polygon 14 . if the orientation decision variable indicates that the sign of the cpt will not accurately indicate the orientation of vertices 16 of analyzed polygon 14 , the orientation decision variable for polygon 14 , which is to be subsequently used in a back face culling decision to denote that the apparent orientation of vertices 16 of analyzed polygon 14 , as indicated by the sign of the cpt , is opposite the actual orientation of vertices 16 of polygon 14 when viewed from a particular reference point r . accordingly , the orientation decision variable indicates that the actual orientation of vertices 16 of polygon 14 is inverted from the apparent orientation of vertices 16 , as indicated by the sign of the cpt . as evidenced in the exemplary set of equations provided above , the orientation decision variable may be a three - bit variable that is determined substantially concurrently with sorting of the positional data for each vertex 16 of a polygon 14 . by way of example , the following table illustrates , for each sort indication variable , the order in which vertices 16 of polygon 14 have been sorted ( from sort step 2 to sort step 0 , or [ 2 : 0 ]), relative to the presorting orientation , as well as the corresponding one bit orientation decision variable ( t ): based on the sorted vertices , a cpt may be calculated ( e . g ., by the processor ), as indicated at reference character 116 of drawing fig2 . the sign of the cpt , which is determined ( e . g ., by the processor ), as known in the art , at reference character 118 of drawing fig2 , along with the orientation decision variable , may then be used in a back face culling decision ( e . g ., by the processor ), as depicted at reference character 120 of drawing fig2 , to determine whether the orientation of an analyzed polygon 14 has changed from its actual orientation . for example , if vertices 16 on each polygon 14 of a digital object 10 are actually oriented cw , the sign of the cpt indicates a ccw orientation , and the decision variable ( e . g ., a “ 1 ”) indicates that sorting has switched the sign of the cpt , the data for an analyzed polygon 14 will be used in rendering an image with that polygon 14 displayed . alternatively , if , for a polygon 14 that is actually cw - oriented , the sign of the cpt indicates a ccw orientation and the decision variable ( e . g ., a “ 0 ”) indicates that sorting has not altered the sign of the cpt , the sign of the cpt and the orientation decision variable together indicate that an analyzed polygon 14 is a back facing polygon and the data for polygon 14 is , therefore , culled . a cpt that has been calculated following sorting of the data may also be used in processing that follows a sorting operation such as triangle setup but that must occur before the digital object is rendered . for example , but not to limit the scope of the present invention , a cpt that is calculated after sorting of the positional data for the vertices of a polygon may be used , as known in the art , to process various characteristic parameters of the polygon , such as the shadowing , color , or texture of the polygon , based on the position of the polygon on the digital object relative to a specific reference point r . accordingly , methods incorporating teachings of the present invention facilitate the faster processing of polygon data , as well as a reduction in the amount of memory required to process the polygon data . as the method of the present invention is particularly useful when embodied as a set of instructions to control various decisions made by logic circuits of a computer processor , the present invention also includes apparatus and systems that process and display one or more images of digital object 10 or a portion thereof in accordance with teachings of the present invention . illustrated in drawing fig4 is an exemplary embodiment of such a system 200 and its component apparatus . for example , a system 200 incorporating teachings of the present invention may include a computer 210 with a processor 212 and memory 214 associated therewith , as well as hardware and programming configured to output one or more full or partial images of a digital object 10 to an apparatus that facilitates viewing of the image by a user , such as a monitor 216 or a printer 218 . various logic circuits of processor 212 may be configured or programmed , such as by a back face culling application , to perform certain tasks in accordance with the inventive method . for example , a first logic circuit of processor 212 may sort data representative of at least three vertices 16 ( fig1 and 3 ) of at least one polygon 14 ( fig1 and 3 ) of digital object 10 ( fig1 ), a second logic circuit of processor 212 may be configured to generate an orientation decision variable based on relative positions of vertices 16 , and a third logic circuit of processor 212 may calculate a cpt of vertices 16 following sorting thereof by the first logic circuit . the first and second logic circuits of processor 212 may operate substantially concurrently , or at different times . when under control of a program that effects the method of the present invention , processor 212 may also include a fourth logic circuit that determines a sign of the cpt . processor 212 may also include a fifth logic circuit that determines an orientation of one or more polygons 14 of digital object 10 based on the sign of the cpt and the orientation decision variable . the fifth logic circuit may also decide whether to cull data of vertices 16 based on the orientation of the corresponding polygon 14 . these logic circuits may comprise completely separate circuits of processor 212 , or any combination of these logic circuits may be partially combined . although the foregoing description contains many specifics , these should not be construed as limiting the scope of the present invention , but merely as providing illustrations of some of the presently preferred embodiments . similarly , other embodiments of the invention may be devised which do not depart from the spirit or scope of the present invention . moreover , features from different embodiments of the invention may be employed in combination . the scope of the invention is , therefore , indicated and limited only by the appended claims and their legal equivalents , rather than by the foregoing description . all additions , deletions , and modifications to the invention , as disclosed herein , which fall within the meaning and scope of the claims are to be embraced thereby .