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Направления совершенствования методов построения теней в компьютерной графике.

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2/2011
ВЕСТНИК
МГСУ
ɇȺɉɊȺȼɅȿɇɂə ɋɈȼȿɊɒȿɇɋɌȼɈȼȺɇɂə ɆȿɌɈȾɈȼ
ɉɈɋɌɊɈȿɇɂə ɌȿɇȿɃ ȼ ɄɈɆɉɖɘɌȿɊɇɈɃ ȽɊȺɎɂɄȿ
AREAS OFIMPROVEMENTOF METHODSFORGENERATING
SHADOWSINCOMPUTERGRAPHICS
ɂ.Ɇ. Ʌɟɛɟɞɟɜɚ
I.M. Lebedeva
ɆȽɋɍ
ȼ ɫɬɚɬɶɟ ɞɚɟɬɫɹ ɤɪɚɬɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɦɟɬɨɞɨɜ ɩɨɫɬɪɨɟɧɢɹ ɦɹɝɤɢɯ ɬɟɧɟɣ
ɧɚ ɨɫɧɨɜɟ ɢɡɜɟɫɬɧɵɯ ɚɥɝɨɪɢɬɦɨɜ ɪɚɫɱɟɬɚ ɨɫɜɟɳɟɧɧɨɫɬɢ, ɬɚɤɢɯ ɤɚɤ: ɦɟɬɨɞ ɬɟɧɟɜɵɯ
ɤɚɪɬ, ɦɟɬɨɞ ɬɟɧɟɜɵɯ ɨɛɴɟɦɨɜ ɢ ɚɥɝɨɪɢɬɦ ɨɛɪɚɬɧɨɣ ɪɟɤɭɪɫɢɜɧɨɣ ɬɪɚɫɫɢɪɨɜɤɢ ɥɭɱɚ.
The article gives a brief description of methods for generating soft shadows based on
the known algorithms for lighting calculations, such as: the method of shadow maps, shadow
volumes method and algorithm of the backwardrecursive ray tracing.
ȼ ɠɢɡɧɢ ɦɵ ɜɢɞɢɦ ɨɛɴɟɤɬɵ, ɩɨɬɨɦɭ ɱɬɨ ɨɧɢ ɨɬɪɚɠɚɸɬ ɩɚɞɚɸɳɢɣ ɧɚ ɧɢɯ ɫɜɟɬ. ȼ
ɤɨɦɩɶɸɬɟɪɧɨɣ ɝɪɚɮɢɤɟ ɬɚɤɠɟ, ɤɚɠɞɚɹ ɜɢɞɢɦɚɹ ɩɨɜɟɪɯɧɨɫɬɶ, ɱɬɨɛɵ ɛɵɬɶ ɜɢɡɭɚɥɢɡɢɪɨɜɚɧɧɨɣ, ɞɨɥɠɧɚ ɩɨɥɭɱɢɬɶ ɤɚɤɨɟ-ɬɨ ɤɨɥɢɱɟɫɬɜɨ ɫɜɟɬɚ. ɉɪɚɜɢɥɶɧɨ ɨɫɜɟɳɟɧɢɟ ɩɨɦɨɠɟɬ
ɜɵɞɟɥɢɬɶ ɝɥɚɜɧɵɟ ɷɥɟɦɟɧɬɵ ɫɰɟɧɵ, ɩɨɞɱɟɪɤɧɭɬɶ ɧɚɫɬɪɨɟɧɢɟ, ɞɨɛɚɜɢɬɶ ɷɦɨɰɢɨɧɚɥɶɧɭɸ
ɨɤɪɚɫɤɭ.
Ɋɟɚɥɢɫɬɢɱɧɨɫɬɶ ɢɡɨɛɪɚɠɟɧɢɸ ɞɨɛɚɜɥɹɸɬ ɬɟɧɢ. Ɉɧɢ ɩɨɦɨɝɚɸɬ ɜɨɫɩɪɢɹɬɢɸ ɮɨɪɦɵ
ɢ ɪɚɡɦɟɪɨɜ ɨɛɴɟɤɬɨɜ ɫɰɟɧɵ, ɢɯ ɜɡɚɢɦɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ, ɭɞɚɥɟɧɧɨɫɬɢ ɨɬ ɧɚɛɥɸɞɚɬɟɥɹ
ɢ ɞɪɭɝ ɨɬ ɞɪɭɝɚ.
ȼ ɤɨɦɩɶɸɬɟɪɧɨɣ ɝɪɚɮɢɤɟ ɩɪɨɛɥɟɦɚ ɬɟɧɟɣ ɪɟɲɚɟɬɫɹ ɪɚɡɥɢɱɧɵɦɢ ɫɩɨɫɨɛɚɦɢ. ȿɫɥɢ
ɫɤɨɪɨɫɬɶ ɩɪɨɪɢɫɨɜɤɢ ɜɚɠɧɟɟ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɬɨɱɧɨɫɬɢ ɬɟɧɢ ɩɪɢɦɟɧɹɸɬ ɦɟɬɨɞ ɬɟɧɟɜɵɯ
ɤɚɪɬ (ShadowMaps) ɢɥɢ ɩɪɨɟɤɬɢɜɧɵɟ ɬɟɧɢ (planeprojections). Ȼɨɥɟɟ ɬɨɱɧɵɟ ɬɟɧɢ ɩɨɡɜɨɥɹɟɬ ɩɨɫɬɪɨɢɬɶ ɦɟɬɨɞ ɬɟɧɟɜɵɯ ɨɛɴɟɦɨɜ (ShadowVolumes). ɋɚɦɭɸ ɪɟɚɥɢɫɬɢɱɧɭɸ ɤɚɪɬɢɧɭ ɨɫɜɟɳɟɧɧɨɫɬɢ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɫ ɩɨɦɨɳɶɸ ɚɥɝɨɪɢɬɦɚ ɥɭɱɟɜɨɣ ɬɪɚɫɫɢɪɨɜɤɢ
(raytracing). ɉɨɦɢɦɨ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɬɨɱɧɨɫɬɢ ɬɟɧɟɣ ɚɥɝɨɪɢɬɦ ɬɪɚɫɫɢɪɨɜɤɢ ɥɭɱɟɣ ɩɨɡɜɨɥɹɟɬ ɩɨɥɭɱɚɬɶ ɬɟɧɢ ɨɬ ɩɨɥɭɩɪɨɡɪɚɱɧɵɯ ɨɛɴɟɤɬɨɜ, ɨɤɪɚɲɢɜɚɬɶ ɨɬɪɚɠɟɧɧɵɣ ɢɥɢ ɩɪɟɥɨɦɥɟɧɧɵɣ ɫɜɟɬ.
ɇɚɛɥɸɞɟɧɢɹ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɬɟɧɶ ɧɟɨɞɧɨɪɨɞɧɚ ɩɨ ɫɜɨɟɣ ɢɧɬɟɧɫɢɜɧɨɫɬɢ. Ɉɧɚ ɫɨɫɬɨɢɬ ɢɡ ɩɨɥɧɨɣ ɬɟɧɢ (umbra) ɢ ɩɟɪɟɯɨɞɧɨɣ ɩɨɥɨɫɵ – ɩɨɥɭɬɟɧɢ (penumbra). Ɍɟɧɢ ɫ ɪɟɡɤɢɦɢ ɝɪɚɧɢɰɚɦɢ ɜɫɬɪɟɱɚɸɬɫɹ ɪɟɞɤɨ ɢ ɱɚɫɬɨɜɵɝɥɹɞɹɬ ɧɟɩɪɚɜɞɨɩɨɞɨɛɧɨ, ɛɭɞɬɨ ɨɧɢ ɧɚɪɢɫɨɜɚɧɵ ɢ ɫɭɳɟɫɬɜɭɸɬ ɨɬɞɟɥɶɧɨ ɨɬ ɨɛɴɟɤɬɚ, ɢɯ ɨɬɛɪɚɫɵɜɚɸɳɟɝɨ. Ɇɹɝɤɢɟ ɬɟɧɢ ɫɩɨɫɨɛɫɬɜɭɸɬ ɭɥɭɱɲɟɧɢɸ ɜɨɫɩɪɢɹɬɢɹ ɜɢɪɬɭɚɥɶɧɨɣ ɫɰɟɧɵ, ɭɜɟɥɢɱɢɜɚɸɬ ɟɟ ɪɟɚɥɢɫɬɢɱɧɨɫɬɶ. ɏɚɪɚɤɬɟɪ ɢ ɫɬɟɩɟɧɶ ɦɹɝɤɨɫɬɢ ɬɟɧɢ ɞɚɸɬ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɜɪɟɦɟɧɢ ɝɨɞɚ ɢ ɫɭɬɨɤ,
ɩɨɝɨɞɟ, ɧɚɥɢɱɢɢ ɨɛɥɚɱɧɨɫɬɢ. ȿɫɥɢ ɪɟɱɶ ɢɞɟɬ ɨɛ ɢɧɬɟɪɶɟɪɟ, ɬɨ ɬɟɧɢ ɨɬɪɚɠɚɸɬ ɫɩɨɫɨɛ
361
ВЕСТНИК
МГСУ
2/2011
ɨɫɜɟɳɟɧɢɹ, ɝɨɜɨɪɹɬ ɨ ɦɨɳɧɨɫɬɢ
ɦ
ɢ ɮɨɪɦɟ
ɮ
ɨɫɜɟɬɢ
ɢɬɟɥɶɧɵɯ ɩɪɢɛɨɪɨɜ, ɢɯ ɤɤɨɥɢɱɟɫɬɜɟ ɢ
ɩɨɥɨɠɟɧɢɢ.Ɋ
Ɋɚɫɫɟɹɧɧɨɟ ɨɫɜɟɳɟɧɢɟ
ɨ
ɬɚɤɠɟ ɩɨɪɨɠɞɚɚɟɬ ɦɹɝɤɢɟ ɬɟɧɢ.
Ɉɞɧɢɦ ɢɡ ɧɚɩɪɚɜɥɟɟɧɢɣ ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɦɟɬɨɞɨɜ ɪɚɫɫɱɟɬɚ ɬɟɧɟɣ ɹɹɜɥɹɟɬɫɹ ɩɨ-ɩɵɬɤɚ ɫɦɹɝɱ
ɱɟɧɢɹ ɝɪɚɧɢɰ
ɰɵ ɦɟɠɞɭ ɩɨɥɥɧɨɣ ɬɟɧɶɸ ɢ ɫɜɟɬɨɦ. ȿɫɬɶɶ ɦɟɬɨɞɢɤɢ ɞ
ɞɥɹ ɪɚɡɦɵɬɢɹɹ
ɝɪɚɧɢɰɵ ɧɚɚ ɮɢɤɫɢɪɨɜɚɧ
ɧɧɭɸ ɜɟɥɢɱɢ
ɢɧɭ. ɂɦɟɸɬɫɹɹ ɬɚɤɠɟ ɦɟɬɬɨɞɵ ɜɵɱɢɫɥɟɧɢɹ ɦɹɝɤɢɯ
ɯ
ɬɟɧɟɣ. ȿɫɥɢ ɪɟɡɤɢɟ ɬɟɧɢ ɜ ɤɨɦɩɶɸɬɟɪɪɧɨɣ ɝɪɚɮɢɤɟɟ ɪɚɫɫɱɢɬɵɜɚɚɸɬɫɹ ɨɬ ɬɨɱɟɟɱɧɵɯ ɢɫɬɨɱ-ɧɢɤɨɜ ɫɜɟɬɚ, ɬɨ ɦɹɝɤɢɟ – ɨɬ ɩɪɨɬɹɠɟɧ
ɧɧɵɯ, ɢɦɟɸɳ
ɳɢɯ ɨɩɪɟɞɟɥɟɧ
ɧɧɭɸ ɩɥɨɳɚɞ
ɞɶ.
Ɋɢɫ. 1 Ɍɟɧɢ: ɫɥɟɜɚ
ɫ
- ɪɟɡɤɚ
ɚɹ, ɫɩɪɚɜɚ - ɦɹɝɤɚɹ
ɦ
ɋɭɳɟɫɬɬɜɭɸɬ ɪɚɡɥɢɱ
ɱɧɵɟ ɦɟɬɨɞɢ
ɢɤɢ ɮɨɪɦɢɪɨ
ɨɜɚɧɢɹ ɦɹɝɤɢ
ɢɯ ɬɟɧɟɣ ɧɚ ɨɫɧɨɜɟ ɜɫɟɯ
ɯ
ɢɦɟɸɳɢɯɫɹ ɚɥɝɨɪɢɬɦɨɜ ɪɚɫɱɟɬɚ ɨɫɜɟɟɳɟɧɧɨɫɬɢ. Ⱦɚɥɟɟ
Ⱦ
ɩɪɢɜɟɞ
ɞɟɧɵ ɫɩɨɫɨɛɵ
ɵ ɩɨɫɬɪɨɟɧɢɹɹ
ɬɟɧɟɣ ɫ ɪɚɡɦ
ɦɵɬɵɦɢ ɝɪɚɧ
ɧɢɰɚɦɢ ɧɚ ɨɫɧ
ɧɨɜɟ ɚɥɝɨɪɢɬɦɨɜ ɬɟɧɟɜɵɯ ɤɚɪɬ, ɬɟɧɟɜɵ
ɵɯ ɨɛɴɟɦɨɜ ɢ
ɬɪɚɫɫɢɪɨɜɤɢ
ɢ ɥɭɱɟɣ.
ɉɨɫɬɪɨɨɟɧɢɟ ɦɹɝɤɢɯɯ ɬɟɧɟɣ ɧɚ ɨɫɫɧɨɜɟ ɚɥɝɨɪɢ
ɢɬɦɚ ɬɟɧɟɜɵ
ɵɯ ɤɚɪɬ
ɇɚ ɦɟɬɬɨɞɟ ɬɟɧɟɜɵɯɯ ɤɚɪɬ ɨɫɧɨɜɚɚɧ ɚɥɝɨɪɢɬɦ Singlesampleesoftshadows. ɗɬɨɬ ɦɟɬɨɞ
ɞ
ɛɵɥ ɨɩɢɫɚɧ ɜ 2002 ɝɨɞɭ. Ɉɛɥɚɫɬɶ ɩɨɥɭɬɟɧɢ ɮɨɪɦ
ɦɢɪɭɟɬɫɹ ɫ ɩɨɨɦɨɳɶɸ ɞɨɩɨɨɥɧɢɬɟɥɶɧɵɯ
ɯ
ɜɵɱɢɫɥɟɧɢɣ
ɣ ɞɥɹ ɤɚɠɞɨɣ ɬɨɱɤɢ ɜ ɦɨɦɟɟɧɬ ɨɩɪɟɞɟɥɟɟɧɢɹ ɟɟ ɨɫɜɟɳ
ɳɟɧɧɨɫɬɢ.
Ʉɚɤ ɢɡɜɜɟɫɬɧɨ, ɜ ɫɨɨɨɬɜɟɬɫɬɜɢɟ ɫ ɚɥɝɨɪɢɬɦɨɦ
ɦ ShadowMapps, ɮɨɪɦɢɪɭɟɬɫɹ ɬɟɧɟɜɚɹɹ
ɤɚɪɬɚ, ɤɨɬɨɪɪɚɹ ɩɪɟɞɫɬɚɜɥɥɹɟɬ ɫɨɛɨɣ ɦɚɚɬɪɢɰɭ ɜɢɞɢɦ
ɦɵɯ ɫɨ ɫɬɨɪɨɨɧɵ ɢɫɬɨɱɧɢɤɤɚ ɨɫɜɟɳɟɧɢɹɹ
ɬɨɱɟɤ ɫ ɪɚɫɫɫɬɨɹɧɢɹɦɢ ɞɨɨ ɧɢɯ. Ⱦɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɨɩɪɟɞɟɥɢɬɶ,
ɨ
ɨ
ɨɫɜɟɳɟɧɚ
ɥɢ ɬɨɱɤɚ ɫɰɟɧɵ
ɵ
ɢɥɢ ɡɚɬɟɧɟɧ
ɧɚ, ɞɥɹ ɧɟɟ ɜɵ
ɵɱɢɫɥɹɸɬ ɪɚɚɫɫɬɨɹɧɢɟ ɞɨ ɢɫɬɨɱɧɢɤɚ ɫɜɟɬɚ
ɫ
ɢ ɫɪɚɜɧ
ɧɢɜɚɸɬ ɩɨɥɭ-ɱɟɧɧɨɟ ɡɧɚɱ
ɱɟɧɢɟ ɫɨ ɡɧɚɱ
ɱɟɧɢɟɦ ɢɡ ɬɟɧ
ɧɟɜɨɣ ɤɚɪɬɵ ɞɥɹ ɫɨɨɬɜɟɬɫɫɬɜɭɸɳɟɣ ɩɨɨɡɢɰɢɢ. ȿɫɥɢ
ɢ
ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɬɨɱɤɢ ɞɨ ɢɫɬɨɱɧɢɤɚ ɫɜɜɟɬɚ ɛɨɥɶɲɟ, ɱɟɦ ɡɧɚɱɟɧɢ
ɢɟ ɢɡ ɬɟɧɟɜɨɣ
ɣ ɤɚɪɬɵ, ɡɧɚ-ɱɢɬ, ɬɨɱɤɚ ɡɚɚɫɥɨɧɟɧɚ ɞɪɭɭɝɢɦ ɨɛɴɟɤɬɨɨɦ, ɬɨ ɟɫɬɶɡɚɬɬɟɧɟɧɚ. ȿɫɥɢ ɪɚɫɫɬɨɹɧɢɹ
ɪ
ɪɪɚɜɧɵ - ɬɨɱɤɚɚ
ɨɫɜɟɳɟɧɚ.
ɇɚ ɫɥɟɞ
ɞɭɸɳɟɦ ɷɬɚɩ
ɩɟ ɩɪɨɜɨɞɢɬɫɫɹ ɩɪɨɜɟɪɤɚ ɧɚ ɩɪɢɧɚɞɥɟɟɠɧɨɫɬɶ ɬɨɱɤɤɢ ɤ ɨɛɥɚɫɬɢ
ɢ
ɩɨɥɭɬɟɧɢ. Ⱦɥɹ
Ⱦ ɨɫɜɟɳɟɧɧ
ɧɨɣ ɬɨɱɤɢ ɩɪɪɨɢɡɜɨɞɹɬ ɩɨ
ɨɢɫɤ ɬɨɱɤɢ ɡɚɚɬɟɧɟɧɧɨɣ ɜ ɩɪɟɞɟɥɚɯ ɡɚ-ɞɚɧɧɨɝɨ ɪɚɞ
ɞɢɭɫɚ. ȿɫɥɢ ɬɚɤɨɜɚɹ
ɬ
ɧɚɯɨɞ
ɞɢɬɫɹ, ɡɧɚɱɢɬɬ, ɬɨɱɤɚ ɥɟɠɢ
ɢɬ ɜ ɨɛɥɚɫɬɢ ɜɧɟɲɧɟɣ ɩɨ-ɥɭɬɟɧɢ, ɢ ɟɟɟ ɨɫɜɟɳɟɧɧɨɫɬɶ ɭɦɟɧɶɲɚɚɸɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɟɟ ɜɢɞɢɦɨɫɬɢ.ȼ
ȼ ɩɪɨɬɢɜɧɨɦ
ɦ
ɫɥɭɱɚɟ ɟɟ ɩɪɪɨɞɨɥɠɚɸɬ ɫɱ
ɱɢɬɚɬɶ ɨɫɜɟɳ
ɳɟɧɧɨɣ.
Ⱦɥɹ ɡɚɬɬɟɧɟɧɧɨɣ ɠɟ ɬɨɱɤɢ
ɬ
ɢɳɭɬ ɬɨɱɤɭ
ɬ
ɨɫɜɟɳɟɟɧɧɭɸ ɜ ɩɪɟɞ
ɞɟɥɚɯ ɬɨɝɨ ɠɟɟ ɪɚɞɢɭɫɚ. ɂ,,
ɟɫɥɢ ɧɚɯɨɞ
ɞɹɬ, ɬɨ ɬɨɱɤɤɟ ɞɨɛɚɜɥɹɸ
ɸɬ ɨɫɜɟɳɟɧɧ
ɧɨɫɬɢ ɩɪɨɩɨɪɪɰɢɨɧɚɥɶɧɨ ɟɟ ɜɢɞɢɦɨ-ɫɬɢ.ɋɱɢɬɚɟɬɬɫɹ, ɱɬɨ ɬɨɱɤɚɚ ɥɟɠɢɬ ɜ ɨɛɥɥɚɫɬɢ ɜɧɭɬɪɟɟɧɧɟɣ ɩɨɥɭɬɟɟɧɢ.ȿɫɥɢ ɠɟ ɧ
ɧɢ ɨɞɧɨɣ ɨɫ-ɜɟɳɟɧɧɨɣ ɬɨɱɤɢ ɪɹɞɨɦ ɧɟ ɧɚɯɨɞɢɬɫɹɹ, ɬɨ ɞɚɧɧɚɹ ɬɨɱɤɚ ɫɱɢɬɚɚɟɬɫɹ ɩɨɥɧɨɫɬɬɶɸ ɡɚɬɟɧɟɧ-ɧɨɣ.Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
ɨ
ɪɟɡɡɤɚɹ ɝɪɚɧɢɰɚ ɬɟɧɢ ɪɚɡɦɵɜɚɟɬɫɹ ɢ ɜɨ ɜɧɟɲɧɸɸ ɫɬɬɨɪɨɧɭ, ɢ ɜɨ
ɨ
ɜɧɭɬɪɟɧɧɸɸ
ɸ, ɨɛɪɚɡɭɹ ɩɨɨɥɭɬɟɧɶ.
ɉɨɥɭɱɟɟɧɧɚɹ ɩɨɥɭɬɟɧɶ ɧɟ ɹɜɥɹɟɬɬɫɹ ɪɟɚɥɢɫɬɢɱ
ɱɧɨɣ, ɬ.ɤ. ɨɧ
ɧɚ ɨɞɢɧɚɤɨɜɨɨ ɪɚɡɦɵɬɚ ɧɚɚ
ɜɫɟɦ ɩɪɨɬɹɠ
ɠɟɧɢɢ, ɜ ɬɨ ɜɪɟɦɹ
ɜ
ɤɚɤ ɪɟɚɥɶɧɚɹ ɬɟɧɶ ɢɦɟɟɬ ɩɨɫɬɟɩ
ɩɟɧɧɨ ɭɜɟɥɢɱɱɢɜɚɸɳɭɸɫɹɹ
ɪɚɡɦɵɬɨɫɬɶ ɩɨ ɦɟɪɟ ɭɞɚɥɥɟɧɢɹ ɨɬ ɨɛɴɟɟɤɬɚ.
362
2/2011
ВЕСТНИК
МГСУ
Ɋɢɫ. 2 ɉɨɫɬɪɨɟɧɢɟɟ ɦɹɝɤɨɣ ɬɟɧɢ ɩɨ ɬɟɧɟɜɨɣ
ɣ ɤɚɪɬɟ
ɇɟɞɨɫɬɚɬɤɢ ɛɚɡɨɜɨɝɝɨ ɚɥɝɨɪɢɬɦɚ ɬɟɧɟɜɵɯ ɤɚɪɬ ɫɤɚɡɵɜɚɸɬɫɫɹ ɢ ɩɪɢ ɩɨɫɬɬɪɨɟɧɢɢ ɦɹɝ-ɤɢɯ ɬɟɧɟɣ. ɗɬɨ
ɗ ɚɥɢɚɫɢɧɝ (ɨɲɢɛɨɱɧɨɟ ɡɚɬɟɧɟɧɢɟ), ɩɪɨɬɟɱɤɢ
ɩ
ɫɜɟɟɬɚ (ɬɟɦɧɵɟ ɩ
ɩɹɬɧɚ ɧɚ ɫɬɵ-ɤɚɯ) ɢ ɬɟɦɧɵ
ɵɟ ɩɨɥɨɫɵ ɧɚɚ ɝɪɚɧɢɰɚɯ ɫɦ
ɦɟɠɧɵɯ ɩɥɨɫɤɤɨɫɬɟɣ.
Ɋɢɫɫ. 3Ⱥɥɢɚɫɢɧɝɝ ɩɪɢ ɩɨɫɬɪɨɨɟɧɢɢ ɦɹɝɤɢ
ɢɯ ɬɟɧɟɣ ɧɚ ɨɫɧɨɜɟ
ɨ
ɬɟɧɟɜɵɯ ɤɚɪɬ
ɇɚ ɪɢɫɭɭɧɤɟ ɯɨɪɨɲɨɨ ɜɢɞɧɨ ɩɪɨɹɹɜɥɟɧɢɟ ɚɥɢɚɫɫɢɧɝɚ ɜ ɜɢɞɟɟ ɡɭɛɱɚɬɨɣ ɝɪɪɚɧɢɰɵ ɬɟɧɢ..
ɗɬɨ ɜɨɡɦɨɠ
ɠɧɨ ɜ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɨɞɧɨɣ
ɣ ɬɨɱɤɟ ɬɟɧɟɜɜɨɣ ɤɚɪɬɵ ɩɨɨɫɬɚɜɥɟɧɨ ɜ ɫɫɨɨɬɜɟɬɫɬɜɢɟɟ
ɧɟɫɤɨɥɶɤɨ ɩɢɤɫɟɥɟɣ
ɩ
ɢɡɨɨɛɪɚɠɟɧɢɹ. Ɍɟɦɧɵɟ
Ɍ
ɩɹɬɧɚ ɢ ɩɨɥɨɫɵ ɧɚ ɫɬɵɤɚɯ ɩ
ɩɨɜɟɪɯɧɨɫɬɟɣ
ɣ
ɝɨɜɨɪɹɬ ɨ ɬɨɦ, ɱɬɨ ɜ ɩɪɪɨɰɟɫɫɟ ɪɚɫɱɟɬɚ ɨɫɜɟɳɟɧɧ
ɧɨɫɬɢ ɛɵɥɢ ɨɲɢɛɨɱɧɨ ɢ
ɢɫɩɨɥɶɡɨɜɚɧɵ
ɵ
ɷɥɟɦɟɧɬɵ ɬɟɧɟɜɨɣ
ɬ
ɤɚɪɬɬɵ, ɫɨɨɬɜɟɬɫɬɬɜɭɸɳɢɟ ɞɪɭ
ɭɝɢɦ ɩɨɜɟɪɯɯɧɨɫɬɹɦ. ɂ, ɧɚɤɨɧɟɰ, ɧɚɚ
ɩɥɨɫɤɨɫɬɹɯ, ɩɨɥɨɠɟɧɢɟ ɤɨɬɨɪɵɯ ɩɪɢ
ɢɛɥɢɠɚɟɬɫɹ ɤ ɩɚɪɚɥɥɟɥɶɧ
ɧɨɫɬɢ ɧɚɩɪɚɜɜɥɟɧɢɸ ɨɫɜɟ-ɳɟɧɢɹ, ɩɪɨɹɹɜɥɹɟɬɫɹ ɚɥɢɚɚɫɢɧɝ ɜ ɜɢɞɟ ɧɟɫɭɳɟɫɬɜɭɸ
ɧ
ɸɳɢɯ ɬɟɧɟɜɵɯɯ ɩɨɥɨɫ.
ɉɨɫɬɪɨɨɟɧɢɟ ɦɹɝɤɢɯɯ ɬɟɧɟɣ ɧɚ ɨɫɫɧɨɜɟ ɚɥɝɨɪɢ
ɢɬɦɚ ɬɟɧɟɜɵ
ɵɯ ɨɛɴɟɦɨɜ
Ⱥɥɝɨɪɢ
ɢɬɦ ɬɟɧɟɜɵɯ ɨɛɴɟɦɨɜ (ShadowVolumes) ɛɵɥ ɜɩɟɪɜɜɵɟ ɩɪɟɞɥɨɠɟɧ Ɏɪɚɧɤɥɢ-ɧɨɦ Ʉɪɨɭ ɜ 1977 ɝɨɞɭ ɞɥɥɹ ɝɟɧɟɪɚɰɢɢ ɬɟɧɟɣ ɜ ɬɪɟɯɦ
ɦɟɪɧɨɦ ɩɪɨɫɬɬɪɚɧɫɬɜɟ
ɉɨ ɞɚɧɧ
ɧɨɦɭ ɚɥɝɨɪɢɬɬɦɭ ɬɨɱɤɚ ɫɱɢ
ɢɬɚɟɬɫɹ ɡɚɬɟɧ
ɧɟɧɧɨɣ, ɟɫɥɢ ɨɧɚ ɥɟɠɢɬ ɜɧ
ɧɭɬɪɢ ɨɞɧɨɝɨ
ɨ
ɢɡ ɬɟɧɟɜɵɯ ɨɛɴɟɦɨɜ. ɂ, ɧɚɨɛɨɪɨɬ, ɬɨɨɱɤɚ ɨɫɜɟɳɟɧ
ɧɚ, ɟɫɥɢ ɨɧɚ ɧɚɯɨɞɢɬɫɹ
ɧ
ɜɧ
ɧɟ ɥɸɛɨɝɨ ɢɡɡ
ɬɟɧɟɜɵɯ ɨɛɴ
ɴɟɦɨɜ.
363
ВЕСТНИК
МГСУ
2/2011
Ɇɟɬɨɞɵ
ɵ, ɨɫɧɨɜɚɧɧɵɟ ɧɚ ɚɥɝɨɨɪɢɬɦɟ ɬɟɧɟɜɵɯ ɨɛɴɟɦɨɨɜ, ɧɚɩɪɢɦɟɪɪ, ɚɥɝɨɪɢɬɦ
ɦ
PenumbraWeedges (ɩɨɥɭɬɬɟɧɟɜɵɯ ɤɥɢɧ
ɧɶɟɜ), ɩɨɡɜɨɥ
ɥɹɸɬ ɩɨɥɭɱɢ
ɢɬɶ ɛɨɥɟɟ ɬɨɱɱɧɵɟ ɦɹɝɤɢɟɟ
ɬɟɧɢ.
ȿɫɥɢ ɬɟɟɧɟɜɨɣ ɨɛɴɟɦ
ɦ ɜɵɬɹɝɢɜɚɟɬɬɫɹ ɨɬ ɬɨɱɟɱɧ
ɧɨɝɨ ɢɫɬɨɱɧɢɤɤɚ ɫɜɟɬɚ ɱɟɪɟɟɡ ɫɢɥɭɷɬɧɵɟɟ
ɪɟɛɪɚ ɨɛɴɟɤɤɬɚ, ɬɨ ɩɨɥɭɬɬɟɧɟɜɵɟ ɤɥɢɧ
ɧɶɹ ɦɨɝɭɬ ɛɵ
ɵɬɶ ɩɨɥɭɱɟɧɵ
ɵ ɬɨɥɶɤɨ ɨɬ ɩ
ɩɪɨɬɹɠɟɧɧɵɯ
ɯ
ɢɫɬɨɱɧɢɤɨɜ ɫɜɟɬɚ.Ʉ ɫɢɥɥɭɷɬɧɨɦɭ ɪɟɛ
ɛɪɭ ɨɛɴɟɤɬɚ ɩɪɨɜɨɞɹɬ ɩɥɥɨɫɤɨɫɬɢ, ɤɚɚɫɚɬɟɥɶɧɵɟ ɤ
ɩɪɨɬɢɜɨɩɨɥɨɨɠɧɵɦ ɫɬɨɪɨɨɧɚɦ ɢɫɬɨɱɧɢ
ɢɤɚ ɨɫɜɟɳɟɧɢɹ. ɗɬɢ ɝɪɚɧ
ɧɢ ɨɛɪɚɡɭɸɬ ɩɨɥɭɬɟɧɟɜɨɣ
ɣ
ɤɥɢɧ. ȼɫɟ, ɱɬɨ
ɱ ɩɨɩɚɥɨ ɜ ɨɛɥɚɫɬɶ ɩɟɧ
ɧɭɦɛɟɪɚɥɶɧɨɝɝɨ ɤɥɢɧɚ, ɥɟɠ
ɠɢɬ ɜ ɨɛɥɚɫɬɬɢ ɩɨɥɭɬɟɧɢ..
ɑɬɨɛɵ ɜɵɱɢ
ɢɫɥɢɬɶ ɨɫɜɟɳ
ɳɟɧɧɨɫɬɶ ɜ ɥɸɛɨɣ ɢɡ ɬɨɱ
ɱɟɤ ɢɡ ɨɛɥɚɫɬɬɢ ɩɨɥɭɬɟɧɢ, ɧɟɨɛɯɨɞɢɦɨ
ɨ
ɨɩɪɟɞɟɥɢɬɶ, ɤɚɤɭɸ ɱɚɫɬɶɶ ɢɫɬɨɱɧɢɤɚ ɫɜɟɬɚ
ɫ
ɜɢɞɧɨ ɢɡ
ɢ ɷɬɨɣ ɬɨɱɤɢ.
Ɋɢɫ. 4 ɉɨɫɬɬɪɨɟɧɢɟ ɩɨɥɭ
ɭɬɟɧɟɜɨɝɨ ɤɥ
ɥɢɧɚ
ɢ ɨɱɟɧɶ ɬɪɭɞɧ
ɧɨ ɩɨɫɬɪɨɢɬɶɶ ɩɥɨɫɤɨɫɬɶ, ɩɪɨɯɨɞɹɳɭɸ
ɸ ɱɟɪɟɡ ɪɟɛɪɨ
ɨ
ȼ ɪɟɚɥɶɶɧɨɦ ɜɪɟɦɟɧɢ
ɨɛɴɟɤɬɚ ɢ ɤɚɫɚɬɟɥɶɧɭɸ
ɤ
ɤ ɨɛɴɟɦɧɨɦɭɭ ɢɫɬɨɱɧɢɤɭ ɫɜɟɬɚ ɩɪɨɢɡɜɨɥɶɧɨɣ ɮɨɪɪɦɵ. ɗɬɨ ɩɨ-ɬɪɟɛɭɟɬ ɞɨɩ
ɩɨɥɧɢɬɟɥɶɧɵɯɯ ɤɨɦɩɶɸɬɟɪɧɵɯ ɦɨɳɧɨɫɫɬɟɣ. Ⱦɥɹ ɩɨɫɫɬɪɨɟɧɢɹ ɝɪɚɧ
ɧɢ ɩɨɥɭɬɟɧɟ-ɜɨɝɨ ɤɥɢɧɚ ɦɨɠɧɨ ɜɨɫɩɨɨɥɶɡɨɜɚɬɶɫɹ ɫɥɟɞɭɸɳɢɦ ɩɪɢɛɥɢɠɟɧɢɟɦ. Ʉɚɠɞɨɣ ɜɟɪɲɢɧɟ ɫɢ-ɥɭɷɬɚ ɩɪɢɜɨɨɞɹɬɫɹ ɜ ɫɨɨɬɜɜɟɬɫɬɜɢɟ ɞɜɟ ɩɪɨɬɢɜɨɩɨɥɨ
ɨɠɧɵɟ ɬɨɱɤɢ
ɢ ɧɚ ɢɫɬɨɱɧɢɤɤɟ ɫɜɟɬɚ. ɗɬɢ
ɢ
ɬɨɱɤɢ ɧɚɯɨɞ
ɞɹɬɫɹ ɜ ɪɟɡɭɥɥɶɬɚɬɟ ɩɟɪɟɫɟɟɱɟɧɢɹ ɝɪɚɧɢ
ɢɰɵ ɢɫɬɨɱɧɢɤɤɚ ɥɢɧɢɟɣ, ɩ
ɩɚɪɚɥɥɟɥɶɧɨɣ
ɣ
ɧɟɤɨɬɨɪɨɦɭ ɜɟɤɬɨɪɭ, ɩɪɟɟɞɫɬɚɜɥɹɸɳɟɟɦɭ ɫɨɛɨɣ ɢɧɬɬɟɪɩɨɥɢɪɨɜɚɧ
ɧɧɭɸ ɧɨɪɦɚɥɥɶ ɜ ɜɟɪɲɢɧɟɟ
ɫɢɥɭɷɬɚ. ɑɟɪɪɟɡ ɨɞɧɭ ɢɯ ɷɬɢɯ
ɷ
ɬɨɱɟɤ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸ
ɸɳɭɸ ɜɟɪɲɢ
ɢɧɭ ɫɢɥɭɷɬɚ ɜɜɵɬɹɝɢɜɚɟɬɫɹɹ
ɝɪɚɧɶ ɩɨɥɭɬɟɧɟɜɨɝɨ ɤɥɢɧ
ɧɚ. Ⱥ ɱɟɪɟɡ ɞɪɪɭɝɭɸ – ɝɪɚɧɶ ɬɟɧɟɜɨɝɨ ɨɛ
ɛɴɟɦɚ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,
ɨ
ɦɟɬɬɨɞ PenumbraaWedges ɩɨɡɜɜɨɥɹɟɬ ɩɨɥɭɱɢ
ɢɬɶ ɝɪɚɧɢɰɭ ɩ
ɩɨɥɧɨɣ ɬɟɧɢ,,
ɨɩɪɟɞɟɥɢɬɶ ɨɛɥɚɫɬɶ ɩɨɥɭɭɬɟɧɢ ɢ ɪɚɫɫɱ
ɱɢɬɚɬɶ ɞɥɹ ɧɟɟɟ ɨɫɜɟɳɟɧɧɨɫɬɶ.
Ʉ ɧɟɞɨɨɫɬɚɬɤɚɦ ɦɟɬɬɨɞɚ ɦɨɠɧɨ ɨɬɧɟɫɬɢ ɬɪɭ
ɭɞɨɟɦɤɨɫɬɶ ɩɨɫɬɪɨɟɧɢɹ
ɩ
ɩ
ɩɨɥɭɬɟɧɟɜɨɝɨ
ɨ
ɤɥɢɧɚ ɞɥɹ ɡɚɚɬɟɧɹɸɳɢɯ ɨɛɴɟɤɬɨɜ
ɨ
ɫɨ ɫɥɥɨɠɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ.
ɉɨɫɬɪɨɨɟɧɢɟ ɦɹɝɤɢ
ɢɯ ɬɟɧɟɣ ɧɚ ɨɫɧɨɜɟ
ɨ
ɚɥɝɨɪ
ɪɢɬɦɚ ɨɛɪɚɬɬɧɨɣ ɪɟɤɭɪɫɢ
ɢɜɧɨɣ ɥɭɱɟ-ɜɨɣ ɬɪɚɫɫɢɪ
ɪɨɜɤɢ(ɈɊɅɌ
Ɍ).
Ⱥɥɝɨɪɢ
ɢɬɦ ɥɭɱɟɜɨɣ ɬɪɚɫɫɢɪɨɜɤɢ
ɬ
ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɥɭɱɢ
ɢɬɶ ɧɚɢɛɨɥɟɟɟ ɩɪɢɛɥɢɠɟɧ-ɧɭɸ ɤ ɪɟɚɥɶɶɧɨɫɬɢ ɤɚɪɬɢɧ
ɧɭ ɨɫɜɟɳɟɧɧɨɫɬɢ. Ɍɟɧɢ ɢɦɟɸɬ ɝɟɨɦɟɬɬɪɢɱɟɫɤɢ ɩɪɚɜɜɢɥɶɧɵɟ ɝɪɚ-ɧɢɰɵ. ɉɨɥɭɭɩɪɨɡɪɚɱɧɵɟ ɨɛɴɟɤɬɵ ɨɤɪɚɚɲɢɜɚɸɬ ɜ ɫɜɨɣ ɰɜɟɬ ɜɡɚɢ
ɢɦɨɞɟɣɫɬɜɭɸ
ɸɳɢɣ ɫ ɧɢɦɢ
ɢ
ɫɜɟɬ.
ɋ ɩɨɦɨɨɳɶɸ ɚɥɝɨɪɢɬɬɦɚ ɨɛɪɚɬɧɨɣ
ɣ ɪɟɤɭɪɫɢɜɧɨ
ɨɣ ɥɭɱɟɜɨɣ ɬɪɪɚɫɫɢɪɨɜɤɢ ((ɈɊɅɌ) ɦɨɠ-ɧɨ ɪɚɫɫɱɢɬɚɚɬɶ ɨɫɜɟɳɟɧɢɟ ɬɨɥɶɤɨ ɨɬ ɬɨɱɟɱɧɵɯ
ɬ
ɢɫɬɬɨɱɧɢɤɨɜ ɫɜɟɟɬɚ ɢ ɩɨɥɭɱɢɬɬɶ ɫɨɨɬɜɟɬɫɬ-ɜɟɧɧɨ ɱɟɬɤɢ
ɢɟ, ɪɟɡɤɢɟ ɬɟɧ
ɧɢ. Ɍɟɦ ɧɟ ɦɟɟɧɟɟ, ɫɭɳɟɫɬɜɜɭɸɬ ɦɟɬɨɞɵ
ɵ ɩɨɥɭɱɟɧɢɹ ɦ
ɦɹɝɤɢɯ ɬɟɧɟɣ
ɣ
ɧɚ ɨɫɧɨɜɟ ɥɭɱɟɜɨɣ ɬɪɚɫɫɫɢɪɨɜɤɢ. ɇɚɩ
ɩɪɢɦɟɪ, ɦɨɠɧ
ɧɨ ɩɨɥɭɱɢɬɶ ɦɹɝɤɢɟ ɬɟɧɢ, ɤɚɤ ɨɬ ɩɪɨ-ɬɹɠɟɧɧɵɯ ɢɫɬɨɱɧɢɤɨɜ,
ɢ
ɟ
ɟɫɥɢ
ɜɦɟɫɬɨ ɨɞɧɨɝɨ
ɨ
ɢɫɩɭɫɤɚɬɶ ɤ ɢɫɬɨɱɧɢɤɭ ɫɜɟɬɚ ɧ
ɧɟɫɤɨɥɶɤɨ ɥɭ-ɱɟɣ ɫ ɨɩɪɟɞɟɟɥɟɧɧɵɦ ɭɝɥɨɨɜɵɦ ɲɚɝɨɦ.
364
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Ɋɚɫɫɦɨɬɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɫɩɨɫɨɛɵ
ɵ ɩɨɫɬɪɨɟɧɢɹɹ ɦɹɝɤɢɯ ɬɟɧ
ɧɟɣ ɧɚ ɨɫɧɨɜɜɟ ɚɥɝɨɪɢɬɦɚɚ
ɈɊɅɌ.
ɦ
ɬɨɱɟɱɧɵɯ ɢɫɬɨɱɧɢɤɨɜ
Ɂɚɦɟɧɚɚ ɨɛɴɟɦɧɨɝɨ ɢɫɬɨɱɧɢɤɚ ɦɧɨɠɟɫɬɜɨɦ
Ɇɹɝɤɢɟɟ ɬɟɧɢ ɦɨɠɧɨɨ ɩɨɥɭɱɢɬɶ, ɟɫɥɢ
ɟ
ɫɦɨɞɟɥɢ
ɢɪɨɜɚɬɶ ɩɪɨɬɬɹɠɟɧɧɵɣ ɢɫɬɬɨɱɧɢɤ ɫɜɟɬɚɚ
ɢɡ ɦɧɨɠɟɫɬɜɜɚ ɬɨɱɟɱɧɵɯ, ɪɚɫɫɱɢɬɚɜ ɨɫɫɜɟɳɟɧɧɨɫɬɶ ɞɥɹ ɤɚɠɞɨɝɨɨ ɢɡ ɧɢɯ ɫ ɩɨɦ
ɦɨɳɶɸ ɚɥɝɨ-ɪɢɬɦɚ ɥɭɱɟɜɜɨɣ ɬɪɚɫɫɢɪɨɜɜɤɢ. ȿɫɥɢ ɤɨɥɥɢɱɟɫɬɜɨ ɬɨɱ
ɱɟɱɧɵɯ ɢɫɬɨɱ
ɱɧɢɤɨɜ ɫɜɟɬɚ ɛɭɞɟɬ ɞɨɫɬɚ-ɬɨɱɧɨ ɛɨɥɶɲ
ɲɢɦ, ɬɨ ɨɛɳɚɚɹ ɨɫɜɟɳɟɧɧɨɫɬɶ ɫɰɟɧɵ ɛɭɞɟɬ
ɛ
ɮɢɡɢɱɟɟɫɤɢ ɩɪɚɜɢɥɶɶɧɨɣ, ɢɡɨɛɪɚ-ɠɟɧɢɟ ɛɭɞɟɬɬ ɪɟɚɥɢɫɬɢɱɟɟɫɤɢɦ. ɉɨɧɹɬɬɧɨ, ɱɬɨ ɤɚɠɞ
ɞɵɣ ɞɨɩɨɥɧɢ
ɢɬɟɥɶɧɵɣ ɢɫɬɬɨɱɧɢɤ ɫɜɟɬɚɚ
ɛɭɞɟɬ ɭɜɟɥɢ
ɢɱɢɜɚɬɶ ɜɪɟɦɹɹ ɧɚ ɩɪɨɪɢɫɨɜɜɤɭ ɢɡɨɛɪɚɠɟɟɧɢɹ.
Ɋɢɫɫ. 5 Ɍɟɧɢ ɨɬ ɪɚɡɧɨɝɨ
ɪ
ɤɨɥɢ
ɢɱɟɫɬɜɚ ɢɫɬɨ
ɨɱɧɢɤɨɜ ɫɜɟɬɬɚ ɫ ɪɟɡɤɢɦɢ
ɢ ɬɟɧɹɦɢ.
Ʉɨɥɢɱ
ɱɟɫɬɜɨ ɢɫɬɨɱ
ɱɧɢɤɨɜ ɫɥɟɜɚ
ɚ ɧɚɩɪɚɜɨ: 1 , 6 , 11
ɇɚ ɪɢɫɭɭɧɤɟ ɩɨɤɚɡɚɧ
ɧɨ, ɤɚɤ ɦɟɧɹɟɬɬɫɹ ɜɢɞ ɬɟɧɢ ɩɪɢ ɭɜɟɥɢɱɟɟɧɢɢ ɤɨɥɢɱɟɫɬɜɚ ɢɫɬɨɱɧɢ-ɤɨɜ ɫɜɟɬɚ. ɇɚ
ɇ ɥɟɜɨɦ ɤɚɞɪɪɟ ɬɟɧɢ ɩɨɫɬɪɪɨɟɧɵ ɬɪɚɫɫɢɪ
ɪɨɜɤɨɣ ɥɭɱɚ ɨɬ ɨɞɧɨɝɨ ɢɫɫɬɨɱɧɢɤɚ ɫɜɟ-ɬɚ, ɧɚ ɰɟɧɬɪɪɚɥɶɧɨɦ ɤɚɞɪɟ- ɨɬ ɲɟɫɬɢ, ɢ ɧɚ ɩɪɚɜɨɦ – ɨɬ ɨɞɢɧɧɚɞ
ɞɰɚɬɢ ɬɨɱɟɱɧ
ɧɵɯ ɢɫɬɨɱɧɢ-ɤɨɜ ɫɜɟɬɚ. ȼɪɟɦɹ
ȼ
ɧɚ ɜɢɡɭɭɚɥɢɡɚɰɢɸ ɛɵ
ɵɥɨ ɩɨɬɪɚɱɟɧ
ɧɨ ɫɨɨɬɜɟɬɫɬɜɜɟɧɧɨ: 4, 13 ɢ 21 ɫɟɤɭɧɞɭ..
Ɋɢɫɭɧɤɢ ɜɵɩ
ɩɨɥɧɟɧɵ ɜ AuutoCAD .
Ɇɟɬɨɞ ɫɜɟɬɨɜɵɯ ɫɟɟɬɨɤ
Ɇɟɬɨɞ ɫɜɟɬɨɜɵɯ ɫɟɬɬɨɤ ɛɵɥ ɪɚɡɪɪɚɛɨɬɚɧ ɜ 200
04 ɝɨɞɭ ɜ ɇɨɨɜɨɫɢɛɢɪɫɤɨɦ
ɦ ɝɨɫɭɞɚɪɫɬ-ɜɟɧɧɨɦ ɭɧɢɜɜɟɪɫɢɬɟɬɟ ɢɦ
ɦ. ɉɢɪɨɝɨɜɚ (Ⱦɟɛɟɥɨɜ
(
ȼ.Ⱥ
Ⱥ. ɢ ɞɪ.) ɤɚɤ ɚɞɚɩɬɚɰɢɹ ɚɥɥɝɨɪɢɬɦɚ ɨɛ-ɪɚɬɧɨɣ ɥɭɱɟɟɜɨɣ ɪɟɤɭɪɫɢɜɜɧɨɣ ɬɪɚɫɫɢɪɪɨɜɤɢ ɞɥɹ ɩɨɫɫɬɪɨɟɧɢɹ ɦɹɝɤɤɢɯ ɬɟɧɟɣ.
ȼ ɫɨɨɬɜɜɟɬɫɬɜɢɟ ɫ ɦɟɟɬɨɞɨɦ ɫɜɟɬɨɜɵɯ ɫɟɬɨɤ ɜɫɫɟ ɩɪɨɫɬɪɚɧɫɬɬɜɨ ɫɰɟɧɵ ɩɪɪɨɧɢɡɵɜɚɟɬɫɹɹ
ɬɪɟɯɦɟɪɧɨɣ ɫɟɬɤɨɣ ɫ ɨɩɪɪɟɞɟɥɟɧɧɵɦ ɲɚɝɨɦ. Ⱦɥɹ ɤɚɠɞɨɝɨ
ɤ
ɭɡɥɚɚ ɫɟɬɤɢ ɨɩɪɟɞ
ɞɟɥɟɧɚ ɦɚɫɤɚɚ
ɜɢɞɢɦɨɫɬɢ ɢɫɬɨɱɧɢɤɨɜ
ɢ
ɫ
ɫɜɟɬɚ
(0 ɢɥɢ 1).
1
Ⱦɚɥɟɟ ɜ ɬɨɱɤɟ ɩɟɪɟɫɫɟɱɟɧɢɹ ɥɭɱɚɚ ɫ ɨɛɴɟɤɬɨɦ ɫɰɟɧɵ (ɬɨɱɤɚ P)ɫɬɪɨɢɬɫɹɹ ɢɧɬɟɪɩɨɥɹ-ɰɢɨɧɧɚɹ ɫɮɟɟɪɚ ɡɚɞɚɧɧɨɝɨɨ ɪɚɞɢɭɫɚ.Ɉɫɫɜɟɳɟɧɧɨɫɬɶ ɬɨɱɤɢ
ɬ
P ɜɵɱɢ
ɢɫɥɹɟɬɫɹ ɤɚɤ ɭɫɪɟɞɧɟɧɧɨɟɟ
ɡɧɚɱɟɧɢɟ ɜɢ
ɢɞɢɦɨɫɬɢ ɜɫɟɯɯ ɫɜɟɬɨɜɵɯ ɬɨɨɱɟɤ, ɩɨɩɚɜɲ
ɲɢɯ ɜɧɭɬɪɶ ɫɮ
ɮɟɪɵ.
Ɉɱɟɜɢɞ
ɞɧɨ, ɱɬɨ, ɟɫɥɥɢ ɜ ɢɧɬɟɪɩɨɥɹɰɢɨɧɧɭɸ
ɸ ɫɮɟɪɭ ɩɨɩɚɚɥɢ ɬɨɥɶɤɨ ɨɫɜɟɳɟɧɧɵɟɟ
ɬɨɱɤɢ (ɢɥɢ ɬɨɥɶɤɨ ɡɚɬɟɧ
ɧɟɧɧɵɟ), ɬɨ ɬɨɱɤɚ
ɬ
P ɛɭɞɟɟɬ ɩɨɥɧɨɫɬɶɸ
ɸ ɨɫɜɟɳɟɧɚ (ɢɥɢ ɡɚɬɟɧɟ-ɧɚ). Ⱥ ɞɥɹ ɬɨɱɟɤ,
ɬ
ɧɚɯɨɞ
ɞɹɳɢɯɫɹ ɨɬ ɝɪɚɧɢɰɵ
ɝ
ɬɟɧɢ
ɢ ɧɚ ɪɚɫɫɬɨɹɹɧɢɢ, ɧɟ ɛɨɥɟɟɟ ɪɚɞɢɭɫɚ ɜ
ɤɚɠɞɭɸ ɫɬɨɨɪɨɧɭ,ɢɧɬɟɪɩ
ɩɨɥɹɰɢɨɧɧɨɟɟ ɦɧɨɠɟɫɬɜɨ
ɨ ɛɭɞɟɬ ɫɨɞɟɪɪɠɚɬɶ ɫɜɟɬɨɜɵɟ ɬɨɱɤɢ ɫ
ɪɚɡɥɢɱɧɨɣ ɜɢɞɢɦɨɫɬɶɸ
ɜ
. ɂɯ ɭɫɪɟɞɧɟɟɧɧɚɹ ɨɫɜɟɳɟɟɧɧɨɫɬɶ ɨɛɟɫɫɩɟɱɢɬ ɩɥɚɜɧ
ɧɵɣ ɩɟɪɟɯɨɞ
ɞ
ɨɬɬɟɧɢ ɤ ɫɜɟɟɬɭ.
Ⱦɨɩɨɥɧ
ɧɢɬɟɥɶɧɵɟ ɜɵ
ɵɱɢɫɥɟɧɢɹ, ɟɫɫɬɟɫɬɜɟɧɧɨ, ɜɥɢɹɸɬ
ɜ
ɧɚ ɫɤɤɨɪɨɫɬɶ ɜɢɡɭɚɚɥɢɡɚɰɢɢ. ɇɨ
ɨ
ɚɜɬɨɪɵ ɭɬɜɟɟɪɠɞɚɸɬ, ɱɬɨ ɩɪɢ ɞɨɫɬɢɠɟɟɧɢɢ ɨɩɪɟɞɟɥ
ɥɟɧɧɵɯ ɭɫɥɨɜɜɢɣ (ɪɚɡɪɟɲɟɟɧɢɟ ɷɤɪɚɧɚ ɢ
ɤɨɥɢɱɟɫɬɜɨ ɢɫɬɨɱɧɢɤɨɜ ɫɜɟɬɚ) ɫɤɨɪɨɨɫɬɶ ɪɚɫɱɟɬɚ ɩɨ ɦɟɬɨɞɭ ɫɜɟɬɨɜɵɯ ɫɟɬɨɨɤ ɞɚɠɟ ɩɪɟ-ɜɵɲɚɟɬ ɫɤɨɪɪɨɫɬɶ ɛɚɡɨɜɨɝɝɨ ɚɥɝɨɪɢɬɦɚɚ ɨɛɪɚɬɧɨɣ ɪɟɟɤɭɪɫɢɜɧɨɣ ɥɭɭɱɟɜɨɣ ɬɪɚɫɫɫɢɪɨɜɤɢ.
365
ВЕСТНИК
МГСУ
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Ʌɢɬɟɪɚɬɭɪɚ
1. Ⱦɟɛɟɥɨɜ ȼ.Ⱥ., ɇɨɜɢɤɨɜ ɂ.ȿ. Ƚɟɧɟɪɚɰɢɹ ɦɹɝɤɢɯ ɬɟɧɟɣ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɚɥɝɨɪɢɬɦɚ
ɬɪɚɫɫɢɪɨɜɤɢ ɥɭɱɟɣ 2009 ɢɧɫɬɢɬɭɬ ɜɵɱɢɫɥɢɬɟɥɶɧɨɣ ɦɚɬɟɦɚɬɢɤɢ ɢ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɝɟɨɮɢɡɢɤɢ ɋɈ
ɊȺɇ.
2. Ⱦɟɛɟɥɨɜ ȼ.Ⱥ., ȼɚɫɢɥɶɟɜɚ Ʌ.Ɏ., ɇɨɜɢɤɨɜ ɂ.ȿ. Ɋɚɡɜɢɬɢɟ ɦɟɬɨɞɚ ɫɜɟɬɨɜɵɯ ɫɟɬɨɤ ɞɥɹ ɚɥɝɨɪɢɬɦɚ ɥɭɱɟɜɨɣ ɬɪɚɫɫɢɪɨɜɤɢ: ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɪɟɲɟɧɢɹ, ɪɟɚɥɢɡɚɰɢɹ ɧɚ ɝɪɚɮɢɱɟɫɤɨɦ ɚɤɫɟɥɟɪɚɬɨɪɟ
Ɍɪ. 15-ɣ ɦɟɠɞɭɧɚɪ. ɤɨɧɮ. ɩɨ ɤɨɦɩɶɸɬɟɪɧɨɣ ɝɪɚɮɢɤɟ ɢ ɟɟ ɩɪɢɥɨɠɟɧɢɹɦ Ƚɪɚɮɢɤɨɧ 2005. ɇɨɜɨɫɢɛɢɪɫɤ: ɂȼɆɢɆȽ ɋɈ ɊȺɇ. 2005. ɋ. 355–359.
3. Ɍɪɢɮɨɧɨɜ Ⱦ. Ɇɹɝɤɢɟ ɬɟɧɢ ɧɚ GPU 2008 http://www.uraldev.ru/articles/id/18
4. Variance Shadow Maps (VSM) http://steps3d.narod.ru/tutorials/vsm-tutorial.html
The literature
1. Debelov V.A., NovikovI.E. Generating soft shadows using ray tracing algorithm 2009 Institute of Computational Mathematics and Mathematical Geophysics
2. Debelov VA, Vasil'eva LF, Novikov, E. Development of the light grid algorithm for ray tracing: approximation solutions, the implementation of the graphics accelerator Proc. 15-th Intern. Conf.
onComputerGraphicsandApplicationsGraphiCon 2005. Novosibirsk
3. Trifonov D. Soft Shadows on the GPU 2008 http://www.uraldev.ru/articles/id/18
4. Variance Shadow Maps (VSM) http://steps3d.narod.ru/tutorials/vsm-tutorial.html
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ:ɨɫɜɟɳɟɧɧɨɫɬɶ, ɬɟɧɢ, ɦɹɝɤɢɟ ɬɟɧɢ, ɩɨɥɭɬɟɧɟɜɨɣ ɤɥɢɧ, ɬɟɧɟɜɨɣ ɨɛɴɟɦ,
ɬɟɧɟɜɚɹ ɤɚɪɬɚ, ɬɪɚɫɫɢɪɨɜɤɚ ɥɭɱɚ, ɩɨɥɭɬɟɧɶ.
Keywords: illumination, shadows, soft shadowspenumbral wedge, shadow volume, shadow map,
ray tracing, penumbra.
e-mail ɚɜɬɨɪɚ: grafika@mgsu.ru.
Ɋɟɰɟɧɡɟɧɬ: ɤɚɧɞɢɞɚɬ ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɞɨɰɟɧɬ, Ƚɂɉ ɈɈɈ «ɆȺɄɄɈɆ-ɋɌɊɈɃ»,
Ʉɪɭɬɢɤɨɜ ɘɪɢɣ Ⱥɥɟɤɫɚɧɞɪɨɜɢɱ.
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