O HOA RASTERO HOA RASTER

THUAT TOANTHUAT TOANVE NG BAC HAIVE NG BAC HAI

Giang vien : Bui Tien Len

Thuat toan ve ng bac haiThuat toan ve ng bac haiBc 1 Rut gon ng cong can ve (Da tren tnh oi

xng cua ng cong).

Bc 2 Phan vung ng cong can ve. Da tren ket qua cua viec khao sat ham so ng cong cu the la s bien thien cua ao ham e phan ng cong thanh tng vung khac nhau.

Bc 3 Xay dng thuat toan MidPoint ve cho tng

Trang Trang 22

Bc 3 Xay dng thuat toan MidPoint ve cho tng vung.

V du

Bc 1 Rut gon ng congBc 1 Rut gon ng cong

Trang Trang 33

Bc 2 Phan vung ng congBc 2 Phan vung ng cong

Tang cham Tang nhanh

Trang Trang 44

Giam cham Giam nhanh

Bc 2 Phan vung ng cong Bc 2 Phan vung ng cong

ng cong giam cham

ng cong giam nhanh

Trang Trang 55

giam nhanh

Bc 3 Xay dng thuat toan MidPointBc 3 Xay dng thuat toan MidPoint

Thuat toan 1

Thuat toan 2

Trang Trang 66

V duV du

dng) nguyen b (a, 1by

ax (E)

trnh phng co ellipse ng vetoan thuat dng Xay

2

2

2

2

=+

Trang Trang 77

V duV du

+

==

aba

a0x

sat khao Bangxa

xab- y' co a] [0, x vixa

ab

y

Ham

22

2

22

22

B(0, b)

Trang Trang 88

+

+

1

0

'y

0ba

bb

y

ba

22

2

22I

A(a, 0)

B(0, b)

V duV duHam kiem tra ben trong / ben ngoai cua ellipse

F(x, y) = b2x2 + a2y2 a2b2

ben ngoai

Trang Trang 99

ben trong

V duV duNhan xet iem sang th i

A(xi + 1, yi)

B(xi + 1, yi 1)

Xay dng bien fiTrung iem M cua AB

i A

Myi-1/2

yi

Trang Trang 1010

Trung iem M cua AB

M(xi + 1, yi 1/2)

Bien fifi = F(M)

B

xi xi+1

yi-1

V duV du

i

2222

i2

i22

i22

i2

i

i

nguyen f tnh thc Cong

bab4a

yaxb2yaxbf

goc f tnh thc Cong

++++=

Trang Trang 1111

2222

i2

i22

i22

i2

i bab4a

yaxb2yaxbf +

+++=

V duV duCach tnh fi cai tien

3) (2xb f f

th 0 f neu

ba b 4a

f

2

i

222

1

++=

= 0 Tang 1 Giam 1 Tang 2b2 Tang 2a2 + 2b2

V duV duCach tnh fi cai tien cai tien

222

2

2221

th 0 fi neuth 0 f neu

3b b2a - 2a N

3b M

ba b 4a f