mirror of
https://github.com/Pomax/BezierInfo-2.git
synced 2025-08-30 19:50:01 +02:00
ascii
This commit is contained in:
@@ -11,7 +11,7 @@ Adding these ratio values to the regular Bézier curve function is fairly easy.
|
||||
The function for rational Bézier curves has two more terms:
|
||||
|
||||
\[
|
||||
Rational\ Bézier(n,t) = \frac{ \sum_{i=0}^{n} \binom{n}{i} \cdot (1-t)^{n-i} \cdot t^{i} \cdot w_i \cdot BLUE[ratio_i] }{ BLUE[ \sum_{i=0}^{n} \binom{n}{i} \cdot (1-t)^{n-i} \cdot t^{i} \cdot ratio_i ] }
|
||||
Rational~Bézier(n,t) = \frac{ \sum_{i=0}^{n} \binom{n}{i} \cdot (1-t)^{n-i} \cdot t^{i} \cdot w_i \cdot BLUE[ratio_i] }{ BLUE[ \sum_{i=0}^{n} \binom{n}{i} \cdot (1-t)^{n-i} \cdot t^{i} \cdot ratio_i ] }
|
||||
\]
|
||||
|
||||
In this, the first new term represents an additional weight for each coordinate. For example, if our ratio values are [1, 0.5, 0.5, 1] then <code>ratio<sub>0</sub> = 1</code>, <code>ratio<sub>1</sub> = 0.5</code>, and so on, and is effectively identical as if we were just using different weight. So far, nothing too special.
|
||||
|
Reference in New Issue
Block a user