rotx

roty

rotz

Løsning

Rotationsskydere

Parallelforskydningsskydere

Koordinater for tandrække

for

tandpkt

xkoor

ykoor

zkoor

Hmatrix:

deltaz = -3 (slider from -5 to 5, step 0.001)
deltay = -1.25 (slider from -5 to 5, step 0.001)
deltax = -1 (slider from -5 to 5, step 0.001)
vx = 1.5707963267948966 rad (slider from 0 to 6.283185307179586, step 0.1°)
B17: cos(vx)
C17: (-sin(vx))
B18: sin(vx)
C18: cos(vx)
A16: 1
B16: 0
C16: 0
A17: 0
A18: 0
Rx: {{A16, B16, C16}, {A17, B17, C17}, {A18, B18, C18}}
vy = 2.373647782712288 rad (slider from 0 to 6.283185307179586, step 0.1°)
A20: cos(vy)
A22: sin(vy)
C20: (-sin(vy))
C22: cos(vy)
vz = 5.515240436302081 rad (slider from 0 to 6.283185307179586, step 0.1°)
A24: cos(vz)
A25: sin(vz)
B24: (-sin(vz))
B25: cos(vz)
A21: 0
B20: 0
B21: 1
B22: 0
C21: 0
Ry: {{A20, B20, C20}, {A21, B21, C21}, {A22, B22, C22}}
A26: 0
B26: 0
C24: 0
C25: 0
C26: 1
Rz: {{A24, B24, C24}, {A25, B25, C25}, {A26, B26, C26}}
Rotmatrix: ((Rx * Ry) * Rz)
A3: -5
A4: -4
A5 = -3
B5: sin(A5)
A6 = -2
A7 = -1
A8 = 0
B8: sin(A8)
A9 = 1
A10 = 2
A11 = 3
B11: sin(A11)
A12 = 4
A13 = 5
C3: 4
C4: 5
C5: 5
C: (A5, B5, C5)
C6: 4
C7: 3
C8: 3
F: (A8, B8, C8)
C9: 4
C10: 5
C11: 5.5
I: (A11, B11, C11)
C12: 5
C13: 4
B3: 0.6
A: (A3, B3, C3)
B4: 0.5
B: (A4, B4, C4)
B6: -0.4
D: (A6, B6, C6)
B7: -0.5
E: (A7, B7, C7)
B9: 0.6
G: (A9, B9, C9)
B10: 0.7
H: (A10, B10, C10)
B12: -0.5
J: (A12, B12, C12)
B13: -0.7
K: (A13, B13, C13)
tandpunkter: {A, B, C, D, E, F, G, H, I, J, K}
A57: -1 / sqrt(2)
A56: -1 / 2
C55: -1 / sqrt(2)
B55: -1 / 2
A55: -1 / 2
B56: -1 / 2
C56: 1 / sqrt(2)
C57: 0
B57: 1 / sqrt(2)
Hmatrix: {{A55, B55, C55}, {A56, B56, C56}, {A57, B57, C57}}
L: (A3, B3, C3)
M: (A4, B4, C4)
N: (A5, B5, C5)
O: (A6, B6, C6)
P: (A7, B7, C7)
Q: (A8, B8, C8)
R: (A9, B9, C9)
S: (A10, B10, C10)
T: (A11, B11, C11)
U: (A12, B12, C12)
V: (A13, B13, C13)
tandkurve = PolyLine({L, M, N, O, P, Q, R, S, T, U, V})
tandkurve' = Translate(Translate[ApplyMatrix[(Rotmatrix * Hmatrix), tandpunkter], Vector[(1, 2, 3)]], Vector[(deltax, deltay, deltaz)])
f = PolyLine(tandkurve')
punktdifferens: tandkurve' - {L, M, N, O, P, Q, R, S, T, U, V}
Sumafvigelseskvadrater = Sum((punktdifferens(j) * punktdifferens(j)), j, 1, 11)
A59: 90
B59: 136
C59: 316
A60: -1
B60: -2
C60: -3
tekst2: "Summen af afvigelsernes kvadrater   " + Sumafvigelseskvadrater + ""