qdwang@sohu.com

Interior-Defined

Boundary-Defined

123

1.1.1

P4P0P3P2P1

1.2

113223P4

1 xmin,ymin,xmax,ymax

2PPPi ;PPi ;P

P=P0P1PnP0Framebuffer(x,y)(x,y) for y:= ymin to ymax do for x:= xmin to xmax do if inside(p, x, y) then setpixel(framebuffer, x, y, polygon-color) else setpixel(framebuffer, x, y, back-color);

P

1.3

yk+1ykykyk+1P

y=yky=yk+1PPP{yk , yk+1}PP zPP

ykPX1,X2,.XL

L(Xk, Xk+1),k=1,3,5PP

dd=e-1PPr-1Pry=dy=exexd(mr)

PPPi ;P (yi+1-yi)*(yi-1-yi)>0 Pi ;P

()

3x x(2,4,9,13)24913

p1,p3,p4,p5 y=7(2,7,13)(7,7)(2,7,7,13)p2p6p1p2p3p4p5p6p1p2p3p4p5p6

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

10

11

P2(5,1)

E

P3(11,3)

D

P4(11,8)

G

F

C

B

P5(5,5)

P6(2,7)

A

P1(2,2)

(AET)x xxx()ymaxymax

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

10

11

P2(5,1)

E

P3(11,3)

D

P4(11,8)

G

F

C

B

P5(5,5)

P6(2,7)

A

P1(2,2)

(ET)yminyminxxxxymaxymax

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

10

11

P2(5,1)

E

P3(11,3)

D

P4(11,8)

G

F

C

B

P5(5,5)

P6(2,7)

A

P1(2,2)

ETyETyAELyETAELwhile AELET do begin AELxmin AELx if y=ymaxthen AEL AELx=x+1/m y=y+1yETAEL endend of algorithm

1.4 MM (x,y)

1y=eM for x:= xmin to xmax do setpixel(framebuffer, x, e, M);2xi, for i:= 1 to m do for x:= xi to xmax do complement(framebuffer, x, e) y=e

1.5

1boundary-colorP2boundary-colorx

For y:= ymin to ymax doBegin interior-point := false; for x:= xmin to xmax do begin if getpixel(framebuffer,x,y) = boundary-color then interior-point = not interior-point; if interior-point then setpixel(framebuffer,x,y,polygon-color) else setpixel(framebuffer,x,y,background-color); endend

2. ()

2.1 484

8

2.2 4 procedure flood-fill-4(x,y) begin if getpixel(framebuffer,x,y) = old-color then begin setpixel(framebuffer,x,y,new-color); flood-fill-4(x,y+1); flood-fill-4(x,y-1); flood-fill-4(x-1,y); flood-fill-4(x+1,y); endend of algorithm;

4

2.3

282112272620191125182423171683357234373936384143454042442215141051396302913332431

while do begin xleft xright ifxleftxxright then goto 2 xleftxxright endend of algorithm

2.4

3. (aliasing)(antialiasing)

3.1

3.2 2*23*3()

5)D2/2m4)D - m/21 - D2/m

0

1

1

2

2

3

3

4

4

5

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11

1 577 9881616P88

bufferbxi, yixi+1, yic90 x, yydn

buffer

22.4.2BB{a, b, c, d, e, f, e, g, h, I, j, k ,a, l}

polyline

3880~701 B B8{000012344400012344440666666}

xy45

4676372X7272X72X6763/8=4.4

Bezier/

AppleMicrosoftTrueTypeWindowsMs-WindowsCAD

CADCAD

2 =10-6

11P1P2Q1Q2P(t)=A+Bt (0 t 1)Q(s)=C+Ds (0 s 1)A=P1B=P2-P1C=Q1D=Q2-Q1A+Bt=C+Ds s, tti, siP(ti)=A+Bti

st A+Bt=C+Ds(C D) (A+Bt)=(C D) (C+Ds)C DCD

2 f(x, y)=0, (x, y)=(x1+t(x2-x1), y1+t(y2-y1)), f(x1+t(x2-x1), y1+t(y2-y1))=0at2+bt+c=0t

3 /NURBS

4 P(u, w)=A+uB+wCQ(t)=D+tERR=P(u, w)=Q(t)A+uB+wC=D+tEB CB CA+uB+wC=B CD+tE

B CBC B CA=B CD+tE

5

6

21 P(u, w), Q(s, t), u, w, s, t[0, 1]P(u, w)-Q(s, t)=0u=0, u=1, w=0, w=1, s=0, s=1, t=0, t=1

AB 1AB 2BA 3yx 4ABAB

2 1 Ax2+By2+Cz2+2Dxy+2Eyz+2Fxz+2Gx+2Hy+2Iz+J=0

XOYz=0z

z=0

2

ppp.b, p.wss.c, s.rplane_sphere_intersect(p, s)plane p;sphere s;{ d= if(abs(d)=s.r) { s.c-d * p.w;} else if (abs(d)>s.r) { } else { c=s.c-d * p. w; r=sqr t(s.r2-d2); w=p.w; }}

3 x(s,t), y(s,t), z(s,t) ax+by+cz+d=0st ax(s,t)+by(s,t)+cz(s,t)+d=0 xoy x*, y*, z*=x*(s,t), y*(s,t), z*(s,t) z*(s, t)=0

123Bezier

1 P(x, y, z)P1(x1, y1, z1)P2(x2,y2,z2)PP1P2 d2=(x-x1)2+(y-y1)2+(z-z1)2-[(x2-x1)(x-x1)+(y2-y1)(y-y1)+(z2-z1)(z-z1)]2/[(x2-x1)2+(y2-y1)2+(z2-z1)2]d2

2 (x, y, z)(x0,y0,z0)r12 (x) ax+by+cz+d=0x0, y0r1 2P(x, y)P:Px0, y0r

P

3 P(x, y, z)Q(t)=(x(t), y(t), z(t))1tPQ(t) R(t)=(P-Q(t))(P-Q(t))=|P-Q(t)|22t[01]3Q(t)P

4 P(x, y, z)ax+by+cz+d=0 d=

d<

1P0P1P2PnVi=Pi-P0, i=1, 2, , n, Vn+1=V1P0ViVi+1(i=1, 2, , n)

2 P0P1P2P3P4P5P0PiVi=Pi-P0 PiP0Pi+1=ai P02.5.3(a) P02.5.3(b)aiSi=Vi Vi+1, Ci=ViVi+1tg(ai)=|Si|/Ciai=arctg(|Si|/Ci)ai

3

4/P(x0, y0, z0)Q(x, y, z)=0|Q(x0, y0, z0)|< BezierB

5ax+by+cz+d=0ax+by+cz+d

xyxminxxmaxyminyymaxxminxxmaxyminyymaxzminzzmax

BezierBNURBS