Lines, Curves and Surfaces in 3D

Parametric Equation of a Plane (Cont.)
(x 0 ,y 0 ,z 0 )
O
(f 2 ,g 2 ,h 2 )
(f 1 ,g 1 ,h 1 )
CM0268
MATLAB
DSP
GRAPHICS
522
x = x 0 + f 1 u + f 2 v
y = y 0 + g 1 u + g 2 v
z = z 0 + h 1 u + h 2 v
• A point in the plane is found by adding proportion u of one
vector to a proportion v of the other vector
• If the two vectors are have unit length and are perpendicular,
then:
f 2 1 + g 2 1 + h 2 1 = 1
f 2 2 + g 2 2 + h 2 2 = 1
f 1 f 2 + g 1 g 2 + h 1 h 2 = 0 (scalar product)
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