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Использование программы 3d max для исследования пространственных кривых.

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ВЕСТНИК
МГСУ
2/2011
ɂɋɉɈɅɖɁɈȼȺɇɂȿ ɉɊɈȽɊȺɆɆɕ 3D MAX ȾɅə
ɂɋɋɅȿȾɈȼȺɇɂə ɉɊɈɋɌɊȺɇɋɌȼȿɇɇɕɏ ɄɊɂȼɕɏ
PROGRAM USE 3D MAX FOR RESEARCH OF SPATIAL CURVES
Ⱥ.ȼ. ɂɜɚɳɟɧɤɨ, Ʌ.Ⱥ. ɉɟɬɪɨɜɚ
A.V. Ivaschenko, L.A. Petrova
ȽɈɍ ȼɉɈ ɆȽɋɍ
Ɋɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɜɨɡɦɨɠɧɨɫɬɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɪɨɝɪɚɦɦɵ 3D MAX ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɪɢɜɵɯ, ɡɚɞɚɧɧɵɯ ɩɚɪɚɦɟɬɪɢɱɟɫɤɢɦɢ ɭɪɚɜɧɟɧɢɹɦɢ.
The article is devoted to the possibilities of using the program 3D max for the study of
space curves defined by parametric equations
ɉɪɨɝɪɚɦɦɚ ɜɢɡɭɚɥɶɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ 3dMAX ɩɨɡɜɨɥɹɟɬ ɤɨɧɫɬɪɭɢɪɨɜɚɬɶ ɩɨɜɟɪɯɧɨɫɬɢ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɪɹɞɟ ɫɩɨɫɨɛɨɜ ɮɨɪɦɨɨɛɪɚɡɨɜɚɧɢɹ. Ɉɞɢɧ ɢɡ ɬɚɤɢɯ ɫɩɨɫɨɛɨɜ
– Lofting, ɩɨɡɜɨɥɹɸɳɢɣ ɜɞɨɥɶ ɡɚɞɚɧɧɨɝɨ ɩɭɬɢ ɩɪɨɬɹɝɢɜɚɬɶ ɮɨɪɦɭ. ɉɪɢ ɷɬɨɦ ɜɨɡɦɨɠɧɨ
ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɜɢɡɭɚɥɢɡɢɪɨɜɚɬɶ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɭɸ ɤɪɢɜɭɸ, ɩɪɨɩɭɫɤɚɹ ɜɞɨɥɶ ɧɟɟ ɫɟɱɟɧɢɟ ɜ ɮɨɪɦɟ ɨɤɪɭɠɧɨɫɬɢ.
ɋɚɦɚ ɤɪɢɜɚɹ ɦɨɠɟɬ ɛɵɬɶ ɡɚɞɚɧɚ ɧɟɫɤɨɥɶɤɢɦɢ ɫɩɨɫɨɛɚɦɢ, ɧɚɩɪɢɦɟɪ, ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɧɚ ɨɫɧɨɜɟ ɫɩɥɚɣɧɨɜ, ɩɪɨɯɨɞɹɳɢɯ ɱɟɪɟɡ ɦɧɨɠɟɫɬɜɨ ɨɩɨɪɧɵɯ ɬɨɱɟɤ, ɢɥɢ ɠɟ ɧɚ
ɨɫɧɨɜɟ ɪɹɞɚ ɩɪɟɞɨɩɪɟɞɟɥɟɧɧɵɯ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɪɢɦɢɬɢɜɨɜ, ɬɚɤɢɯ ɤɚɤ ɨɤɪɭɠɧɨɫɬɶ,
ɞɭɝɚ, ɷɥɥɢɩɫ ɢ ɞɪɭɝɢɟ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɬɚɤɨɦ ɩɨɞɯɨɞɟ ɦɵ ɧɟ ɢɦɟɟɦ ɜɨɡɦɨɠɧɨɫɬɢ ɢɫɫɥɟɞɨɜɚɬɶ ɤɪɢɜɭɸ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦɢ ɦɟɬɨɞɚɦɢ.
ɇɚɢɛɨɥɟɟ ɩɨɞɯɨɞɹɳɢɣ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ ɤɥɚɫɫɨɜ ɤɪɢɜɵɯ - ɷɬɨ ɤɪɢɜɵɟ, ɡɚɞɚɧɧɵɟ
ɩɚɪɚɦɟɬɪɢɱɟɫɤɢ. ȼ ɬɚɤɢɯ ɤɪɢɜɵɯ ɜɫɟ ɬɪɢ ɤɨɨɪɞɢɧɚɬɵ ɥɸɛɨɣ ɟɟ ɬɨɱɤɢ ɦɨɠɧɨ ɨɩɢɫɚɬɶ
ɤɚɤ ɮɭɧɤɰɢɢ ɨɬ ɧɟɤɨɟɝɨ ɩɚɪɚɦɟɬɪɚ t.
x=x(t); y=y(t); z=z(t);
ȼɨɩɪɨɫ ɨ ɩɚɪɚɦɟɬɪɢɡɚɰɢɢ ɭɪɚɜɧɟɧɢɹ ɤɪɢɜɨɣ, ɡɚɞɚɧɧɨɣ ɤɚɤ ɫɢɫɬɟɦɚ ɞɜɭɯ ɧɟɥɢɧɟɣɧɵɯ ɭɪɚɜɧɟɧɢɣ ɨɬ ɬɪɟɯ ɩɟɪɟɦɟɧɧɵɯ, ɫɚɦ ɩɨ ɫɟɛɟ ɹɜɥɹɟɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɫɥɨɠɧɵɦ, ɢ ɧɟ
ɜɯɨɞɢɬ ɜ ɧɚɲɟ ɪɚɫɫɦɨɬɪɟɧɢɟ, ɧɨ ɥɸɛɚɹ ɤɪɢɜɚɹ, ɞɨɩɭɫɤɚɸɳɚɹ ɩɚɪɚɦɟɬɪɢɱɟɫɤɨɟ ɩɪɟɞɫɬɚɜɥɟɧɢɟ, ɬɚɤɠɟ ɦɨɠɟɬ ɛɵɬɶ ɨɬɨɛɪɚɠɟɧɚ ɢ ɢɫɫɥɟɞɨɜɚɧɚ ɜ ɪɚɦɤɚɯ ɩɪɨɝɪɚɦɦɵ 3dMAX.
Ⱦɥɹ ɷɬɨɝɨ ɪɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɭɸ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɭɸ ɤɪɢɜɭɸ, ɞɨɩɭɫɤɚɸɳɭɸ ɩɚɪɚɦɟɬɪɢɱɟɫɤɨɟ ɡɚɞɚɧɢɟ, ɧɚɩɪɢɦɟɪ, ɫɩɢɪɚɥɶ (ɡɚɦɟɬɢɦ, ɱɬɨ ɫɩɢɪɚɥɶɧɚɹ ɤɪɢɜɚɹ ɜɯɨɞɢɬ ɜ
ɫɨɫɬɚɜ ɦɧɨɠɟɫɬɜɚ ɩɪɟɞɨɩɪɟɞɟɥɟɧɧɵɯ ɩɪɢɦɢɬɢɜɨɜ, ɧɨ ɦɵ ɩɨɥɭɱɢɦ ɟɟ ɞɪɭɝɢɦ ɫɩɨɫɨɛɨɦ).
ɉɪɢ ɷɬɨɦ ɨɧɚ ɢɦɟɟɬ ɫɥɟɞɭɸɳɭɸ ɫɢɫɬɟɦɭ ɩɚɪɚɦɟɬɪɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ:
x=sin(t); y=cos(t); z=kt;
ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɡɚɞɚɬɶ ɷɬɢ ɭɪɚɜɧɟɧɢɹ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɮɨɪɦɟ ɤɪɢɜɨɣ ɦɵ ɧɟ
ɦɨɠɟɦ, ɧɨ ɡɚɬɨ ɜɨɡɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɪɢɜɭɸ ɤɚɤ ɬɪɚɟɤɬɨɪɢɸ ɞɜɢɠɟɧɢɹ ɧɟɤɨɟɝɨ
ɨɛɴɟɤɬɚ.
358
2/2011
ВЕСТНИК
МГСУ
Ɋɢɫ.1
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɞɟɣɫɬɜɢɣ ɛɭɞɟɬ ɫɥɟɞɭɸɳɟɣ:
1. ɫɨɡɞɚɟɦ ɧɟɤɢɣ ɨɛɴɟɤɬ (ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɧɟɜɚɠɧɨ, ɤɚɤɨɣ ɢɦɟɧɧɨ, ɧɚɩɪɢɦɟɪ, ɩɭɫɬɶ ɛɭɞɟɬ ɫɮɟɪɚ).
2. ȼɨ ɜɤɥɚɞɤɟ Motion (Ⱦɜɢɠɟɧɢɟ) ɢɧɫɬɪɭɦɟɧɬɚɥɶɧɨɣ ɩɚɧɟɥɢ ɜ ɪɚɡɞɟɥɟ Assign Controller (ɇɚɡɧɚɱɢɬɶ ɤɨɧɬɪɨɥɥɟɪ) ɧɚɡɧɚɱɢɦ ɞɥɹ Position (ɉɨɥɨɠɟɧɢɟ) ɤɨɧɬɪɨɥɥɟɪ ɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɜɵɪɚɠɟɧɢɹ – Position Expresion.
3. ȼ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɞɢɚɥɨɝɚ ɜ ɨɤɧɟ Expression (ȼɵɪɚɠɟɧɢɟ) ɨɩɪɟɞɟɥɢɦ
ɜɫɟ ɬɪɢ ɭɪɚɜɧɟɧɢɹ ɤɨɨɪɞɢɧɚɬ. ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɜ ɤɚɱɟɫɬɜɟ ɩɚɪɚɦɟɬɪɚ ɜɵɫɬɭɩɚɟɬ F – ɧɨɦɟɪ ɤɚɞɪɚ. Ʉɨɷɮɮɢɰɢɟɧɬɵ ɩɪɢ ɜɵɪɚɠɟɧɢɢ ɧɭɠɧɵ ɞɥɹ ɤɨɪɪɟɤɰɢɢ ɮɨɪɦɵ ɫɩɢɪɚɥɢ (ɪɚɞɢɭɫ, ɲɚɝ). Ɂɚɞɚɜ ɭɪɚɜɧɟɧɢɹ, ɢ ɡɚɤɪɵɜ ɨɤɧɨ,
ɦɨɠɧɨ ɭɜɢɞɟɬɶ ɫɩɢɪɚɥɶ ɜ ɤɚɱɟɫɬɜɟ ɬɪɚɟɤɬɨɪɢɢ.
4. ɉɨɫɥɟ ɩɨɥɭɱɟɧɢɹ ɬɪɚɟɤɬɨɪɢɢ ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɨɛɪɚɡɨɜɚɬɶ ɟɟ ɜ ɤɪɢɜɭɸ. Ⱦɥɹ
ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɜɵɞɟɥɢɬɶ ɨɛɴɟɤɬ, ɤ ɤɨɬɨɪɨɦɭ ɩɪɢɦɟɧɢɥɢ ɤɨɧɬɪɨɥɥɟɪ
ɞɜɢɠɟɧɢɹ (ɧɚɲɭ ɫɮɟɪɭ), ɢ ɩɟɪɟɣɬɢ ɜ ɪɚɡɞɟɥ Trajectories (Ɍɪɚɟɤɬɨɪɢɢ)
ɜɤɥɚɞɤɢ Motion (Ⱦɜɢɠɟɧɢɟ). Ɂɚɬɟɦ ɭɫɬɚɧɨɜɢɬɶ ɩɚɪɚɦɟɬɪɵ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
ɫɩɥɚɣɧɚ – ɧɚɱɚɥɶɧɵɣ (Start) ɢ ɤɨɧɟɱɧɵɣ (End) ɤɚɞɪ, ɚ ɬɚɤɠɟ ɢ ɤɨɥɢɱɟɫɬɜɨ
ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɬɨɱɟɤ (Sample), ɧɚɠɚɬɶ ɤɧɨɩɤɭ Convert To (ɉɪɟɨɛɪɚɡɨɜɚɬɶ ɜ). ɉɨɫɥɟ ɷɬɨɝɨ ɩɨɥɭɱɚɟɦ ɧɟɡɚɜɢɫɢɦɵɣ ɨɬ ɬɪɚɟɤɬɨɪɢɢ ɢɫɯɨɞɧɨɝɨ ɬɟɥɚ
ɫɩɥɚɣɧ ɤɪɢɜɨɣ.
Ⱦɥɹ ɭɥɭɱɲɟɧɧɨɣ ɜɢɡɭɚɥɢɡɚɰɢɢ ɬɚɤɨɝɨ ɨɛɴɟɤɬɚ ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ ɤ ɧɟɦɭ ɥɨɮɬɢɧɝ,
ɢɫɩɨɥɶɡɭɹ ɜ ɤɚɱɟɫɬɜɟ ɮɨɪɦɵ ɫɟɱɟɧɢɹ ɨɤɪɭɠɧɨɫɬɶ ɩɨɞɯɨɞɹɳɟɝɨ ɪɚɞɢɭɫɚ. ɇɚ ɪɢɫɭɧɤɟ
ɩɨɤɚɡɚɧɚ ɨɫɧɨɜɧɚɹ ɨɩɟɪɚɰɢɹ ɧɚɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ ɤ ɞɜɢɠɟɧɢɸ ɢɫɯɨɞɧɨɝɨ ɨɛɴɟɤɬɚ.
359
ВЕСТНИК
МГСУ
2/2011
Ɇɨɠɧɨ ɫɞɟɥɚɬɶ ɜɵɜɨɞ, ɱɬɨ ɢɫɩɨɥɶɡɭɹ ɩɪɨɝɪɚɦɦɭ 3dMAX ɞɨɫɬɚɬɨɱɧɨ ɭɞɨɛɧɨ ɩɪɨɜɨɞɢɬɶ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɟ ɬɨɥɶɤɨ ɫɜɨɣɫɬɜ ɪɚɡɥɢɱɧɵɯ ɩɨɜɟɪɯɧɨɫɬɟɣ ɢ ɢɯ ɫɟɱɟɧɢɣ, ɧɨ
ɬɚɤɠɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɪɢɜɵɯ, ɡɚɞɚɧɧɵɯ ɩɚɪɚɦɟɬɪɢɱɟɫɤɢɦɢ ɭɪɚɜɧɟɧɢɹɦɢ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɫ ɛɨɥɶɲɨɣ ɫɬɟɩɟɧɶɸ ɧɚɝɥɹɞɧɨɫɬɢ ɩɪɨɜɨɞɢɬɶ ɧɟɨɛɯɨɞɢɦɵɟ ɨɩɟɪɚɰɢɢ ɞɥɹ ɜɵɹɜɥɟɧɢɹ ɨɫɨɛɟɧɧɨɫɬɟɣ ɮɨɪɦɵ ɤɪɢɜɵɯ.
Ʌɢɬɟɪɚɬɭɪɚ:
1. Ʌɟɨɧɬɶɟɜ Ȼ. 3D Studio MAX 5.0. Ʉɨɦɩɶɸɬɟɪɧɚɹ ɝɪɚɮɢɤɚ ɢ ɚɧɢɦɚɰɢɹ . - Ɇ.: ɋɉȺɊɊɄ,
2003. - 315 ɫ.
2. ɋɨɥɨɜɶɟɜ, Ɇ. Ɇ. Ɍɪɟɯɦɟɪɧɵɣ ɦɢɪ 3D Studio Max 5.0 - Ɇ.: ɋɈɅɈɇ-ɉɪɟɫɫ, 2003. - 216 ɫ.
The literature:
1. Ʌɟɨɧɬɶɟɜ B. 3D Studio MAX 5.0. Computer graphics and animation. - Ɇ: SPARRK, 2003. 315 with.
2. Nightingales, M. M. the Three-dimensional world 3D Studio Max 5.0 - Ɇ: the SOLONPRESS, 2003. - 216 with.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɜɢɡɭɚɥɢɡɚɰɢɹ, 3d max, ɮɨɪɦɨɨɛɪɚɡɨɜɚɧɢɟ, ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ, ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɤɪɢɜɚɹ, ɩɚɪɚɦɟɬɪɢɱɟɫɤɢɟ ɭɪɚɜɧɟɧɢɹ ɤɪɢɜɨɣ.
Keywords: visualization, 3d max, morphogenesis, mathematical methods, about-stranstvennaja a
curve, the parametrical equations of a curve.
e-mail ɚɜɬɨɪɚ: grafika@mgsu.ru
Ɋɟɰɟɧɡɟɧɬ: Ʉɭɡɧɟɰɨɜ ɋ.ȼ. ɞɨɤɬɨɪ ɮɢɡ.-ɦɚɬ. ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ ɂɉɆɟɯ ɊȺɇ
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