Algebra linear mudanca de base

Prévia do material em texto

Mudança de base e Transformação linear 
 
-->"normalização do vetor po" 
-->po=[-6;-8;-8]; 
-->v1=po/norm(po) 
 v1 = 
 - 0.4685213 
 - 0.6246950 
 - 0.6246950 
 
-->"para encontrar v2 isolamos o valor de A do produto escalar entre v1 e v2 " 
-->a= sqrt(64/100)*-1 
 a = 
 - 0.8 
-->v2=[a;sqrt(1-a^2);0] 
 v2 = 
 - 0.8 
 0.6 
 0. 
-->"o vetor v3 acharemos com o produtor vetorial entre v1 e v2" 
-->A1 = [ v1(2), v1(3); v2(2), v2(3)]; 
-->A2 = [ v1(3), v1(1); v2(3), v2(1)]; 
-->A3 = [ v1(1), v1(2); v2(1), v2(2)]; 
-->px = det(A1); py = det(A2); pz = det(A3); 
-->v3= [px, py, pz] 
 v3 = 
 0.3748170 0.4997560 - 0.7808688 
 
-->"Base ortonormal da imagem" 
 
-->B=[v1(1),v2(1),v3(1);v1(2),v2(2),v3(2);v1(3),v2(3),v3(3)] 
 B = 
 - 0.4685213 - 0.8 0.3748170 
 - 0.6246950 0.6 0.4997560 
 - 0.6246950 0. - 0.7808688 
 
-->"cálculo de transformação do vetor N 3D para MC em 2D" 
-->N=[0,0,0,0,0,,4,4,5,5,5,1,1,1,1,1,3,3,5,5,4,4,1,1,3,3,1,5; 
-->4,4,1,1,0,0,0,0,0,2,2,4,4,1,1,1,1,1,1,1,1,2,0,0,0,0,2; 
-->0,2,2,4,4,4,2,2,0,0,0,0,2,2,3,3,1,1,2,2,4,1,1,1,3,3,1] 
 N = 
 column 1 to 12 
 
 0. 0. 0. 0. 0. 4. 4. 5. 5. 5. 1. 1. 
 4. 4. 1. 1. 0. 0. 0. 0. 0. 2. 2. 4. 
 0. 2. 2. 4. 4. 4. 2. 2. 0. 0. 0. 0. 
 column 13 to 24 
 
 1. 1. 1. 3. 3. 5. 5. 4. 4. 1. 1. 3. 
 4. 1. 1. 1. 1. 1. 1. 1. 1. 2. 0. 0. 
 2. 2. 3. 3. 1. 1. 2. 2. 4. 1. 1. 1. 
 column 25 to 27 
 
 3. 1. 5. 
 0. 0. 2. 
 3. 3. 1. 
 
-->M=inv(B)*N 
 M = 
 
 
 column 1 to 5 
 
 - 2.4987802 - 3.7481703 - 1.8740851 - 3.1234752 - 2.4987802 
 2.4 2.4 0.6 0.6 2.774D-16 
 1.9990242 0.4372865 - 1.0619816 - 2.6237192 - 3.1234752 
 
 column 6 to 10 
 
 - 4.3728653 - 3.1234752 - 3.5919965 - 2.3426064 - 3.5919965 
 - 3.2 - 3.2 - 4. - 4. - 2.8 
 - 1.6242071 - 0.0624695 0.3123475 1.8740851 2.8735972 
 
 column 11 to 15 
 
 - 1.7179114 - 2.9673015 - 4.2166916 - 2.3426064 - 2.9673015 
 0.4 1.6 1.6 - 0.2 - 0.2 
 1.3743291 2.3738412 0.8121036 - 0.6871646 - 1.4680334 
 
 column 16 to 20 
 
 - 3.904344 - 2.654954 - 3.5919965 - 4.2166916 - 3.7481703 
 - 1.8 - 1.8 - 3.4 - 3.4 - 2.6 
 - 0.7183993 0.8433383 1.5929724 0.8121036 0.4372865 
 
 column 21 to 25 
 
 - 4.9975604 - 2.3426064 - 1.0932163 - 2.0302589 - 3.279649 
 - 2.6 0.4 - 0.8 - 2.4 - 2.4 
 - 1.1244511 0.5934603 - 0.4060518 0.3435823 - 1.2181553 
 
 column 26 to 27 
 
 - 2.3426064 - 4.2166916 
 - 0.8 - 2.8 
 - 1.9677894 2.0927284 
 
-->T=[0,1,0;0,0,1] 
 T = 
 0. 1. 0. 
 0. 0. 1. 
 
-->MC=T*M 
 MC = 
 column 1 to 5 
 
 2.4 2.4 0.6 0.6 2.774D-16 
 1.9990242 0.4372865 - 1.0619816 - 2.6237192 - 3.1234752 
 
 column 6 to 10 
 
 - 3.2 - 3.2 - 4. - 4. - 2.8 
 - 1.6242071 - 0.0624695 0.3123475 1.8740851 2.8735972 
 
 column 11 to 15 
 
 0.4 1.6 1.6 - 0.2 - 0.2 
 1.3743291 2.3738412 0.8121036 - 0.6871646 - 1.4680334 
 
 column 16 to 20 
 
 - 1.8 - 1.8 - 3.4 - 3.4 - 2.6 
 - 0.7183993 0.8433383 1.5929724 0.8121036 0.4372865 
 
 column 21 to 25 
 
 - 2.6 0.4 - 0.8 - 2.4 - 2.4 
 - 1.1244511 0.5934603 - 0.4060518 0.3435823 - 1.2181553 
 
 column 26 to 27 
 
 - 0.8 - 2.8 
 - 1.9677894 2.0927284 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Gráfico da Transformação linear