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 set <svg height="12.0625" id="M151" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 13.2625 12.0625" width="13.2625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.738)"><path d="M417 653l-9 -18q-48 22 -111 22q-76 0 -125 -34q-48 -35 -48 -82q0 -44 37 -74t102 -39q68 109 177 175q108 66 197 66q45 0 74 -20.5t29 -55.5q0 -50 -58 -98q-59 -48 -150 -76q-93 -29 -189 -29q-41 -61 -41 -128q0 -30 17.5 -48.5t48.5 -18.5q104 0 269 151l15 -16
q-35 -35 -66 -121q-83 -224 -330 -224q-72 0 -121 33q-48 34 -48 77q0 30 16.5 49.5t42.5 19.5q20 0 35.5 -14t15.5 -33q0 -22 -12 -36.5t-32 -14.5q-22 0 -29 13h-2q5 -24 41 -44q37 -19 83 -19q84 0 143 46.5t111 145.5l-1 1q-67 -44 -138 -44q-61 0 -99 35t-38 92
q0 54 26 106q-79 13 -123 50t-44 93q0 61 59 103q58 43 148 43q71 0 127 -34zM699 590q0 20 -16 31t-41 11q-66 0 -149 -64q-84 -63 -132 -148q81 0 162 26q80 26 128 65.5t48 78.5z" id="x1D4A2"></path></g>
</svg> for a checkerboard triangulation. </table>

Journal of Mathematics

fig1

Figure 1

Figure 1: 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 1