Компьютерная графика, осень 2011: Математика в компьютерной графике

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  • CG MathCG Math

    ..- 30

    Computer Graphics Support Group

    1

    URL: http://www.school30.spb.ru/cgsg/cgc/

    E-mail: CGSG@yandex.ru

  • CG MathCG Math

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    Computer Graphics Support Group

    2

    , , , (vector dot & cross production)

    , ,

    , ,

  • CG MathCG Math

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    Computer Graphics Support Group

    3 (transformations)

  • CG MathCG Math

    ..- 30

    Computer Graphics Support Group

    4

    (translation)

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    Computer Graphics Support Group

    5

    (scaling)

  • CG MathCG Math

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    Computer Graphics Support Group

    6

    (shearing)

  • CG MathCG Math

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    Computer Graphics Support Group

    7

    (scaling)

  • CG MathCG Math

    ..- 30

    Computer Graphics Support Group

    8

    (rotation)

    r

  • CG MathCG Math

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    Computer Graphics Support Group

    9

    :

  • CG MathCG Math

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    Computer Graphics Support Group

    10 (homogeneous)

    (2D) -:

    w=1

    :

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    Computer Graphics Support Group

    11

    ~ translation

    ~ translation~ shear by x

    ~ shear by y

    ~ rotation

    ~ scaling

  • CG MathCG Math

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    Computer Graphics Support Group

    12

    :

    :

    :

  • CG MathCG Math

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    Computer Graphics Support Group

    13

  • CG MathCG Math

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    Computer Graphics Support Group

    14 ,

    (-) (p):

    (v) (n) ( ):

    :

  • CG MathCG Math

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    Computer Graphics Support Group

    15

  • CG MathCG Math

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    Computer Graphics Support Group

    16 :

    :

    :

  • CG MathCG Math

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    Computer Graphics Support Group

    17:

  • CG MathCG Math

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    Computer Graphics Support Group

    18:

  • CG MathCG Math

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    Computer Graphics Support Group

    19:

    => (direct mapping) =>

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    Computer Graphics Support Group

    20: warping (1)

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    Computer Graphics Support Group

    21: warping (2)

  • CG MathCG Math

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    Computer Graphics Support Group

    22: warping (3)

  • CG MathCG Math

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    Computer Graphics Support Group

    23: morphing

    morphing = warping +

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    Computer Graphics Support Group

    24

  • CG MathCG Math

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    Computer Graphics Support Group

    25 (1)

    :

    :

    w=1, :

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    Computer Graphics Support Group

    26 (2)

    :

    :

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    Computer Graphics Support Group

    27 (3)

    : 4 :

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    Computer Graphics Support Group

    28 (4)

    ( x y):

    8 :

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    Computer Graphics Support Group

    29 (5)

    :

    :

  • CG MathCG Math

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    Computer Graphics Support Group

    30 (6)

    :

    :

  • CG MathCG Math

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    Computer Graphics Support Group

    31

    2D :

    :

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    Computer Graphics Support Group

    32 3D (, )

    ~ translation

    ~ scaling

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    Computer Graphics Support Group

    33 3D ( )

    ~ rotation

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    Computer Graphics Support Group

    34 3D ( )

    , . . ().

    ~ rotation

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    Computer Graphics Support Group

    35: (1)

    : V, U N.

    +:

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    Computer Graphics Support Group

    36: (2)

    :

    ..

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    Computer Graphics Support Group

    37: (3)

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    Computer Graphics Support Group

    38

    warping (

    6.11.2011):

    ( )

    . .