TRANSFORMARI 2D:

*Rotatia fata de origine a unui punct P(x,y):[x y]=[x y]*[ cos(u) sin(u)] [ -sin(u) cos(u)]

*O scalare de origine urmata de o rotatie fata de origine:[x y]=[x y]*[ sx 0 ] *[ cos(u) sin(u)] [0 sy] [-sin(u) cos(u)]

*Translatia:[x y 1]=[x y 1]*[1 0 0] [0 1 0] [tx ty 1]

*Scalarea fata punctual F(xf, yf):[x y 1]=[ x y 1] * [1 0 0] * [sx 0 0 ] * [1 0 0] [0 1 0] [0 sy 0] [ 0 1 0] [-xf -yf 1] [0 0 1] [xf yf 1]

*Rotatia fata de origine:[x y 1]=[x y 1] * [cos(u) sin(u) 0] [-sin(u) cos(u) 0] [0 0 0]

*Rotatia fata de punctual F(xf,yf):[x y 1]=[x y 1] * [1 0 0] * [cos(u) sin(u) 0] * [1 0 0] [0 1 0] [-sin(u) cos(u) 0] [0 1 0] [-xf -yf 1] [0 0 1] [xf yf 0]

REFLEXIAa)Fata de OX [x y 1]=[x y 1] * [1 0 0] [0 -1 0] [0 0 1]b) fata de OY [x y 1]=[x y 1 ] * [-1 0 0] [0 1 0] [0 0 1]

c)fata de origine

[x y 1]=[x y 1 ] * [-1 0 0] [0 -1 0] [0 0 1]

d)fata de dreapta x=y(prima bisectoare):[x y 1]=[x y 1] * [0 1 0] [1 0 0] [0 0 1]

FORFECAREAa)fata de axa OX:[x y 1]=[x y 1] * [1 0 0] [FX 1 0] [0 0 1]

b)fata de axa oy:[x y 1]=[x y 1] * [1 FY 0] [0 1 0] [0 0 1]c)Cazul general:[x y 1]=[x y 1] * [1 Fy 0] [Fx 1 0] [0 0 1]

TRANSFORMARI 3D:

*Translatia: [1 0 0 0][x y z 1]=[x y z 1]*[0 1 0 0] [0 0 1 0] [tx ty tz 1]

*Scalarea:

[sx 0 0 0][x y z 1]=[x y z 1]*[0 sy 0 0] [0 0 sz 0] [0 0 0 1]

*Scalarea fata de un punct fix oarecare:

T(-xF,-yF,-zF)*S(sx,sy,sz)*T(xF,yF,zF)=[sx 0 0 0] [0 sy 0 0] [0 0 sz 0] [(1-sx)*xF (1-sy)*yF (1-sz)*zF 1]

*Rotatiaa)In jurul axei Ox: [1 0 0 0 ][x y z 1]=[x y z 1]*[0 cos(u) sin(u) 0] [0 -sin(u) cos(u) 0] [0 0 0 1]

b)in jurul axei oy: [cos(u) 0 sin(u) 0 ][x y z 1]=[x y z 1]*[0 1 0 0] [-sin(u) 0 cos(u) 0] [0 0 0 1]

c)In jurul axei oz: [cos(u) sin(u) 0 0 ][x y z 1]=[x y z 1]*[-sin(u) cos(u) 0 0] [0 0 1 0] [0 0 0 1]

Forfecarea

[x y z 1]=[x y z 1]*[1 0 shx 0] [0 1 shy 0] [0 0 1 0] [0 0 0 1]

REFLEXIA

[X y z 1]=[x y z 1] * [1 0 0 0] [0 1 0 0] [0 0 -1 0] [0 0 0 1]