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M =

m11 m12 m13 m14

m21 m22 m23 m24

m31 m32 m33 m34

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Pw Xw, Yw, Zw)

Pc Xc, Yc, Zc)

Pw Pc

Pc = R(Pw T)

R =

r11 r12 r13

r21 r22 r23r31 r32 r33

T

1 0 0 Tx

0 1 0 Ty

0 0 1 Tz

0 0 0 1

Xc

Yc

Zc

=

r11 r12 r13

r21 r22 r23

r31 r32 r33

Xw Tx

Yw Ty

Zw Tz

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Xc = RT1 (Pw T)

Yc

= RT2

(Pw T)

Zc = RT3 (Pw T)

RT1 , RT2 , R

T3

x = fXcZc

y = fYcZc

x = fRT1 (Pw T)

RT3 (Pw T)

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y = fRT2 (Pw T)

RT3 (Pw T)

x = (xim ox)sx

y = (yim oy)sy

xim = xsx

+ ox yim = ysy

+ oy

ox oy

ox =N2 oy =

M2

sx sy

xim

ym

1

=

xsx

0 ox

0 ysy

oy

0 0 1

x

y

1

(xim ox)sx = fRT1(PwT)

RT3(PwT)

(yim oy)sy = fRT2(PwT)

RT3(PwT)

xim = f sxRT1(PwT)

RT3(PwT)

+ ox yim = f syRT2(PwT)

RT3(PwT)

+ oy

M = Min Mex

Min =

xsx

0 ox

0 ysy

oy

0 0 1

Mex =

r11 r12 r13 RT1 T

r21 r22 r23 RT2 T

r31 r32 r33 RT3 T

xh

yh

w

= M

Xw

Yw

Zw

1

m11 m12 m13 m14

m21 m22 m23 m24

m31 m32 m33 m34

Xw

Yw

Zw

1

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xim =xhw

= m11Xw+m12Yw+m13Zw+m14m31Xw+m32Yw+m33Zw+m34

yim =yhw

= m21Xw+m22Yw+m23Zw+m24m31Xw+m32Yw+m33Zw+m34

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