olatex 1746855 pbzrI8jxpWHr (PDF)
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Given:
P1 , P2 , Q, w, c, t
P1 and P2 are the two end points, Q is the point we want to get the color
for, and w is the width of the line. c is the color of the line, and t is a fully
transparent color.
# »
#»
v = P1 P2
# »
#»
u = P1 Q
#»
v · #»
u #»
#»
u #»
v
v =
| #»
v|
d = | #»
u − #»
u #»
v|
#» #»
v · #»
u #»
d = u − #» v
|v|
We are dealing with only two dimensions in a cartesian coordinate system:
q
l = #»
v 21 + #»
v 22
m=
d=
x( #»
v ) ∗ x( #»
u ) + y( #»
v ) ∗ y( #»
u)
l
#»
u 1 − m #»
v 1
d = #»
u 2 − m #»
v2
q
2
2
( #»
u 1 − m #»
v 1 ) + ( #»
u 2 − m #»
v 2)
→ The color of Q is the following:
(
c if d < w ∧ 0 <= m <= 1
t else
1
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Document ID: 0000557366.