??? ???o? .NET?

1
?????? ? ??????????? ?????? ????????
?????? 12
?????? 2004
2
?????? ?????? ???????? ?????????? ??????

• ?????? ????????? ??????????????? ??????
  ??????????? ???????? ??????? (?? ????????? ???
  ? ????????????)

- ??????????? ?????
- ???????? ??????? (?????? ???????? ?????????
???????)

• ??? ????????? ?????? ?????? ??????????? ?? M
  ?????

3
?????? ?????? ???????? ??????? ???????

• ????? ??????? ??????? ??? 5 ??????????? ?????

• ?????? ?????. ??????? ?????? N - 1

- ???????? ??????????

• ????? ??????????? ????? Pi ????????? ??????? ??
  ????? ???? ??????

• ??? ???????? ?????????? ????? ??????? ??????
  ???????? ???? ???????.

4
?????? ?????? ???????? B-???????

• ?????? ????????? ??????????????? ??????, ?????
  ??????? ?????????? ???????? ??? ????????? ?????
  ?? ??????????? ?????.

p - ??????? B-???????.

• ???????? ??????? ?????????????? ?? ????????????
  ???????? ?????-?? ????.

5
???????? ??????? ??????
N p 1

• ??????????? ??????

t 0 0 0 0 0.25 0.75 1 1 1 1
p1
p1
N 4, p 3
N 7, p 3
t 0 0 0 0 0.25 0.75 0.875 1 1 1 1
6
????????????? ??????? ??????

• ??????????? ??????

N p 1
t -0.75 -0.5 -0.25 0 0.25 0.75 1.0 1.25 1.5
1.75
p1
p1
N 4, p 3
N 7, p 3
7
????????????? ????
t 0 0 0 0 0.5 0.5 0.5 1 1 1 1
N 7, p 3
8
?????? ???????????

• ???????????? ??? ???????? ????????? ?? ?????? ??
  ?????????? ???????? ???????

• ??????? ??? ?????????? ?????????? ?? ??????
  ?????-??-????

9
???????????? ???????

• ???????????? ?????? ???????? ????????? ????????
  ??????? ?? ???????????? ????? ??????? ???????????
  (??. ?????????? ??????????)

• ??????? ??? ????????? ???????? ???????????
  ?????????.

• w gt 0 ???????? ??c?? ???????. ??? ?????? ???,
  ??? ??????? ??????? ??????? ????????? ?? ?????
  ??????.

10
B-Spline ???????????

• ??????????? ???????? ?? ?????? ???? ???????
  ???????? ???????

• ???? ??????????? ???????? ?-????????, ???????
  ?????????? ????????? ??????????? ????? (???
  ????????? ??????)

11
??????????

• ??????? ?., ????c ??. ?????????????? ??????
  ???????? ???????.

• vprat. ifrance.com - ??????? ??? NURBS

• ????? ???? ?????? ?? ????? cg.cs.msu.su

• www.google.com )

12
??????????????? ?????????? GLU

• ?????? ? ?????? OpenGL ? ???????? ?? ????????
  OpenGL

• ??????? GLU ????? ????????? ?? ?????? ??????

• ??????????????? ??????? (gluPerspective,
  gluLookAt, )
• ??????? ??? ????????? ??????? ??????????????
  ???????? ?????, ????????, ????? ? ??????? ?????.
• ??????? ??? ????????? ?????????? ???????????????
• ??????? ??? ?????? ? ??????? ? ????????????? NURBS

13
????????? ?????????????? ???????? (1/2)
????? ??????? ????????? ?????????? ??????? ??????
GLUQuadricObj, ???????? ?????? ????????? ????????
GLU GLUquadricObj obj gluNewQuadric() ??
? ?????????? ???????? ????????? ?????????????
????????? ??????? gluQuadricDrawStyle ?????????
??? ???????? ????? ????????? gluQuadricOrienta
tion ??????????? ???????? gluQuadricNormals
????? ??????? ???????? gluQuadricTexture ????????
???? ??? ??? ?????????? ??????????
gluQuadricNormals(obj, GL_FLAT)
14
????????? ?????????????? ???????? (2/2)
partial disk
disk
sphere
??? ????????? ???????? ????????????? ???????
gluSphere, gluCylinder, gluDisk ?
gluPartialDisk. gluSphere(obj, 1.0, 20,
10) ????? ?????? ?? ?????, ?????? ?????
?????????? gluDeleteQuadric(obj)
15
????????? ?????? ? ???????????? NURBS (1/2)
????? ??????? ????????? ?????? ??? ???????????
NURBS ?????????? ??????? ?????? ??? ????????
??????? ?????????? NURBS GLUnurbsObj obj
new gluNewNurbsRenderer() ??? ?????? ???????
gluNurbsProperty ????? ?????? ????? ?????????,
????? ????????? ? ?????? ????????? ?????? ?
????????????. ????????????? ????????? ??????
????????? ?????? ? ???????????? 1. ??????????
??? ?? ?????????? u ? v 2. ?????????? ????????? ?
??????????? ?? ????? ??????/??????? ???????????
?? ??????. 3. ?????????? ????????? ? ???????????
?? ?????? ?????????????
16
????????? ?????? ? ???????????? NURBS (2/2)

• ????????? ?????? NURBS
• ????? ????????? gluBeginCurve ? gluEndCurve
  ?????????? ??????? gluNurbsCurve ??? ???????
  ???????? ??????????? ?????, ? ????? ????????,
  ?????? ? ?????????? ????????? ??????.
• ????????? ??????????? NURBS
• ????? ????????? gluBeginSurface ? gluEndSurface
  ?????????? ??????? gluNurbsSurface ??? ???????
  ???????? ??????????? ?????, ? ????? ????????,
  ?????? ? ?????????? ????????? ??????.

17
???????? ?????????? (1/4)
???????, ??????????? P(x1, y1) ? Q(x2, y2)
18
???????? ?????????? (2/4)
F(x,y) 0 -- ????? ?? ??????? F(x,y) lt 0 --
????? ???? F(x,y) gt 0 -- ????? ???? ????? P
??????????, ????? ?????????? ????????? ????? ?
???????? ??????? ? ???? ?????
19
???????? ?????????? (3/4)

• ???? d lt 0, ?? ?????????? ? ?
• ???? d ? 0, ?? ?????????? NE
• ? ????????? ?????

20
???????? ?????????? (4/4)
???? ???????????? -- ??????? ?? 2 ????? ????????
???????????? ??????????, ??????? ??????????????
d0 10 - 7 3 gt 0 (NE) d1 3 - 4 -1 lt
0 (E) d2 -1 10 9 (NE) d3
9 - 4 5 (NE) d4 5 - 4 1
(NE) d5 1 - 4 -3 (E) d6
-3 10 7 (NE)
21
???????? ?????????? (1/4) (??????????)

• ??????? ? ????? ?????????????
• ??????????????? ?????????????

22
???????? ?????????? (2/4) (??????????)
23
???????? ?????????? (3/4) (??????????)

• ??? ????? P c ?????.
• ??? ??????? ?
• ??? ??????? SE

24
???????? ?????????? (4/4) (??????????)

• ? ????????? ?????5 (0, R)
• ? ????? ????? ????????? ???????????? ????????.
• ?????? ?????? h d-1/4, ??????? h 1-R.
• ????? ?????????? ?????????? h ? -1/4, ?? ??? ???
  ?????????? d ????? ?????, ?? ?????????? ????? ?
  ?????.