Transformation Matrix
( translation, scaling, shearing, refraction, reflection )
M
A
A'
M
^{-1}
(determinant)
(trace)
norm
⇒
(trace)
(det)
Reflection/refraction Plane Equ
k1x+l1y+m1z+n1=0
refraction matrix
n= -1
for reflection
x +
y +
z +
= 0
n (refractive index)
Mirror plane
x +
y +
z +
= 0
shear matrix
translation matrix
scaling matrix
click
zshear
yshear
xshear
click
tra14 : X-direction
sca11:x-direct
tra24 : Y-direction
sca22:y-direct
tra34 : Z-direction
sca33:z-direct
(she44)
tr44: (either 1 or 0 )
Rotation
z-axis
y-axis
x-axis
click
(angle in degree +/-)
Reflection of a
point (x0,y0,z0)
by a plane
point
(x0)
(y0)
(z0)
Equn of plane
x +
y +
z +
= 0
Reflected point
(x10)
(y10)
(z10)