Fisheye-Lens-Based Visual Sun Compass for Perception of Spatial Orientation

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Project type</td><td align="center">Model</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Stereographic</td><td align="center"><span style="width: 157.41251px;"><svg height="16.6625" id="M48" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 157.41251 16.6625" width="157.41251" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q13 -21 0 -43z" id="x1D45F"></path></g><g transform="matrix(.017,-0,0,-.017,11.945,12.162)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,26.649,12.162)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,34.808,12.162)"><path d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19
q34 34 71 253l54 315h-90l-3 12l31 30h70q28 138 90 204q35 37 75 57.5t70 20.5q26 0 45 -14t19 -28z" id="x1D453"></path></g><g transform="matrix(.017,-0,0,-.017,48.56,12.162)"><path d="M298 36l-68 -35q-25 -13 -42 -13q-98 0 -98 119v290h-69l-4 11l28 29h45v72l65 67l14 -2v-137h113q8 -8 6 -21t-12 -19h-107v-256q0 -96 59 -96q29 0 61 17z" id="x74"></path></g><g transform="matrix(.017,-0,0,-.017,53.745,12.162)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g><g transform="matrix(.017,-0,0,-.017,61.207,12.162)"><path d="M524 0h-209v26q44 5 55 18t11 65v167q0 114 -91 114q-50 0 -109 -51v-235q0 -50 10 -61.5t55 -16.5v-26h-217v26q51 5 62 17t11 61v206q0 47 -9.5 58.5t-50.5 19.5v23q82 15 139 40v-79l67 47q47 30 83 30q60 0 94.5 -40t34.5 -112v-193q0 -50 10 -61.5t54 -16.5v-26z
" id="x6E"></path></g><g transform="matrix(.017,-0,0,-.017,70.505,12.162)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,76.387,12.162)"><use xlink:href="#x1D703"></use></g><g transform="matrix(.017,-0,0,-.017,84.852,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,93.012,12.162)"><path d="M536 404q0 -17 -13.5 -31.5t-26.5 -14.5q-8 0 -15 10q-11 14 -25 14q-22 0 -67 -50q-47 -52 -68 -82l37 -102q31 -88 55 -88t78 59l16 -23q-32 -48 -68.5 -78t-65.5 -30q-19 0 -37.5 20t-29.5 53l-41 116q-72 -106 -114.5 -147.5t-79.5 -41.5q-21 0 -34.5 14t-13.5 37
q0 16 13.5 31.5t28.5 15.5q12 0 17 -11q5 -10 25 -10q22 0 57.5 36t89.5 111l-40 108q-22 58 -36 58q-21 0 -67 -57l-19 20q81 107 125 107q17 0 30 -22t39 -88l22 -55q68 92 108.5 128.5t74.5 36.5q20 0 32.5 -14t12.5 -30z" id="x1D465"></path></g><g transform="matrix(.017,-0,0,-.017,102.514,12.162)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,110.673,12.162)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,118.833,12.162)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,126.992,12.162)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,135.152,12.162)"><use xlink:href="#x34"></use></g><g transform="matrix(.017,-0,0,-.017,143.311,12.162)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,151.47,12.162)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg></span></td></tr><tr><td align="left">Orthogonal</td><td align="center"><span style="width: 86.449997px;"><svg height="16.6625" id="M49" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 86.449997 16.6625" width="86.449997" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D45F"></use></g><g transform="matrix(.017,-0,0,-.017,11.945,12.162)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,26.649,12.162)"><use xlink:href="#x1D453"></use></g><g transform="matrix(.017,-0,0,-.017,40.401,12.162)"><path d="M319 325l-25 -7q-33 99 -103 99q-29 0 -47 -19.5t-18 -49.5t22 -49.5t62 -36.5q63 -26 95 -57t32 -79q0 -64 -50 -101t-115 -37q-35 0 -67.5 10.5t-46.5 23.5q-5 11 -11 51t-6 67l27 5q14 -53 46.5 -88.5t75.5 -35.5q29 0 50 19.5t21 50.5t-19.5 51.5t-59.5 39.5
q-28 12 -46 22.5t-38.5 27t-30.5 38.5t-10 49q0 54 42.5 92t109.5 38q48 0 88 -18q6 -15 13 -50.5t9 -55.5z" id="x73"></path></g><g transform="matrix(.017,-0,0,-.017,46.639,12.162)"><path d="M135 536q-20 0 -35 15.5t-15 35.5q0 22 15 37t36 15t35.5 -15t14.5 -37q0 -21 -15 -36t-36 -15zM252 0h-220v26q48 5 59 17t11 63v206q0 47 -9 58t-54 18v24q78 12 142 39v-345q0 -51 11.5 -63t59.5 -17v-26z" id="x69"></path></g><g transform="matrix(.017,-0,0,-.017,51.195,12.162)"><use xlink:href="#x6E"></use></g><g transform="matrix(.017,-0,0,-.017,66.154,12.162)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,72.035,12.162)"><use xlink:href="#x1D703"></use></g><g transform="matrix(.017,-0,0,-.017,80.501,12.162)"><use xlink:href="#x29"></use></g>
</svg></span></td></tr><tr><td align="left">Equidistant</td><td align="center"><span style="width: 46.099998px;"><svg height="16.6625" id="M50" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 46.099998 16.6625" width="46.099998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D45F"></use></g><g transform="matrix(.017,-0,0,-.017,11.945,12.162)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,26.649,12.162)"><use xlink:href="#x1D453"></use></g><g transform="matrix(.017,-0,0,-.017,37.562,12.162)"><use xlink:href="#x1D703"></use></g>
</svg></span></td></tr><tr><td align="left">Equisolid angle</td><td align="center"><span style="width: 109.775px;"><svg height="16.6625" id="M51" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 109.775 16.6625" width="109.775" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D45F"></use></g><g transform="matrix(.017,-0,0,-.017,11.945,12.162)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,26.649,12.162)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,34.808,12.162)"><use xlink:href="#x1D453"></use></g><g transform="matrix(.017,-0,0,-.017,48.56,12.162)"><use xlink:href="#x73"></use></g><g transform="matrix(.017,-0,0,-.017,54.798,12.162)"><use xlink:href="#x69"></use></g><g transform="matrix(.017,-0,0,-.017,59.354,12.162)"><use xlink:href="#x6E"></use></g><g transform="matrix(.017,-0,0,-.017,74.313,12.162)"><use xlink:href="#x28"></use></g><g transform="matrix(.017,-0,0,-.017,80.195,12.162)"><use xlink:href="#x1D703"></use></g><g transform="matrix(.017,-0,0,-.017,88.66,12.162)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,95.663,12.162)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,103.823,12.162)"><use xlink:href="#x29"></use></g>
</svg></span></td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Fisheye-Lens-Based Visual Sun Compass for Perception of Spatial Orientation 