, . , 1, 2 . . : ( 10)
(x' y' 1) = (x y 1)∙M1
(x' y' 1) = (x y 1) ∙M2
(x' y' 1) = (x y' 1) ∙M3
(x' y' 1) = (((x y 1) ∙M1) ∙M2) ∙M3
,
(x' y' 1) = (x y 1)∙ (M1 ∙M2 ∙M3)
(x' y' 1) = (x y 1) ∙M transform
, . . . , , .
3- - . , , , , , , .
. , .
, , , .
? , , . . .
. , (, ) . .
0, 0 |
β |
β |
, b |
v (- - b) v R (β) v T (a b) |
() , . , , . . .
3 ():
1) (- - b) (, b) ;
2) β => R(β);
3) , . . - , - (, b).
:
(-, -b)∙R(β)∙T(a, b).
, , , . . . , - .
|
|
5 -( 11).
, . . , ,
∙ ־¹ = 1.
־¹ = ∙ , || - , ; .
:
־¹ =
, :
6 ?
.
1. . .
2. . , () , ( , , ∞-). a, b, c d. l m , , ( 12).
3. . , . 12
(-) (p):
(v) (n)
( , w=0)
,
. . (. ), 12. x 2 x 2 . , x. ( ). y. , , ! . 13 ( ) ..
: ) - 0; ) Q n, v Mtransform
:
.
. ,..:
n ∙ v = 0
n' ∙ v' = 0,
, , . , .
n' = n ∙ Q transform, v' = v ∙ M transform,
(n ∙ Q t ransform ) ∙ (v ∙ M transform) = 0
|
|
n v: n = (A, B), v = (x, y), ; ,
(A B 0) ∙ (Q transform ∙ M transform) ∙ (x y 0) = 0.
, Q transform ∙ M transform = E = 1,
Q transform = (M־¹transform).
, n v M , .
. . 14. , - .
-. . -. .
, - , - .
, :
.