Log-Aesthetic Curves for Shape Completion Problem

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="960302.fig.003a" src="https://static.hindawi.com/articles/jam/volume-2014/960302/figures/960302.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Original position of control points</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="960302.fig.003b" src="https://static.hindawi.com/articles/jam/volume-2014/960302/figures/960302.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Position of control points after transformation</td></tr></table></td></tr></table>

<table>The configuration of triangle consists of three control points for case <svg height="9.14503pt" id="M42" style="vertical-align:-0.5419302pt" version="1.1" viewbox="0 -8.6031 29.7226 9.14503" width="29.7226pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="568" vert-adv-y="568"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,11.482,0)"><path d="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z" id="g117-93"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,23.219,0)"><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" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg>. The curve inside the triangle represents the generated LAC segment.</table>

Journal of Applied Mathematics

Log-Aesthetic Curves for Shape Completion Problem

Figure 3