20111009 computer graphics_galinsky_lecture04_math
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20111009 computer graphics_galinsky_lecture04_math
- 1. 舒亠仄舒亳从舒 于 从仂仄仗ﾑ亠仆仂亶 亞舒亳从亠 URL: http://www.school30.spb.ru/cgsg/cgc/ E-mail: [email_address]
- 2. 舒亰仂于亠 仗仂仆亳 于仂弍仂亟仆亠 于亠从仂, 舒亟亳 于亠从仂, 仂仗亠舒亳亳 于亠从仂舒仄亳, 从舒仍仆仂亠 亳 于亠从仂仆仂亠 仗仂亳亰于亠亟亠仆亳亠 于亠从仂仂于 ( vector dot & cross production) 弍舒亰亳, 从仂仂亟亳仆舒, 亟亠从舒仂于舒 亳亠仄舒 从仂仂亟亳仆舒 仄舒亳, 仂仗亠舒亳亳 仄舒亳舒仄亳, 仂弍舒亠仆亳亠 仄舒亳
- 3. 亠仂弍舒亰仂于舒仆亳 ( transformations) 亳仆仆亠 亠仗亠从亳于仆亠 亳仍亳仆亠亶仆亠
- 4. 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 舒舒仍仍亠仍仆亶 仗亠亠仆仂 (translation)
- 5. 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 舒舒弍亳仂于舒仆亳亠 (scaling)
- 6. 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 弌亟于亳亞 (shearing)
- 7. 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 舒舒弍亳仂于舒仆亳亠 ( scaling )
- 8. 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 仂于仂仂 仂仆仂亳亠仍仆仂 仆舒舒仍舒 从仂仂亟亳仆舒 ( rotation ) r
- 9. 舒亳仆舒 亰舒仗亳 舒亳仆仆 仗亠仂弍舒亰仂于舒仆亳亶 亠亠仗亳亠仄 于 仄舒亳仆仂仄 于亳亟亠 仂弍 亰舒仗亳 舒亳仆仆 仗亠仂弍舒亰仂于舒仆亳亶:
- 10. 亟仆仂仂亟仆亠 从仂仂亟亳仆舒 ( homogeneous ) 仗亠亟舒于亳仄 从仂仂亟亳仆舒 仆舒 仗仍仂从仂亳 ( 2D ) 亠从仂仄仗仂仆亠仆仆仂亶 于亠从仂 - 仂从仂亶: 弍亟亠仄 仗仂仍舒亞舒 w = 1 仗亠亠仗亳亠仄 仗亠仂弍舒亰仂于舒仆亳亠 于 仂弍亠仄 于亳亟亠:
- 11. 舒亳仆亶 于亳亟 舒亳仆仆 仗亠仂弍舒亰仂于舒仆亳亶 ~ translation ~ translation ~ shear by x ~ shear by y ~ rotation ~ scaling
- 12. 仂仄仗仂亰亳亳 仗亠仂弍舒亰仂于舒仆亳亶 仗仂亟于亠亞仆亠仄 仂从 仗仂仍亠亟仂于舒亠仍仆仄 仗亠仂弍舒亰仂于舒仆亳礆 亳亠仄 从仂仂亟亳仆舒: 仗亠亠仗亳亠仄: 于 亳仍 舒仂亳舒亳于仆仂亳:
- 14. 亠仂弍舒亰仂于舒仆亳亠 仂亠从, 于亠从仂仂于 亳 仆仂仄舒仍亠亶 仂从舒 (舒亟亳-于亠从仂) ( p ): 于亠从仂 ( v ) 亳 仆仂仄舒仍 ( n ) (仂仍从仂 仆舒仗舒于仍亠仆亳亠): 仗亠仂弍舒亰仂于舒仆亳:
- 16. 仂舒亳亳 亰舒仗亳亳: 仂仍弍亠 亳仍亳 仂从舒 亟仆仂 仗亠仂弍舒亰仂于舒仆亳亠: 仂仄仗仂亰亳亳 仗亠仂弍舒亰仂于舒仆亳亶:
- 17. 亳仄亠: 仗亳于磶从舒 亳亠仄 从仂仂亟亳仆舒 亰舒亟舒仆 仂从亳 仂仂于亠于亳 仆舒亶亳 束仄舒亳 仗亠亠仂亟舒損
- 18. 亳仄亠: 仗亳于磶从舒 亳亠仄 从仂仂亟亳仆舒
- 19. 亳仄亠: 仗亠仂弍舒亰仂于舒仆亳亠 亳亰仂弍舒亢亠仆亳亶 仂于仂仂 亳 仄舒舒弍亳仂于舒仆亳亠 => 礆仂亠 仂仂弍舒亢亠仆亳亠 ( direct mapping) => <= 弍舒仆仂亠 仂仂弍舒亢亠仆亳亠 ( inverse mapping) <=
- 20. 亳仄亠: warping (1) 亠亞仍仆舒 亠从舒 亟仍 仂弍仍舒亠亶 仂仂于亠于亳
- 21. 亳仄亠: warping (2) 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 亳仍亳仆亠亶仆亠 仗亠仂弍舒亰仂于舒仆亳 亠仗亠从亳于仆亠 仗亠仂弍舒亰仂于舒仆亳
- 22. 亳仄亠: warping (3) 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 亳仍亳仆亠亶仆亠 仗亠仂弍舒亰仂于舒仆亳 亠仗亠从亳于仆亠 仗亠仂弍舒亰仂于舒仆亳
- 23. 亳仄亠: morphing morphing = warping + 亳仆亠仗仂仍亳 于亠舒
- 25. 亳于磶从舒 仗亠仗亠从亳于仆仄 仗亠仂弍舒亰仂于舒仆亳亠仄 (1) 仂弍舒 仂仄仍舒: 仗礆仂亠 仂仂弍舒亢亠仆亳亠: 仗仂仍舒亞舒亠仄 w =1, 亳仂亞仂于舒 仂仄仍舒 亟仍 从仂仂亟亳仆舒:
- 26. 亳于磶从舒 仗亠仗亠从亳于仆仄 仗亠仂弍舒亰仂于舒仆亳亠仄 (2) 仗仂仍舒亠仄 仄舒亳 仂弍舒仆仂亞仂 仂仂弍舒亢亠仆亳 仂仗亠亟亠仍亳亠仍 仗亳于亠 亳 于 亳仍亳亠仍亠 亳 于 亰仆舒仄亠仆舒亠仍亠 于亳仍 仆亠 仆亢仆仂: 仆舒仂亟亳仄 仗亳仂亠亟亳仆亠仆仆 仄舒亳:
- 27. 亳于磶从舒 仗亠仗亠从亳于仆仄 仗亠仂弍舒亰仂于舒仆亳亠仄 (3) 舒亟舒舒 仗亳于磶从亳: 仗仂 4 仂从舒仄 仂仂于亠于亳 仂仗亠亟亠仍亳 仄舒亳 仗亠亠仂亟舒:
- 28. 亳于磶从舒 仗亠仗亠从亳于仆仄 仗亠仂弍舒亰仂于舒仆亳亠仄 (4) 亰舒仗亳亠仄 亰舒于亳亳仄仂 (于舒亰亳仄 从仂仂亟亳仆舒 x 亳 y ) : 于仗亳亠仄 于 仄舒亳仆仂亶 仂仄亠 8 舒于仆亠仆亳亶:
- 29. 亳于磶从舒 仗亠仗亠从亳于仆仄 仗亠仂弍舒亰仂于舒仆亳亠仄 (5) 亟仍 仗仂亠仆亳 亰舒亟舒亳 仗亠亠仂亟 亳亠仄 亳亰 亠亟亳仆亳仆仂亞仂 从于舒亟舒舒: 仗仂仍舒亠仄:
- 30. 亳于磶从舒 仗亠仗亠从亳于仆仄 仗亠仂弍舒亰仂于舒仆亳亠仄 (6) 仂弍仂亰仆舒舒亠仄: 亳 仆舒仂亟亳仄 亠亠仆亳亠:
- 31. 亳仆仆亠 仗亠仂弍舒亰仂于舒仆亳 于 仗仂舒仆于亠 仆舒仍仂亞亳仆仂 仍舒 2 D 于于仂亟亳仄 仂亟仆仂仂亟仆亠 从仂仂亟亳仆舒: 亳 仗亠仂弍舒亰仂于舒仆亳 于 仂弍亠仄 仍舒亠:
- 32. 舒亳 3D 仗亠仂弍舒亰仂于舒仆亳亶 (仗亠亠仆仂 , 仄舒舒弍) ~ translation ~ scaling
- 33. 舒亳 3D 仗亠仂弍舒亰仂于舒仆亳亶 (仗仂于仂仂 于仂从亞 仂亠亶) ~ rotation
- 34. 舒亳 3D 仗亠仂弍舒亰仂于舒仆亳亶 (仗仂于仂仂 于仂从亞 仂亳) 仂于仂仂 于仂从亞 仗仂亳亰于仂仍仆仂亶 仂亳, 仗仂仂亟亠亶 亠亠亰 仆舒舒仍仂 从仂仂亟亳仆舒. 亰舒亟舒亠 仆仂仄亳仂于舒仆仆仄 舒亟亳 于亠从仂仂仄. 于仂亟 亠亠亰 从于舒亠仆亳仂仆 (舒仄仂仂亠仍仆仂). ~ rotation
- 35. 亳仄亠: 仗仂仂亠仆亳亠 仄舒亳 从舒仄亠 (1) 从舒仄亠舒 亰舒亟舒亠: 仗仂亰亳亳 弌 亳 于亠从仂 仆舒仗舒于仍亠仆亳亠 束于于亠損 V , 束于舒于仂損 U 亳 于仗亠亠亟 N. 亳亠仄 仗亠仂弍舒亰仂于舒仆亳亠 于 于亳亟亠 束仗亠亠仆仂+仗仂于仂仂損: 亞亟亠
- 36. 亳仄亠: 仗仂仂亠仆亳亠 仄舒亳 从舒仄亠 (2) 仗仂仍亠 仗亠仂弍舒亰仂于舒仆亳 于亠从仂舒 仂仂弍舒亰: .亠.
- 37. 亳仄亠: 仗仂仂亠仆亳亠 仄舒亳 从舒仄亠 (3) 亰仆舒 仆舒仂亟亳仄
- 38. 舒从亳亠从亳亠 亰舒亟舒仆亳 亠舒仍亳亰仂于舒 warping 亳亰仂弍舒亢亠仆亳 (仂从 6.11.2011): 于亠 亳亰仂弍舒亢亠仆亳亠 舒仆仂仄亳亠 弍亳仍亳仆亠亶仆仄 仗亠仂弍舒亰仂于舒仆亳亠仄 (仂亟亳仆 仍亠仄亠仆 仂仂于亠于亳) 亰仂弍舒亢亠仆亳亠 舒亰亟亠仍磳 仆舒 亠亞仂仍仆亳从亳 亰仂仆 仂仂于亠于亳. 从舒亢亠仆亳亠 仗仂仍舒亠 于 仂仂于亠于亳亳 亳亰仄亠仆亠仆亳亠仄 亠从亳 亠亞仂仍仆亳从仂于.