()
, ( ). , , , . . : |x y|. , (2*2). ; xn = xa + yc yn = xb + yd . , . : A(0, 0), B(1, 0), C(1, 1), D(0, 1), A*(0, 0), B*(a, b), C*(a + c, b + d), D*(c, d). . . . , . , : S2 = S1 * |ad - bc|. |
,
, (1, 2, 3), . , n- : n + 1. , , . : , , , z = 1. , ( , ) z = 1. z = 1 , . , 1. . |
c
m n, m x n - y:
a d ( ) (x, y) a d x y : s < 1 (x, y) s ; s > 1 - (x, y) s . q q - , (x, y). : (0, 0) ! . q = 90o. () : A(3, -1), B(4, 1), C(2, 1). 90o, , : , , : , , y = x: (m, n) a , . (m, n) a : 1) A(-m, -n) (m, n) ; 2) a; 3) A'(m, n) . , 1) - 3) . . A(x, y), B(x1, y1), C(x2, y2) D(m, n) a. P-s - A(-m, -n), Va - a, Ps - A'(m, n). , , - A(x, y): , x y ( . . 1.6). , , . () px + qy + 1 = H - . , - ; - , , , - (. 1); - () . , , . |
|
|
3.
1
30 .
(3,3), (6,3), (4,1).
1.
3 3 1 6 3 1 4 1 1 | * | 0,85 0,52 0 -0,52 0,85 0 2,46 -2,67 1 | = | 3,45 1,44 1 6,00 3,00 1 5,34 0,26 1 |
2
, 2, , , Y, , ZOX 45 XOY (zc=10, yc=0, xc=0)
|
|
0 0 0 1 1.41 0 1.41 1 0 0 2.82 1 -1.41 0 1.41 1 0 2 0 1 1.41 2 1.41 1 0 2 2.82 1 -1.41 2 1.41 1 | * | 1 0 0 0 0 1 0 0 0 0 0 -0.1 0 0 0 1 | = | 0 0 0 1 1.41 0 0 0.859 0 0 0 0.718 -1.41 0 0 0.859 0 2 0 1 1.41 2 0 0.859 0 2 0 0.718 -1.41 2 0 0.859 | = | 0 0 0 1 1.64 0 0 1 0 0 0 1 -1.64 0 0 1 0 2 0 1 1.64 2.33 0 1 0 2.79 0 1 -1.64 2.33 0 1 |
XOY , ( ). , XOY, , (1 2, 2 3, 3 4, 4 1, 5 6, 6 7, 7 8, 8 5, 1 5, 2 6, 3 7, 4 8). , .
3.
. 3-4 . . .
. Ȼ . 128..
4.
(200,-100), (100,200), (-50,300), (20,-50), (-100,100) , , , (1024,768). .
, :
- : xmin, ymin, xmax, ymax : Xmin, Ymin, Xmax, Ymax;
xmin= -50, ymin=-100, xmax=200, ymax=300
Xmin=1, Ymin=1, Xmax=1024, Ymax=768
- :
fx = (Xmax - Xmin) / (xmax - xmin)=(1024-1)/(200+50)=4.092,
fy = (Ymax - Ymin) / (ymax - ymin)=(768-1)/(300+100)= 1.9175,
fx = fy = min(fx, fy) = min(4.092, 1.9175)= 1.9175 - : (480,1),
x = Xmin + fx * (x - xmin)=1+1.9175*(200+50)=480,
y = Ymin + fy * (y - ymin)=1+1.9175*(-100+100)=1,
x, y - , x, y - .
5.
, 3 , 2 , 1 ? , 1024*768? .
= 1024*768=786432
1= 8 | 28=256 | 786432*1=786432 | 786432/1024=768 |
2= 16 | 216=65536 | 786432*2=1572864 | 1572864/1024= 1536/1024=1,5 |
3= 24 | 224 = | 786432*3=2359296 | 2359296/1024= 2304/1024=2,25 |
6.
(0,0,-10), (100,0,-100), (50,50,-100) (0,40,-80),(40,40,-80),(20,20,-120) (0,10,100) . , z- . 1, 2, 0.
(z=0) (. 2). (. 4). , .
Z- (a,c) ax + by + cz + d = 0 :
a = S(yi - yi+1) * (zi + zi+1)
b = S(zi - zi+1) * (xi + xi+1)
c = S(xi - xi+1) * (yi + yi+1).
z:= z - (a/c). .
|
|
Z- 21.
7.
(10,10,10) , XOZ , 100, (30,30,10). . (-10,10,10)?
, . l = 2. XOY (30-10)/(30-10)=tg(a), a=45..
.-. Is = Il * w(i, l) * cosna,
Is - , , Il - , 100, w(i,l) - , i l, 0,2 0,9 (..24.3 ), a - , 45 ., n - , , 5.
(30-10)/(30-10))=20/20=1,
a=45 , 45 ..
Is = 100 * 0,2*0,9 * cos5(45)=3.24, cos(45)=0,71 cos5(45) = 0.18.
(30-10)/(30-(-10))=20/40=0,5,
= pi/2 arctg(0.5) = 1.107 .
cos(1.107)=0.45
cos5 (1.107)=0.018
Is = 100 * 0,2*0,9 * cos5(1,107)=0,324.
, 10 . , .