Drawing Parametric Surfaces with GeoGebra

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2013-11-11 20:37

In collections surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1

This example demonstrates how to draw parametric surfaces using GeoGebra and animate their rotating grid effect. Key math concepts include parametric equations, function graphs, integrals, and trigonometry. Construction highlights involve commands like Corner, If, Join, Zip, Min, Max, Sequence, Element, Polygon, Vector, Textfield, Ray, Length, OrthogonalLine, Mod, and objects such as β, C, Eckpunkt3, etc. Suitable for high school students and educators for learning and teaching demonstrations.

GeoGebra Commands & Parameters

Corner(3) → Eckpunkt3
Corner(2) → Eckpunkt2
If(c, β, y(Eckpunkt3 - C) / y(Eckpunkt3 - Eckpunkt2) * c_{Move}) → β1
Corner(1) → Eckpunkt1
If(c, α, x(Eckpunkt2 - C) / x(Eckpunkt2 - Eckpunkt1) * c_{Move}) → α1
If(f0, N_0, N) → NN
Join(Sequence[Sequence[(u_{min} + i * dx, v_{min} + j * dy), i, 0, NN - 1], j, 0, NN - 1]) → uv
Zip(fz(a, b), a, u, b, v) → Z1
Min(RemoveUndefined[Z1]) → x3mina
Zip(fy(a, b), a, u, b, v) → Y1
Max(RemoveUndefined[Y1]) → x2maxa
Min(RemoveUndefined[Y1]) → x2mina
Zip(fx(a, b), a, u, b, v) → X1
Min(RemoveUndefined[X1]) → x1mina
Max(RemoveUndefined[X1]) → x1maxa
Sequence(a11 * Element[zWX1, i] + a12 * Element[zWY1, i] + a13 * Element[zWZ1, i], i, 1, 4) → zWX1'
Max(RemoveUndefined[Z1]) → x3maxa
Min(RemoveUndefined[X1']) → x1'mina
Max(RemoveUndefined[X1']) → x1'maxa
Max(Sequence[If[Element[X1', i] ≟ x1'maxa, i, 0], i, 1, läX1]) → X1''
Element(ylPunkten10, X1'') → ylPunkten10max
Sequence(Segment[Element[zTT0, i], Element[zTT0, i + 1]], i, 1, 7) → BoxStr
Polygon(Eckpunkt1, Eckpunkt2, Eckpunkt3, Corner[4]) → Vieleck11, b_1, c_1, d_1, e_1
Vector(Element[zTT0, 4], Element[zTT0, 3]) → zVecty
Vector(Element[zTT0, 4], Element[zTT0, 1]) → zVectx
Vector(Element[zTT0, 4], Element[zTT0, 5]) → zVectz
If(x ≟ 0, 1, sin(x) / x) → sinc
Polygon({Element[zTT0, Element[zWW_0, 4]], Element[zTT0, Element[zWW_0, 3]], Element[zTT0, 9 - Element[zWW_0, 3]], Element[zTT0, 9 - Element[zWW_0, 4]]}) → Vgrund01, a, m, p, q
Textfield(fx) → inputBox3
Textfield(fy) → inputBox4
Textfield(fz) → inputBox5
Textfield(u_{min}) → inputBox6
Textfield(u_{max}) → inputBox7
Textfield(v_{min}) → inputBox8
Textfield(v_{max}) → inputBox9
Textfield(N_0) → inputBox10
Textfield(N) → inputBox11
Sequence(If[i ≟ ceil(i / NN) * NN, 0, i], i, 1, zk3) → ll
Zip(Polygon[Element[ylPunkten10, i], Element[ylPunkten10, i + NN], Element[ylPunkten10, i + NN + 1], Element[ylPunkten10, i + 1]], i, ll) → yylPolyy
Ray(B, Element[zTT0, 9]) → ox
Ray(B, Element[zTT0, 10]) → oy
Ray(B, Element[zTT0, 11]) → oz
Length(X1) → zk3b
Textfield(r_x) → Textfeld1
Textfield(r_y) → Textfeld2
Textfield(r_z) → Textfeld3
OrthogonalLine(P_{HV}, yAxis) → horizontal
OrthogonalLine(P_{HV}, xAxis) → vertikal
Mod(β1, 6.283) → β2
Mod(α1, 6.283) → α2
Textfield(Typ) → Textfeld4
If(¬j_1, NN * (NN - 1), n) → zk31
Sequence(Element[yylPolyy, Element[zup, i]], i, 1, zk31) → zll
Element(zll, m1) → z
Polygon(Eck11, Eckpunkt2, Eckpunkt3, Eck12) → Vieleck2, eck11_1, eckpunkt2, eckpunkt3, eck12_1
Element(zll, 1) → M_{1}
Element(zll, 2) → M_{2}
Element(zll, 3) → M_{3}
Element(zll, 4) → M_{4}
Element(zll, 5) → M_{5}
Element(zll, 6) → M_{6}
Element(zll, 7) → M_{7}
Element(zll, 8) → M_{8}
Element(zll, 9) → M_{9}
Element(zll, 10) → M_{10}
Element(zll, 11) → M_{11}
Element(zll, 12) → M_{12}
Element(zll, 13) → M_{13}
Element(zll, 14) → M_{14}
Element(zll, 15) → M_{15}
Element(zll, 16) → M_{16}
Element(zll, 17) → M_{17}
Element(zll, 18) → M_{18}
Element(zll, 19) → M_{19}
Element(zll, 20) → M_{20}
Element(zll, 21) → M_{21}
Element(zll, 22) → M_{22}
Element(zll, 23) → M_{23}
Element(zll, 24) → M_{24}
Element(zll, 25) → M_{25}
Element(zll, 26) → M_{26}
Element(zll, 27) → M_{27}
Element(zll, 28) → M_{28}
Element(zll, 29) → M_{29}
Element(zll, 30) → M_{30}
Element(zll, 31) → M_{31}
Element(zll, 32) → M_{32}
Element(zll, 33) → M_{33}
Element(zll, 34) → M_{34}
Element(zll, 35) → M_{35}
Element(zll, 36) → M_{36}
Element(zll, 37) → M_{37}
Element(zll, 38) → M_{38}
Element(zll, 39) → M_{39}
Element(zll, 40) → M_{40}
Element(zll, 41) → M_{41}
Element(zll, 42) → M_{42}
Element(zll, 43) → M_{43}
Element(zll, 44) → M_{44}
Element(zll, 45) → M_{45}
Element(zll, 46) → M_{46}
Element(zll, 47) → M_{47}
Element(zll, 48) → M_{48}
Element(zll, 49) → M_{49}
Element(zll, 50) → M_{50}
Element(zll, 51) → M_{51}
Element(zll, 52) → M_{52}
Element(zll, 53) → M_{53}
Element(zll, 54) → M_{54}
Element(zll, 55) → M_{55}
Element(zll, 56) → M_{56}
Element(zll, 57) → M_{57}
Element(zll, 58) → M_{58}
Element(zll, 59) → M_{59}
Element(zll, 60) → M_{60}
Element(zll, 61) → M_{61}
Element(zll, 62) → M_{62}
Element(zll, 63) → M_{63}
Element(zll, 64) → M_{64}
Element(zll, 65) → M_{65}
Element(zll, 66) → M_{66}
Element(zll, 67) → M_{67}
Element(zll, 68) → M_{68}
Element(zll, 69) → M_{69}
Element(zll, 70) → M_{70}
Element(zll, 71) → M_{71}
Element(zll, 72) → M_{72}
Element(zll, 73) → M_{73}
Element(zll, 74) → M_{74}
Element(zll, 75) → M_{75}
Element(zll, 76) → M_{76}
Element(zll, 77) → M_{77}
Element(zll, 78) → M_{78}
Element(zll, 79) → M_{79}
Element(zll, 80) → M_{80}
Element(zll, 81) → M_{81}
Element(zll, 82) → M_{82}
Element(zll, 83) → M_{83}
Element(zll, 84) → M_{84}
Element(zll, 85) → M_{85}
Element(zll, 86) → M_{86}
Element(zll, 87) → M_{87}
Element(zll, 88) → M_{88}
Element(zll, 89) → M_{89}
Element(zll, 90) → M_{90}
Element(zll, 91) → M_{91}
Element(zll, 92) → M_{92}
Element(zll, 93) → M_{93}
Element(zll, 94) → M_{94}
Element(zll, 95) → M_{95}
Element(zll, 96) → M_{96}
Element(zll, 97) → M_{97}
Element(zll, 98) → M_{98}
Element(zll, 99) → M_{99}
Element(zll, 100) → M_{100}
Element(zll, 101) → M_{101}
Element(zll, 102) → M_{102}
Element(zll, 103) → M_{103}
Element(zll, 104) → M_{104}
Element(zll, 105) → M_{105}
Element(zll, 106) → M_{106}
Element(zll, 107) → M_{107}
Element(zll, 108) → M_{108}
Element(zll, 109) → M_{109}
Element(zll, 110) → M_{110}
Element(zll, 111) → M_{111}
Element(zll, 112) → M_{112}
Element(zll, 113) → M_{113}
Element(zll, 114) → M_{114}
Element(zll, 115) → M_{115}
Element(zll, 116) → M_{116}
Element(zll, 117) → M_{117}
Element(zll, 118) → M_{118}
Element(zll, 119) → M_{119}
Element(zll, 120) → M_{120}
Element(zll, 121) → M_{121}
Element(zll, 122) → M_{122}
Element(zll, 123) → M_{123}
Element(zll, 124) → M_{124}
Element(zll, 125) → M_{125}
Element(zll, 126) → M_{126}
Element(zll, 127) → M_{127}
Element(zll, 128) → M_{128}
Element(zll, 129) → M_{129}
Element(zll, 130) → M_{130}
Element(zll, 131) → M_{131}
Element(zll, 132) → M_{132}
Element(zll, 133) → M_{133}
Element(zll, 134) → M_{134}
Element(zll, 135) → M_{135}
Element(zll, 136) → M_{136}
Element(zll, 137) → M_{137}
Element(zll, 138) → M_{138}
Element(zll, 139) → M_{139}
Element(zll, 140) → M_{140}
Element(zll, 141) → M_{141}
Element(zll, 142) → M_{142}
Element(zll, 143) → M_{143}
Element(zll, 144) → M_{144}
Element(zll, 145) → M_{145}
Element(zll, 146) → M_{146}
Element(zll, 147) → M_{147}
Element(zll, 148) → M_{148}
Element(zll, 149) → M_{149}
Element(zll, 150) → M_{150}
Element(zll, 151) → M_{151}
Element(zll, 152) → M_{152}
Element(zll, 153) → M_{153}
Element(zll, 154) → M_{154}
Element(zll, 155) → M_{155}
Element(zll, 156) → M_{156}
Element(zll, 157) → M_{157}
Element(zll, 158) → M_{158}
Element(zll, 159) → M_{159}
Element(zll, 160) → M_{160}
Element(zll, 161) → M_{161}
Element(zll, 162) → M_{162}
Element(zll, 163) → M_{163}
Element(zll, 164) → M_{164}
Element(zll, 165) → M_{165}
Element(zll, 166) → M_{166}
Element(zll, 167) → M_{167}
Element(zll, 168) → M_{168}
Element(zll, 169) → M_{169}
Element(zll, 170) → M_{170}
Element(zll, 171) → M_{171}
Element(zll, 172) → M_{172}
Element(zll, 173) → M_{173}
Element(zll, 174) → M_{174}
Element(zll, 175) → M_{175}
Element(zll, 176) → M_{176}
Element(zll, 177) → M_{177}
Element(zll, 178) → M_{178}
Element(zll, 179) → M_{179}
Element(zll, 180) → M_{180}
Element(zll, 181) → M_{181}
Element(zll, 182) → M_{182}
Element(zll, 183) → M_{183}
Element(zll, 184) → M_{184}
Element(zll, 185) → M_{185}
Element(zll, 186) → M_{186}
Element(zll, 187) → M_{187}
Element(zll, 188) → M_{188}
Element(zll, 189) → M_{189}
Element(zll, 190) → M_{190}
Element(zll, 191) → M_{191}
Element(zll, 192) → M_{192}
Element(zll, 193) → M_{193}
Element(zll, 194) → M_{194}
Element(zll, 195) → M_{195}
Element(zll, 196) → M_{196}
Element(zll, 197) → M_{197}
Element(zll, 198) → M_{198}
Element(zll, 199) → M_{199}
Element(zll, 200) → M_{200}
Element(zll, 201) → M_{201}
Element(zll, 202) → M_{202}
Element(zll, 203) → M_{203}
Element(zll, 204) → M_{204}
Element(zll, 205) → M_{205}
Element(zll, 206) → M_{206}
Element(zll, 207) → M_{207}
Element(zll, 208) → M_{208}
Element(zll, 209) → M_{209}
Element(zll, 210) → M_{210}
Element(zll, 211) → M_{211}
Element(zll, 212) → M_{212}
Element(zll, 213) → M_{213}
Element(zll, 214) → M_{214}
Element(zll, 215) → M_{215}
Element(zll, 216) → M_{216}
Element(zll, 217) → M_{217}
Element(zll, 218) → M_{218}
Element(zll, 219) → M_{219}
Element(zll, 220) → M_{220}
Element(zll, 221) → M_{221}
Element(zll, 222) → M_{222}
Element(zll, 223) → M_{223}
Element(zll, 224) → M_{224}
Element(zll, 225) → M_{225}
Element(zll, 226) → M_{226}
Element(zll, 227) → M_{227}
Element(zll, 228) → M_{228}
Element(zll, 229) → M_{229}
Element(zll, 230) → M_{230}
Element(zll, 231) → M_{231}
Element(zll, 232) → M_{232}
Element(zll, 233) → M_{233}
Element(zll, 234) → M_{234}
Element(zll, 235) → M_{235}
Element(zll, 236) → M_{236}
Element(zll, 237) → M_{237}
Element(zll, 238) → M_{238}
Element(zll, 239) → M_{239}
Element(zll, 240) → M_{240}
Element(zll, 241) → M_{241}
Element(zll, 242) → M_{242}
Element(zll, 243) → M_{243}
Element(zll, 244) → M_{244}
Element(zll, 245) → M_{245}
Element(zll, 246) → M_{246}
Element(zll, 247) → M_{247}
Element(zll, 248) → M_{248}
Element(zll, 249) → M_{249}
Element(zll, 250) → M_{250}
Element(zll, 251) → M_{251}
Element(zll, 252) → M_{252}
Element(zll, 253) → M_{253}
Element(zll, 254) → M_{254}
Element(zll, 255) → M_{255}
Element(zll, 256) → M_{256}
Element(zll, 257) → M_{257}
Element(zll, 258) → M_{258}
Element(zll, 259) → M_{259}
Element(zll, 260) → M_{260}
Element(zll, 261) → M_{261}
Element(zll, 262) → M_{262}
Element(zll, 263) → M_{263}
Element(zll, 264) → M_{264}
Element(zll, 265) → M_{265}
Element(zll, 266) → M_{266}
Element(zll, 267) → M_{267}
Element(zll, 268) → M_{268}
Element(zll, 269) → M_{269}
Element(zll, 270) → M_{270}
Element(zll, 271) → M_{271}
Element(zll, 272) → M_{272}
Element(zll, 273) → M_{273}
Element(zll, 274) → M_{274}
Element(zll, 275) → M_{275}
Element(zll, 276) → M_{276}
Element(zll, 277) → M_{277}
Element(zll, 278) → M_{278}
Element(zll, 279) → M_{279}
Element(zll, 280) → M_{280}
Element(zll, 281) → M_{281}
Element(zll, 282) → M_{282}
Element(zll, 283) → M_{283}
Element(zll, 284) → M_{284}
Element(zll, 285) → M_{285}
Element(zll, 286) → M_{286}
Element(zll, 287) → M_{287}
Element(zll, 288) → M_{288}
Element(zll, 289) → M_{289}
Element(zll, 290) → M_{290}
Element(zll, 291) → M_{291}
Element(zll, 292) → M_{292}
Element(zll, 293) → M_{293}
Element(zll, 294) → M_{294}
Element(zll, 295) → M_{295}
Element(zll, 296) → M_{296}
Element(zll, 297) → M_{297}
Element(zll, 298) → M_{298}
Element(zll, 299) → M_{299}
Element(zll, 300) → M_{300}
Element(zll, 301) → M_{301}
Element(zll, 302) → M_{302}
Element(zll, 303) → M_{303}
Element(zll, 304) → M_{304}
Element(zll, 305) → M_{305}
Element(zll, 306) → M_{306}
Element(zll, 307) → M_{307}
Element(zll, 308) → M_{308}
Element(zll, 309) → M_{309}
Element(zll, 310) → M_{310}
Element(zll, 311) → M_{311}
Element(zll, 312) → M_{312}
Element(zll, 313) → M_{313}
Element(zll, 314) → M_{314}
Element(zll, 315) → M_{315}
Element(zll, 316) → M_{316}
Element(zll, 317) → M_{317}
Element(zll, 318) → M_{318}
Element(zll, 319) → M_{319}
Element(zll, 320) → M_{320}
Element(zll, 321) → M_{321}
Element(zll, 322) → M_{322}
Element(zll, 323) → M_{323}
Element(zll, 324) → M_{324}
Element(zll, 325) → M_{325}
Element(zll, 326) → M_{326}
Element(zll, 327) → M_{327}
Element(zll, 328) → M_{328}
Element(zll, 329) → M_{329}
Element(zll, 330) → M_{330}
Element(zll, 331) → M_{331}
Element(zll, 332) → M_{332}
Element(zll, 333) → M_{333}
Element(zll, 334) → M_{334}
Element(zll, 335) → M_{335}
Element(zll, 336) → M_{336}
Element(zll, 337) → M_{337}
Element(zll, 338) → M_{338}
Element(zll, 339) → M_{339}
Element(zll, 340) → M_{340}
Element(zll, 341) → M_{341}
Element(zll, 342) → M_{342}
Element(zll, 343) → M_{343}
Element(zll, 344) → M_{344}
Element(zll, 345) → M_{345}
Element(zll, 346) → M_{346}
Element(zll, 347) → M_{347}
Element(zll, 348) → M_{348}
Element(zll, 349) → M_{349}
Element(zll, 350) → M_{350}
Element(zll, 351) → M_{351}
Element(zll, 352) → M_{352}
Element(zll, 353) → M_{353}
Element(zll, 354) → M_{354}
Element(zll, 355) → M_{355}
Element(zll, 356) → M_{356}
Element(zll, 357) → M_{357}
Element(zll, 358) → M_{358}
Element(zll, 359) → M_{359}
Element(zll, 360) → M_{360}
Element(zll, 361) → M_{361}
Element(zll, 362) → M_{362}
Element(zll, 363) → M_{363}
Element(zll, 364) → M_{364}
Element(zll, 365) → M_{365}
Element(zll, 366) → M_{366}
Element(zll, 367) → M_{367}
Element(zll, 368) → M_{368}
Element(zll, 369) → M_{369}
Element(zll, 370) → M_{370}
Element(zll, 371) → M_{371}
Element(zll, 372) → M_{372}
Element(zll, 373) → M_{373}
Element(zll, 374) → M_{374}
Element(zll, 375) → M_{375}
Element(zll, 376) → M_{376}
Element(zll, 377) → M_{377}
Element(zll, 378) → M_{378}
Element(zll, 379) → M_{379}
Element(zll, 380) → M_{380}
Element(zll, 381) → M_{381}
Element(zll, 382) → M_{382}
Element(zll, 383) → M_{383}
Element(zll, 384) → M_{384}
Element(zll, 385) → M_{385}
Element(zll, 386) → M_{386}
Element(zll, 387) → M_{387}
Element(zll, 388) → M_{388}
Element(zll, 389) → M_{389}
Element(zll, 390) → M_{390}
Element(zll, 391) → M_{391}
Element(zll, 392) → M_{392}
Element(zll, 393) → M_{393}
Element(zll, 394) → M_{394}
Element(zll, 395) → M_{395}
Element(zll, 396) → M_{396}
Element(zll, 397) → M_{397}
Element(zll, 398) → M_{398}
Element(zll, 399) → M_{399}
Element(zll, 400) → M_{400}
Element(zll, 401) → M_{401}
Element(zll, 402) → M_{402}
Element(zll, 403) → M_{403}
Element(zll, 404) → M_{404}
Element(zll, 405) → M_{405}
Element(zll, 406) → M_{406}
Element(zll, 407) → M_{407}
Element(zll, 408) → M_{408}
Element(zll, 409) → M_{409}
Element(zll, 410) → M_{410}
Element(zll, 411) → M_{411}
Element(zll, 412) → M_{412}
Element(zll, 413) → M_{413}
Element(zll, 414) → M_{414}
Element(zll, 415) → M_{415}
Element(zll, 416) → M_{416}
Element(zll, 417) → M_{417}
Element(zll, 418) → M_{418}
Element(zll, 419) → M_{419}
Element(zll, 420) → M_{420}
Element(zll, 421) → M_{421}
Element(zll, 422) → M_{422}
Element(zll, 423) → M_{423}
Element(zll, 424) → M_{424}
Element(zll, 425) → M_{425}
Element(zll, 426) → M_{426}
Element(zll, 427) → M_{427}
Element(zll, 428) → M_{428}
Element(zll, 429) → M_{429}
Element(zll, 430) → M_{430}
Element(zll, 431) → M_{431}
Element(zll, 432) → M_{432}
Element(zll, 433) → M_{433}
Element(zll, 434) → M_{434}
Element(zll, 435) → M_{435}
Element(zll, 436) → M_{436}
Element(zll, 437) → M_{437}
Element(zll, 438) → M_{438}
Element(zll, 439) → M_{439}
Element(zll, 440) → M_{440}
Element(zll, 441) → M_{441}
Element(zll, 442) → M_{442}
Element(zll, 443) → M_{443}
Element(zll, 444) → M_{444}
Element(zll, 445) → M_{445}
Element(zll, 446) → M_{446}
Element(zll, 447) → M_{447}
Element(zll, 448) → M_{448}
Element(zll, 449) → M_{449}
Element(zll, 450) → M_{450}
Element(zll, 451) → M_{451}
Element(zll, 452) → M_{452}
Element(zll, 453) → M_{453}
Element(zll, 454) → M_{454}
Element(zll, 455) → M_{455}
Element(zll, 456) → M_{456}
Element(zll, 457) → M_{457}
Element(zll, 458) → M_{458}
Element(zll, 459) → M_{459}
Element(zll, 460) → M_{460}
Element(zll, 461) → M_{461}
Element(zll, 462) → M_{462}
Element(zll, 463) → M_{463}
Element(zll, 464) → M_{464}
Element(zll, 465) → M_{465}
Element(zll, 466) → M_{466}
Element(zll, 467) → M_{467}
Element(zll, 468) → M_{468}
Element(zll, 469) → M_{469}
Element(zll, 470) → M_{470}
Element(zll, 471) → M_{471}
Element(zll, 472) → M_{472}
Element(zll, 473) → M_{473}
Element(zll, 474) → M_{474}
Element(zll, 475) → M_{475}
Element(zll, 476) → M_{476}
Element(zll, 477) → M_{477}
Element(zll, 478) → M_{478}
Element(zll, 479) → M_{479}
Element(zll, 480) → M_{480}
Element(zll, 481) → M_{481}
Element(zll, 482) → M_{482}
Element(zll, 483) → M_{483}
Element(zll, 484) → M_{484}
Element(zll, 485) → M_{485}
Element(zll, 486) → M_{486}
Element(zll, 487) → M_{487}
Element(zll, 488) → M_{488}
Element(zll, 489) → M_{489}
Element(zll, 490) → M_{490}
Element(zll, 491) → M_{491}
Element(zll, 492) → M_{492}
Element(zll, 493) → M_{493}
Element(zll, 494) → M_{494}
Element(zll, 495) → M_{495}
Element(zll, 496) → M_{496}
Element(zll, 497) → M_{497}
Element(zll, 498) → M_{498}
Element(zll, 499) → M_{499}
Element(zll, 500) → M_{500}
Element(zll, 501) → M_{501}
Element(zll, 502) → M_{502}
Element(zll, 503) → M_{503}
Element(zll, 504) → M_{504}
Element(zll, 505) → M_{505}
Element(zll, 506) → M_{506}
Element(zll, 507) → M_{507}
Element(zll, 508) → M_{508}
Element(zll, 509) → M_{509}
Element(zll, 510) → M_{510}
Element(zll, 511) → M_{511}
Element(zll, 512) → M_{512}
Element(zll, 513) → M_{513}
Element(zll, 514) → M_{514}
Element(zll, 515) → M_{515}
Element(zll, 516) → M_{516}
Element(zll, 517) → M_{517}
Element(zll, 518) → M_{518}
Element(zll, 519) → M_{519}
Element(zll, 520) → M_{520}
Element(zll, 521) → M_{521}
Element(zll, 522) → M_{522}
Element(zll, 523) → M_{523}
Element(zll, 524) → M_{524}
Element(zll, 525) → M_{525}
Element(zll, 526) → M_{526}
Element(zll, 527) → M_{527}
Element(zll, 528) → M_{528}
Element(zll, 529) → M_{529}
Element(zll, 530) → M_{530}
Element(zll, 531) → M_{531}
Element(zll, 532) → M_{532}
Element(zll, 533) → M_{533}
Element(zll, 534) → M_{534}
Element(zll, 535) → M_{535}
Element(zll, 536) → M_{536}
Element(zll, 537) → M_{537}
Element(zll, 538) → M_{538}
Element(zll, 539) → M_{539}
Element(zll, 540) → M_{540}
Element(zll, 541) → M_{541}
Element(zll, 542) → M_{542}
Element(zll, 543) → M_{543}
Element(zll, 544) → M_{544}
Element(zll, 545) → M_{545}
Element(zll, 546) → M_{546}
Element(zll, 547) → M_{547}
Element(zll, 548) → M_{548}
Element(zll, 549) → M_{549}
Element(zll, 550) → M_{550}
Element(zll, 551) → M_{551}
Element(zll, 552) → M_{552}
Element(zll, 553) → M_{553}
Element(zll, 554) → M_{554}
Element(zll, 555) → M_{555}
Element(zll, 556) → M_{556}
Element(zll, 557) → M_{557}
Element(zll, 558) → M_{558}
Element(zll, 559) → M_{559}
Element(zll, 560) → M_{560}
Element(zll, 561) → M_{561}
Element(zll, 562) → M_{562}
Element(zll, 563) → M_{563}
Element(zll, 564) → M_{564}
Element(zll, 565) → M_{565}
Element(zll, 566) → M_{566}
Element(zll, 567) → M_{567}
Element(zll, 568) → M_{568}
Element(zll, 569) → M_{569}
Element(zll, 570) → M_{570}
Element(zll, 571) → M_{571}
Element(zll, 572) → M_{572}
Element(zll, 573) → M_{573}
Element(zll, 574) → M_{574}
Element(zll, 575) → M_{575}
Element(zll, 576) → M_{576}
Element(zll, 577) → M_{577}
Element(zll, 578) → M_{578}
Element(zll, 579) → M_{579}
Element(zll, 580) → M_{580}
Element(zll, 581) → M_{581}
Element(zll, 582) → M_{582}
Element(zll, 583) → M_{583}
Element(zll, 584) → M_{584}
Element(zll, 585) → M_{585}
Element(zll, 586) → M_{586}
Element(zll, 587) → M_{587}
Element(zll, 588) → M_{588}
Element(zll, 589) → M_{589}
Element(zll, 590) → M_{590}
Element(zll, 591) → M_{591}
Element(zll, 592) → M_{592}
Element(zll, 593) → M_{593}
Element(zll, 594) → M_{594}
Element(zll, 595) → M_{595}
Element(zll, 596) → M_{596}
Element(zll, 597) → M_{597}
Element(zll, 598) → M_{598}
Element(zll, 599) → M_{599}
Element(zll, 600) → M_{600}
Element(zll, 601) → M_{601}
Element(zll, 602) → M_{602}
Element(zll, 603) → M_{603}
Element(zll, 604) → M_{604}
Element(zll, 605) → M_{605}
Element(zll, 606) → M_{606}
Element(zll, 607) → M_{607}
Element(zll, 608) → M_{608}
Element(zll, 609) → M_{609}
Element(zll, 610) → M_{610}
Element(zll, 611) → M_{611}
Element(zll, 612) → M_{612}
Element(zll, 613) → M_{613}
Element(zll, 614) → M_{614}
Element(zll, 615) → M_{615}
Element(zll, 616) → M_{616}
Element(zll, 617) → M_{617}
Element(zll, 618) → M_{618}
Element(zll, 619) → M_{619}
Element(zll, 620) → M_{620}
Element(zll, 621) → M_{621}
Element(zll, 622) → M_{622}
Element(zll, 623) → M_{623}
Element(zll, 624) → M_{624}
Element(zll, 625) → M_{625}
Element(zll, 626) → M_{626}
Element(zll, 627) → M_{627}
Element(zll, 628) → M_{628}
Element(zll, 629) → M_{629}
Element(zll, 630) → M_{630}
Element(zll, 631) → M_{631}
Element(zll, 632) → M_{632}
Element(zll, 633) → M_{633}
Element(zll, 634) → M_{634}
Element(zll, 635) → M_{635}
Element(zll, 636) → M_{636}
Element(zll, 637) → M_{637}
Element(zll, 638) → M_{638}
Element(zll, 639) → M_{639}
Element(zll, 640) → M_{640}
Element(zll, 641) → M_{641}
Element(zll, 642) → M_{642}
Element(zll, 643) → M_{643}
Element(zll, 644) → M_{644}
Element(zll, 645) → M_{645}
Element(zll, 646) → M_{646}
Element(zll, 647) → M_{647}
Element(zll, 648) → M_{648}
Element(zll, 649) → M_{649}
Element(zll, 650) → M_{650}
Element(zll, 651) → M_{651}
Element(zll, 652) → M_{652}
Element(zll, 653) → M_{653}
Element(zll, 654) → M_{654}
Element(zll, 655) → M_{655}
Element(zll, 656) → M_{656}
Element(zll, 657) → M_{657}
Element(zll, 658) → M_{658}
Element(zll, 659) → M_{659}
Element(zll, 660) → M_{660}
Element(zll, 661) → M_{661}
Element(zll, 662) → M_{662}
Element(zll, 663) → M_{663}
Element(zll, 664) → M_{664}
Element(zll, 665) → M_{665}
Element(zll, 666) → M_{666}
Element(zll, 667) → M_{667}
Element(zll, 668) → M_{668}
Element(zll, 669) → M_{669}
Element(zll, 670) → M_{670}
Element(zll, 671) → M_{671}
Element(zll, 672) → M_{672}
Element(zll, 673) → M_{673}
Element(zll, 674) → M_{674}
Element(zll, 675) → M_{675}
Element(zll, 676) → M_{676}
Element(zll, 677) → M_{677}
Element(zll, 678) → M_{678}
Element(zll, 679) → M_{679}
Element(zll, 680) → M_{680}
Element(zll, 681) → M_{681}
Element(zll, 682) → M_{682}
Element(zll, 683) → M_{683}
Element(zll, 684) → M_{684}
Element(zll, 685) → M_{685}
Element(zll, 686) → M_{686}
Element(zll, 687) → M_{687}
Element(zll, 688) → M_{688}
Element(zll, 689) → M_{689}
Element(zll, 690) → M_{690}
Element(zll, 691) → M_{691}
Element(zll, 692) → M_{692}
Element(zll, 693) → M_{693}
Element(zll, 694) → M_{694}
Element(zll, 695) → M_{695}
Element(zll, 696) → M_{696}
Element(zll, 697) → M_{697}
Element(zll, 698) → M_{698}
Element(zll, 699) → M_{699}
Element(zll, 700) → M_{700}
Element(zll, 701) → M_{701}
Element(zll, 702) → M_{702}
Element(zll, 703) → M_{703}
Element(zll, 704) → M_{704}
Element(zll, 705) → M_{705}
Element(zll, 706) → M_{706}
Element(zll, 707) → M_{707}
Element(zll, 708) → M_{708}
Element(zll, 709) → M_{709}
Element(zll, 710) → M_{710}
Element(zll, 711) → M_{711}
Element(zll, 712) → M_{712}
Element(zll, 713) → M_{713}
Element(zll, 714) → M_{714}
Element(zll, 715) → M_{715}
Element(zll, 716) → M_{716}
Element(zll, 717) → M_{717}
Element(zll, 718) → M_{718}
Element(zll, 719) → M_{719}
Element(zll, 720) → M_{720}
Element(zll, 721) → M_{721}
Element(zll, 722) → M_{722}
Element(zll, 723) → M_{723}
Element(zll, 724) → M_{724}
Element(zll, 725) → M_{725}
Element(zll, 726) → M_{726}
Element(zll, 727) → M_{727}
Element(zll, 728) → M_{728}
Element(zll, 729) → M_{729}
Element(zll, 730) → M_{730}
Element(zll, 731) → M_{731}
Element(zll, 732) → M_{732}
Element(zll, 733) → M_{733}
Element(zll, 734) → M_{734}
Element(zll, 735) → M_{735}
Element(zll, 736) → M_{736}
Element(zll, 737) → M_{737}
Element(zll, 738) → M_{738}
Element(zll, 739) → M_{739}
Element(zll, 740) → M_{740}
Element(zll, 741) → M_{741}
Element(zll, 742) → M_{742}
Element(zll, 743) → M_{743}
Element(zll, 744) → M_{744}
Element(zll, 745) → M_{745}
Element(zll, 746) → M_{746}
Element(zll, 747) → M_{747}
Element(zll, 748) → M_{748}
Element(zll, 749) → M_{749}
Element(zll, 750) → M_{750}
Element(zll, 751) → M_{751}
Element(zll, 752) → M_{752}
Element(zll, 753) → M_{753}
Element(zll, 754) → M_{754}
Element(zll, 755) → M_{755}
Element(zll, 756) → M_{756}
Element(zll, 757) → M_{757}
Element(zll, 758) → M_{758}
Element(zll, 759) → M_{759}
Element(zll, 760) → M_{760}
Element(zll, 761) → M_{761}
Element(zll, 762) → M_{762}
Element(zll, 763) → M_{763}
Element(zll, 764) → M_{764}
Element(zll, 765) → M_{765}
Element(zll, 766) → M_{766}
Element(zll, 767) → M_{767}
Element(zll, 768) → M_{768}
Element(zll, 769) → M_{769}
Element(zll, 770) → M_{770}
Element(zll, 771) → M_{771}
Element(zll, 772) → M_{772}
Element(zll, 773) → M_{773}
Element(zll, 774) → M_{774}
Element(zll, 775) → M_{775}
Element(zll, 776) → M_{776}
Element(zll, 777) → M_{777}
Element(zll, 778) → M_{778}
Element(zll, 779) → M_{779}
Element(zll, 780) → M_{780}
Element(zll, 781) → M_{781}
Element(zll, 782) → M_{782}
Element(zll, 783) → M_{783}
Element(zll, 784) → M_{784}
Element(zll, 785) → M_{785}
Element(zll, 786) → M_{786}
Element(zll, 787) → M_{787}
Element(zll, 788) → M_{788}
Element(zll, 789) → M_{789}
Element(zll, 790) → M_{790}
Element(zll, 791) → M_{791}
Element(zll, 792) → M_{792}
Element(zll, 793) → M_{793}
Element(zll, 794) → M_{794}
Element(zll, 795) → M_{795}
Element(zll, 796) → M_{796}
Element(zll, 797) → M_{797}
Element(zll, 798) → M_{798}
Element(zll, 799) → M_{799}
Element(zll, 800) → M_{800}
Element(zll, 801) → M_{801}
Element(zll, 802) → M_{802}
Element(zll, 803) → M_{803}
Element(zll, 804) → M_{804}
Element(zll, 805) → M_{805}
Element(zll, 806) → M_{806}
Element(zll, 807) → M_{807}
Element(zll, 808) → M_{808}
Element(zll, 809) → M_{809}
Element(zll, 810) → M_{810}
Element(zll, 811) → M_{811}
Element(zll, 812) → M_{812}
Element(zll, 813) → M_{813}
Element(zll, 814) → M_{814}
Element(zll, 815) → M_{815}
Element(zll, 816) → M_{816}
Element(zll, 817) → M_{817}
Element(zll, 818) → M_{818}
Element(zll, 819) → M_{819}
Element(zll, 820) → M_{820}
Element(zll, 821) → M_{821}
Element(zll, 822) → M_{822}
Element(zll, 823) → M_{823}
Element(zll, 824) → M_{824}
Element(zll, 825) → M_{825}
Element(zll, 826) → M_{826}
Element(zll, 827) → M_{827}
Element(zll, 828) → M_{828}
Element(zll, 829) → M_{829}
Element(zll, 830) → M_{830}
Element(zll, 831) → M_{831}
Element(zll, 832) → M_{832}
Element(zll, 833) → M_{833}
Element(zll, 834) → M_{834}
Element(zll, 835) → M_{835}
Element(zll, 836) → M_{836}
Element(zll, 837) → M_{837}
Element(zll, 838) → M_{838}
Element(zll, 839) → M_{839}
Element(zll, 840) → M_{840}
Element(zll, 841) → M_{841}
Element(zll, 842) → M_{842}
Element(zll, 843) → M_{843}
Element(zll, 844) → M_{844}
Element(zll, 845) → M_{845}
Element(zll, 846) → M_{846}
Element(zll, 847) → M_{847}
Element(zll, 848) → M_{848}
Element(zll, 849) → M_{849}
Element(zll, 850) → M_{850}
Element(zll, 851) → M_{851}
Element(zll, 852) → M_{852}
Element(zll, 853) → M_{853}
Element(zll, 854) → M_{854}
Element(zll, 855) → M_{855}
Element(zll, 856) → M_{856}
Element(zll, 857) → M_{857}
Element(zll, 858) → M_{858}
Element(zll, 859) → M_{859}
Element(zll, 860) → M_{860}
Element(zll, 861) → M_{861}
Element(zll, 862) → M_{862}
Element(zll, 863) → M_{863}
Element(zll, 864) → M_{864}
Element(zll, 865) → M_{865}
Element(zll, 866) → M_{866}
Element(zll, 867) → M_{867}
Element(zll, 868) → M_{868}
Element(zll, 869) → M_{869}
Element(zll, 870) → M_{870}

AI Drawing Prompt Reference

Draw a parametric surface with a rotating grid effect. Start by creating three corner points and a center point, then calculate direction vectors based on conditions to generate a grid point sequence. Use functions to compute the coordinates of the grid vertices and determine the boundary of the surface. Finally, draw the surface grid, add coordinate axes, and include auxiliary shapes to complete the overall effect.

The prompt above was compiled from the original drawing commands and is for reference only.