Representation and Reasoning of Three-Dimensional Spatial Relationships Based on R5DOS-Intersection Model Representation and Reasoning Based on R5DOS Model

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">RCC5 relationships</td><td class="align_center">DR (<i>A</i>, <i>B</i>)</td><td class="align_center">PO (<i>A</i>, <i>B</i>)</td><td class="align_center">PP (<i>A</i>, <i>B</i>)</td><td class="align_center">EQ (<i>A</i>, <i>B</i>)</td><td class="align_center">PPI (<i>A</i>, <i>B</i>)</td></tr><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr><td class="align_left">Extended 4-intersection matrix representation</td><td class="align_center"><span style="width: 40.7099ptpx;"><svg height="31.1785pt" id="M3" style="vertical-align:-12.2618pt" version="1.1" viewbox="-0.0498162 -18.9167 40.7099 31.1785" width="40.7099pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,2.51347e-05)"><path d="M520 -816C310 -597 186 -177 186 271C186 720 307 1139 520 1358L491 1388C219 1134 96 727 96 272V271C96 -188 219 -597 491 -846L520 -816Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,-9.733)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,-9.733)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,8.297)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,8.297)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g 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xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,2.51347e-05)"><path d="M520 -816C310 -597 186 -177 186 271C186 720 307 1139 520 1358L491 1388C219 1134 96 727 96 272V271C96 -188 219 -597 491 -846L520 -816Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,-9.733)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,-9.733)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,8.297)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,8.297)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.546,2.51347e-05)"><path d="M522 271V272C522 727 399 1134 127 1388L98 1358C311 1139 432 720 432 271C432 -177 308 -597 98 -816L127 -846C399 -597 522 -188 522 271Z"></path></g></svg></span></td><td class="align_center"><span style="width: 40.7099ptpx;"><svg height="31.1785pt" id="M6" style="vertical-align:-12.2618pt" version="1.1" viewbox="-0.0498162 -18.9167 40.7099 31.1785" width="40.7099pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,2.51347e-05)"><path d="M520 -816C310 -597 186 -177 186 271C186 720 307 1139 520 1358L491 1388C219 1134 96 727 96 272V271C96 -188 219 -597 491 -846L520 -816Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,-9.733)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,-9.733)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,8.297)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,8.297)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.546,2.51347e-05)"><path d="M522 271V272C522 727 399 1134 127 1388L98 1358C311 1139 432 720 432 271C432 -177 308 -597 98 -816L127 -846C399 -597 522 -188 522 271Z"></path></g></svg></span></td><td class="align_center"><span style="width: 40.7099ptpx;"><svg height="31.1785pt" id="M7" style="vertical-align:-12.2618pt" version="1.1" viewbox="-0.0498162 -18.9167 40.7099 31.1785" width="40.7099pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,2.51347e-05)"><path d="M520 -816C310 -597 186 -177 186 271C186 720 307 1139 520 1358L491 1388C219 1134 96 727 96 272V271C96 -188 219 -597 491 -846L520 -816Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,-9.733)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,-9.733)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.053,8.297)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.294,8.297)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.546,2.51347e-05)"><path d="M522 271V272C522 727 399 1134 127 1388L98 1358C311 1139 432 720 432 271C432 -177 308 -597 98 -816L127 -846C399 -597 522 -188 522 271Z"></path></g></svg></span></td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Matrix representation of the RCC-5 relationships.</div>

Complexity

tab1

Table 1

Table 1: Representation and Reasoning of Three-Dimensional Spatial Relationships Based on R5DOS-Intersection Model Representation and Reasoning Based on R5DOS Model 

Table 1 | Representation and Reasoning of Three-Dimensional Spatial Relationships Based on R5DOS-Intersection Model Representation and Reasoning Based on R5DOS Model 