Cálculo de vetor normal

Cálculo de Vetor Normal

Realize o cálculo do vetor normal dos objetos abaixo:

a) glBegin(GL_QUADS);

glVertex3i(200,100,100); (x1,y1,z1)

glVertex3i(200,200,100); (x2,y2,z2)

glVertex3i(200,200,0); (x3,y3,z3)

glVertex3i(200,100,0); (x4,y4,z4)

glEnd();

Vetor1:

Xvet1 = 200 – 200 = 0

Yvet1 = 200 – 100 = 100

Zvet1 = 100 – 100 = 0

Vetor2:

Xvet2 = 200 – 200 = 0

Yvet2 = 200 – 200 = 0

Zvet2 = 0 – 100 = -100

|v1| = √02 + 1002 + 02

|v1| = 100

|v2| = √02 + 02 + (-100)2

|v2| = 100

Vet1= (0/100, 100/100, 0/100) = (0, 1, 0)

Vet2= (0/100, 0/100, -100/100) = (0, 0, -1)

nx = 1 . (-1) – 0 . 0 = -1

ny = 0 . 0 – 0 . (-1) = 0

nz = 0 . 0 – 1 . 0 = 0

Resultado: Vetor Normal = (-1, 0, 0)

b) glBegin(GL_QUADS);

glVertex3i(100,200,0); (x1,y1,z1)

glVertex3i(100,200,100); (x2,y2,z2)

glVertex3i(200,200,100); (x3,y3,z3)

glVertex3i(200,200,0); (x4,y4,z4)

glEnd();

Vetor1:

Xvet1 = 100 – 100 = 0

Yvet1 = 200 – 200 = 0

Zvet1 = 100 – 0 = 100

Vetor2:

Xvet2 = 200 – 100 = 100

Yvet2 = 200 – 200 = 0

Zvet2 = 100 – 100 = 0

|v1| = √02 + 02 + 1002

|v1| = 100

|v2| = √1002 + 02 + 02

|v2| = 100

Vet1= (0/100, 0/100, 100/100) = (0, 0, 1)

Vet2= (100/100, 0/100, 0/100) = (1, 0, 0)

nx = 0 . 0 – 1 . 0 = 0

ny = 1 . 1 – 0 . 0 = 1

nz = 0 . 0 – 0 . 1 = 0

Resultado: Vetor Normal = (0, 1, 0)

c) glBegin(GL_QUADS);

glVertex3i(100,100,0);