An Approach to Computing Multipoint Inversion and Multiray Surface Intersection on Parametric Surface

<table class="fixed-width table-group" id="tab1"><tr><td><table class="table"><colgroup><col style="width:9.13em"/><col style="width:9.55em"/><col style="width:9.02em"/></colgroup><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center">New Method</td><td class="align_center">Wang’s Method</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Number of points</td><td class="align_center">2000</td><td class="align_center">2000</td></tr><tr><td class="align_left">CPU Time(s)</td><td class="align_center">29.322629806545390</td><td class="align_center">273.7031542564848</td></tr><tr><td class="align_left">Error</td><td class="align_center"><span style="width: 23.1538ptpx;"><svg height="11.6425pt" id="M242" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 23.1538 11.6425" width="23.1538pt" xmlns="http://www.w3.org/2000/svg" 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337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z"></path></g></svg></span></td></tr><tr><td class="align_left">Failure</td><td class="align_center">0</td><td class="align_center">0</td></tr><tr><td class="align_left">Maximum iteration</td><td class="align_center">200</td><td class="align_center">200</td></tr><tr><td class="align_left">Parametric range</td><td class="align_center"><span style="width: 59.4975ptpx;"><svg height="11.439pt" id="M244" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 59.4975 11.439" width="59.4975pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"></path></g><g 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<div>Two different methods in solving multipoint inversion on hyperbolic paraboloid.</div>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: An Approach to Computing Multipoint Inversion and Multiray Surface Intersection on Parametric Surface 