chuong_2a [Compatibility Mode].pdf
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Transcript of chuong_2a [Compatibility Mode].pdf
![Page 1: chuong_2a [Compatibility Mode].pdf](https://reader034.fdocuments.net/reader034/viewer/2022051417/55cf8ffb550346703ba1f536/html5/thumbnails/1.jpg)
ÑOÀ HOÏA RASTERÑOÀ HOÏA RASTER
CAÙC THUAÄT TOAÙN TOÂ MAØUCAÙC THUAÄT TOAÙN TOÂ MAØU
Giaûng vieân : Buøi Tieán Leân
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Baøi toaùn toâ maøuBaøi toaùn toâ maøuToâ maøu laø thao taùc tìm caùc ñieåm saùng “naèm beân trong” moät vuøng kheùp kín.Input :
Vuøng SOutput :
{(x1, y1), (x2, y2) … (xn, yn)}
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{(x1, y1), (x2, y2) … (xn, yn)}
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Caùc höôùng tieáp caänCaùc höôùng tieáp caänCoù hai phöông phaùp - Toâ maøu theo laân caän- Toâ maøu theo doøng queùt
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Toâ maøu theo laân caänToâ maøu theo laân caän
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Laân caän laø gì ?Laân caän laø gì ?Coù hai loaïi laân caän : laân caän 4 vaø laân caän 8.Laân caän 4
N4(x, y) = {(x-1, y), (x, y+1), (x+1, y), (x, y-1)}Laân caän 8
N8(x, y) = {(x-1, y), (x-1, y+1), (x, y+1), (x+1, y+1), (x+1, y), (x+1, y-1), (x, y-1), (x-1, y-1)}
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(x,y) phaûitraùi
döôùi
treân
x
y (x,y)
x
y
traùi
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Thuaät toaùn ñeä quiThuaät toaùn ñeä quiböôùc 1 Keû bieân vuøng caàn toâböôùc 2 Xaùc ñònh moät ñieåm (x, y) naèm beân trong vuøng caàn toâböôc 3 Toâ ñieåm (x, y), sau ñoù toâ loang sang nhöõng ñieåm laân caän
Trang Trang 66x
y
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Caøi ñaët ñeä quiCaøi ñaët ñeä qui// To loang
void BoundaryFill(CDC *pDC, int x, int y,
int fill_color, int boundary_color)
{
int color;
color = pDC->GetPixel(x, y);
if((color != fill_color) && (color != boundary_color))
{
pDC->SetPixel(x, y, fill_color);
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pDC->SetPixel(x, y, fill_color);
BoundaryFill(pDC, x-1, y, fill_color, boundary_color);
BoundaryFill(pDC, x, y+1, fill_color, boundary_color);
BoundaryFill(pDC, x+1, y, fill_color, boundary_color);
BoundaryFill(pDC, x, y-1, fill_color, boundary_color);
}
}
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Nhaän xeùt thuaät toaùn ñeä quiNhaän xeùt thuaät toaùn ñeä quiÖu ñieåm
Coù theå toâ vuøng coù hình daïng baát kyø.
Khuyeát ñieåmKhoâng theå duøng ñeå toâ caùc
vuøng coù kích thöôùc lôùn.
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kích thöôùc !
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Thuaät toaùn caûi tieánThuaät toaùn caûi tieánböôùc 1
Caát ñieåm haït gioáng ñaàu tieân vaøo kho.böôùc 2
Laëp neáu kho khoâng roãng- c1 Laáy ñieåm haït gioáng.- c Toâ ñieåm haït gioáng sau ñoù toâ loang sang traùi vaø
Trang Trang 99
- c2 Toâ ñieåm haït gioáng sau ñoù toâ loang sang traùi vaø sang phaûi.
- c3 Boå sung nhöõng ñieåm haït gioáng môùi vaøo kho töø doøng treân vaø doøng döôùi.
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Thuaät toaùn caûi tieánThuaät toaùn caûi tieánhaït gioáng : ñieåm saùng
kho : chöùa caùc ñieåm haït gioáng
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Thuaät toaùn caûi tieánThuaät toaùn caûi tieán
bieân bieân
Minh hoïa toâ loang
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Thuaät toaùn caûi tieánThuaät toaùn caûi tieánTieâu chuaån ñeå laø ñieåm haït gioáng
1. Ñieåm naøy chöa ñöôïc toâ vaø khoâng phaûi ñieåm bieân.2. Ñieåm naøy thoaû :
- Ñieåm traùi ñaàu tieân.- hoaëc beân traùi cuûa noù laø ñieåm bieân (neáu noù khoâng
phaûi laø ñieåm traùi ñaàu tieân).
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phaûi laø ñieåm traùi ñaàu tieân).
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Thuaät toaùn caûi tieánThuaät toaùn caûi tieán
bieân bieân
Minh hoïa boå sung nhöõng ñieåm haït gioáng môùi
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bieân bieân
bieân
haït gioáng
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Toâ theo laân caän Toâ theo laân caän -- Moät soá vaán ñeàMoät soá vaán ñeà
Söû duïng laân caän naøo ?
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Toâ theo laân caän Toâ theo laân caän -- Moät soá vaán ñeàMoät soá vaán ñeà
Ñöôøng bieânmaøu gì ?
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Toâ theo laân caän Toâ theo laân caän -- Moät soá vaán ñeàMoät soá vaán ñeà
Trang Trang 1616
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Toâ maøu theo doøng queùtToâ maøu theo doøng queùt
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Khaùi nieäm doøng queùtKhaùi nieäm doøng queùtDoøng queùt laø doøng ñieåm saùng treân maøn hình
y
Trang Trang 1818
y
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Toâ hình chöõ nhaätToâ hình chöõ nhaät
l r
ty
Trang Trang 1919
b
y
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Toâ hình tam giaùcToâ hình tam giaùcInput
(X1, Y1), (X2, Y2), (X3, Y3)
Caùch toâ
böôùc 1 : Saép xeáp caùc ñænhY ≤ Y ≤ Y
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Y1 ≤ Y2 ≤ Y3
böôùc 2 : Phaân tröôøng hôïpTheo tung ñoä
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Toâ hình tam giaùcToâ hình tam giaùc
Y1 = Y2 = Y3
1 3 2
Y1 < Y2 = Y3
1
2 3
Trang Trang 2121
Y1 = Y2 < Y3
12
3
Y1 < Y2 < Y3
1
2
3
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Toâ hình tam giaùcToâ hình tam giaùc
1 3 2Y1
X X
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Toâ tam giaùc (Y1 = Y2 = Y3)1. Tìm Xmin, Xmax
2. Toâ doøng Y1 baét ñaàu taïi coät Xmin, keát thuùc taïi coät Xmax
Xmin Xmax
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Toâ hình tam giaùcToâ hình tam giaùc
Toâ tam giaùc (Y1 < Y2 = Y3)Laëp y : Y1 … Y2
1. Tìm hoaønh ñoä giao ñieåm xl, xrgiöõa doøng queùt y vôùi caùc caïnh
2 3Y2
y
Trang Trang 2323
l rgiöõa doøng queùt y vôùi caùc caïnh traùi vaø caïnh phaûi cuûa tam giaùc.
2. Toâ doøng y baét ñaàu taïi coät xl, keát thuùc taïi coät xr.1
Y1y
y
xl xr
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Toâ hình tam giaùcToâ hình tam giaùcVí duï
Caùc hoaønh ñoä giao ñieåm cuûa caùc doøng queùt vôùi caïnh (2, 2), (11, 6).
654
2
Trang Trang 2424
5432
1
84
174
264
354
444
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Toâ hình tam giaùcToâ hình tam giaùc
12
cumoi
1
XXk
vôùi
kxx
X laø ñaàu x
ñieåm giao ñoä hoaønh tính Caùch
−=
+=
1
2
Trang Trang 2525
12
12
YYk
−= 1
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Toâ hình tam giaùcToâ hình tam giaùc
2
3
Y2
Y3
Trang Trang 2626
1Y1y
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Toâ hình ña giaùc loàiToâ hình ña giaùc loài
Caùch toâ1. Chia ña giaùc loài coù n ñænh
{p0, p1, ... , pn-1} thaønh n-2 tam giaùc.- ∆1 p0p1p2
- ∆ p p p
p0
p1
p2
p3
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- ∆2 p0p2p3
- ...- ∆i p0pipi+1
- ...- ∆n-2 p0pn-2pn-1
2. Toâ töøng tam giaùc.
p1
p2
p3
pn-2
pn-1
p0
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Toâ hình ña giaùcToâ hình ña giaùcNguyeân lyù chia tam giaùc
Moïi ña giaùc khoâng töï caét ñeàu coù theå phaân chia thaønh caùc tam giaùc.
Trang Trang 2828
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ThuThuậật toaùn toâ ña giaùc toång quaùtt toaùn toâ ña giaùc toång quaùt
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Thuaät toaùnThuaät toaùn
böôùc 1 Tìm ymin vaø ymax
ymin = min{yi, (xi, yi) ∈ P}ymax = max{yi, (xi, yi) ∈ P}
böôùc 2 Toâ töøng doøng
ymax
yI1 I2 I3 I4
P
Trang Trang 3030
böôùc 2 Toâ töøng doøngLaëp y : ymin … ymax
c1 Tìm caùc giao ñieåm.c2 Saép xeáp caùc giao ñieåm.c3 Toâ caùc ñoaïn thaúng.
ymin
P
y
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Löu yùLöu yùBoû caïnh naèm ngang
Trang Trang 3131
boû
boû
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Löu yùLöu yùDoøng queùt ñi qua ñænh
a
b
cd
e
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a c e
f
g
h
I1 I2 I3 I4
Bình thöôøng
y
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Löu yùLöu yùDoøng queùt ñi qua ñænh
a
b
cd
eI1 I2 I3 I4 I5
Loãi
y
Trang Trang 3333
a c e
f
g
h
I1 I2 I3 I4 I5
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Löu yùLöu yùCaét bôùt caïnh c theo truïc y 1 ñôn vò
a
b
cd
eI1 I2 I3 I41y
1
Trang Trang 3434
a c e
f
g
h
I1 I2 I3 I4
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Ví duïVí duï
6
7
8
9b
c
d
{(1, 1) (2, 7) (4, 9) (7, 9) (9, 5) (9, 1) (7, 1) (5, 5) (4, 1)}
Trang Trang 35351 2 3 4 5 6 7 8 9
1
2
3
4
5
6
a
e
f
gh
i
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Tieàn xöû lyù 1Tieàn xöû lyù 1
6
7
8
9b
d
Loaïi boû caùc caïnh
c
Trang Trang 36361 2 3 4 5 6 7 8 9
1
2
3
4
5
6
a
egh
Loaïi boû caùc caïnh{c, f, i}
fi
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Tieàn xöû lyù 2Tieàn xöû lyù 2
6
7
8
9b
d
Trang Trang 37371 2 3 4 5 6 7 8 9
1
2
3
4
5
6
Xöû lyù caùc caïnh{a, e}a
egh
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ToâToâ
6
7
8
9b
dk=1
k=-3/4
Trang Trang 38381 2 3 4 5 6 7 8 9
1
2
3
4
5
6
a
egh
k=1/6
k=0k=-1/2k=1/4
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Thoâng tin caïnh ña giaùcThoâng tin caïnh ña giaùc
caïnh ylower yupper xlower k
a 1 7 1 1/6
b 7 9 2 1
d 5 9 9 -3/4
e 1 5 9 0
g 1 5 7 -1/2
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g 1 5 7 -1/2
h 1 5 4 1/4
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Thoâng tin caùc caïnh ña giaùcThoâng tin caùc caïnh ña giaùc
caïnh ylower yupper xlower k
a 1 6 1 1/6
b 7 9 2 1
d 5 9 9 -3/4
e 1 4 9 0
g 1 5 7 -1/2
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g 1 5 7 -1/2
h 1 5 4 1/4
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Phöông trình ñoaïn thaúngPhöông trình ñoaïn thaúngF(x, y) = (Y2 – Y1)(x – X1) – (X2 – X1)(y – Y1)
(X2,Y2)
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(X1,Y1)
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Xaùc ñònh beân trong tam giaùc nhö theá naøo ? Xaùc ñònh beân trong tam giaùc nhö theá naøo ?
(X3,Y3)
Trang Trang 4242(X1,Y1)
(X2,Y2)
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Chieàu caùc ñænh cuûa tam giaùcChieàu caùc ñænh cuûa tam giaùcTính dieän tích tam giaùc
(X2,Y2) (X2,Y2)
( ) ( ) ( )
2yyxyyxyyx
S 213132321 −+−+−=
Trang Trang 4343
S>0 S<0(X1,Y1)
(X3,Y3)
(X1,Y1)
(X3,Y3)
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Thuaät toaùnThuaät toaùn1. Tìm xmin, xmax, ymin, ymax
2. Laëp y : ymin … ymax, x : xmin … xmax
Neáu (x, y) naèm beân trong tam giaùc thìToâ (x, y)
y
Trang Trang 4444xmin xmax
ymin
ymax