A Generalized Cubic Exponential B-Spline Scheme with Shape Control

<p>Curves generated by the cubic B-spline scheme (left column) cubic exponential B-spline (middle column), and the scheme <svg height="16.3727pt" id="M255" style="vertical-align:-7.08437pt" version="1.1" viewbox="-0.0498162 -9.28833 43.8209 16.3727" width="43.8209pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.511,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 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263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,33.137,3.132)"><path d="M552 293V344L59 566V507L489 319L59 131V72L552 293ZM552 -41V12H59V-41H552Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,38.697,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g></svg> (right column) with <span class="nowrap"><svg height="11.8239pt" id="M256" style="vertical-align:-0.2325001pt" version="1.1" viewbox="-0.0498162 -11.5914 32.1178 11.8239" width="32.1178pt" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 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Mathematical Problems in Engineering

A Generalized Cubic Exponential B-Spline Scheme with Shape Control

Figure 3