1
0
mirror of https://github.com/Pomax/BezierInfo-2.git synced 2025-09-01 20:33:34 +02:00

formula fix

This commit is contained in:
Pomax
2020-08-22 10:23:36 -07:00
parent ad5da1f088
commit 87aaff414d
30 changed files with 74 additions and 74 deletions

View File

@@ -248,6 +248,18 @@ First, let's just do that translation step as a "preprocessing" operation so we
\cdot
\left ( x_4 - \frac{x_2 \cdot y_4}{y_2} / x_3-\frac{x_2 \cdot y_3}{y_2} \right )
\end{matrix}
\right ) = \left (
\begin{matrix}
x_{43}
\\
\\
\frac{y_4}{y_2}
+
x_{43}
\left ( 1 - \frac{y_3}{y_2} \right )
\end{matrix}
\right ),\textit{ where } x_{43} = \left (
x_4 - \frac{x_2 \cdot y_4}{y_2} \middle / x_3-\frac{x_2 \cdot y_3}{y_2}
\right )
\]
@@ -256,16 +268,17 @@ Suddenly things look a lot simpler: the mapped x is fairly straight forward to c
\[
... = \left (
\begin{matrix}
\left ( x_4 - x_2 \cdot y_{42} \right ) / \left ( x_3- x_2 \cdot y_{32} \right )
x_{43}
\\
\\
y_{42}
+
x_{43}
\left ( 1 - y_{32} \right )
\cdot
x
\end{matrix}
\right ),\textit{ where } y_{32} = \frac{y_3}{y_2},\textit{ and } \ y_{42} = \frac{y_4}{y_2}
\right ), \textit{ where } x_{43} = \left (
\frac{x_4 - x_2 \cdot y_{42}}{x_3 - x_2 \cdot y_{32}}
\right ), \textit{ } y_{42} = \frac{y_4}{y_2}, \textit{ and } y_{32} = \frac{y_3}{y_2}
\]
That's kind of super-simple to write out in code, I think you'll agree. Coding math tends to be easier than the formulae initially make it look!