Local Lagrange Interpolations Using Bivariate <svg style="vertical-align:-0.306pt;width:24.0875px;" id="M1" height="21.225" version="1.1" viewBox="0 0 24.0875 21.225" width="24.0875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.022,-0,0,-.022,.062,20.788)"><path id="x1D436" d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
t325.5 101.5q114 0 204 -38z" /></g><g transform="matrix(.016,-0,0,-.016,15.862,10.025)"><path id="x32" 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" /></g></svg> Splines of Degree Seven on Triangulated Quadrangulations

<table>The point set <svg height="11.9" id="M340" style="vertical-align:-0.25935pt" version="1.1" viewbox="0 0 18.35 11.9" width="18.35" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.525)"><path d="M1048 672l8 -13q-142 -225 -231 -393q-88 -167 -88 -213q0 -35 33 -35q54 0 170 132l19 -16q-120 -146 -203 -146q-38 0 -62 22t-24 60q0 148 308 563l-1 2q-65 -25 -145 -120q-79 -95 -185 -284q-82 -144 -113 -181q-46 -54 -100 -54q-25 0 -40.5 19t-15.5 51
q0 87 143 307q126 197 192 270l-1 1q-54 -23 -119 -91q-65 -69 -120 -156l-52 -84l-47 -76l-40 -64q-21 -33 -39 -58q-47 -63 -70 -83q-61 -51 -107 -47q-34 0 -57 22.5t-23 55.5q0 27 17.5 46t41.5 19q21 0 36.5 -15.5t15.5 -36.5q0 -18 -12.5 -31t-30.5 -13q-8 0 -15 4h-3
q3 -21 31 -21q50 0 98 51q47 50 127 184q146 243 238 333q94 91 180 91q3 0 17 -2l15 -12q-100 -141 -192 -297q-89 -151 -130 -245q-17 -46 -17 -61q0 -18 13 -18q17 0 34.5 20.5t51.5 74.5l60 100l68 117q30 51 72 110q42 58 83 103q41 44 89 74t94 36q12 0 28 -2z" id="x2133"></path></g>
</svg> produced by Lemma <a href="https://static.hindawi.com/articles/jmath/volume-2013/638254/figures/#lem6">7</a>.</table>

Journal of Mathematics

fig6

Figure 6

Figure 6: Local Lagrange Interpolations Using Bivariate <svg style="vertical-align:-0.306pt;width:24.0875px;" id="M1" height="21.225" version="1.1" viewBox="0 0 24.0875 21.225" width="24.0875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.022,-0,0,-.022,.062,20.788)"><path id="x1D436" d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
t325.5 101.5q114 0 204 -38z" /></g><g transform="matrix(.016,-0,0,-.016,15.862,10.025)"><path id="x32" 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" /></g></svg> Splines of Degree Seven on Triangulated Quadrangulations 

Journal of Mathematics

Local Lagrange Interpolations Using Bivariate Splines of Degree Seven on Triangulated Quadrangulations

Figure 6