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Therefore, we can create E6 using E1 - m (E2):
b ( p y - mq y ) + c ( p z - mq z ) + d + md = 0
(6)
Let
n = ( p y - mq y )/( q y - kr y )
We can create E7 using E6 - n (E5):
c ( p z - mq z - n ) ( q z - kr z ) + d (1 - m - n + kn )=0
(7)
Let
p z - mq z - n ( q z - kr z )
n + kn -1+ m
s =
( m -1) s - p z + mq z
P y - mq y
v =
vp y + p z + s
p x
w =
With some careful manipulation, we get
(1/(1 + w 2 + v 2 ))
d = cs
b = cv
a =- cw
c =
A quadric matrix for a single plane is defined from these values using
a 2
ab
ac
ad
ab
b 2
bc
bd
ac
bc
c 2
cd
ad
bd
cd
d 2
K p =
Since this matrix is symmetrical about the leading diagonal (top left to
bottom right), we do not need to store 16 values, we can make do with just
10:
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