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mirror of https://github.com/Pomax/BezierInfo-2.git synced 2025-08-30 03:30:34 +02:00
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Pomax
2020-10-18 14:27:57 -07:00
parent 133105d44e
commit 0f6683ca6d
314 changed files with 11182 additions and 266 deletions

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@@ -9,12 +9,12 @@ If we know the distance between those two points, and we want a new point that i
\[
Given \left (
\begin{aligned}
p_1 &= some\ point \\
p_2 &= some\ other\ point \\
p_1 &= some~point \\
p_2 &= some~other~point \\
distance &= (p_2 - p_1) \\
ratio &= \frac{percentage}{100} \\
\end{aligned}
\right ),\ our\ new\ point = p_1 + distance \cdot ratio
\right ),~our~new~point = p_1 + distance \cdot ratio
\]
So let's look at that in action: the following graphic is interactive in that you can use your up and down arrow keys to increase or decrease the interpolation ratio, to see what happens. We start with three points, which gives us two lines. Linear interpolation over those lines gives us two points, between which we can again perform linear interpolation, yielding a single point. And that point —and all points we can form in this way for all ratios taken together— form our Bézier curve:

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@@ -9,12 +9,12 @@
\[
Given \left (
\begin{aligned}
p_1 &= some\ point \\
p_2 &= some\ other\ point \\
p_1 &= some~point \\
p_2 &= some~other~point \\
distance &= (p_2 - p_1) \\
ratio &= \frac{percentage}{100} \\
\end{aligned}
\right ),\ our\ new\ point = p_1 + distance \cdot ratio
\right ),~our~new~point = p_1 + distance \cdot ratio
\]
让我们来通过实际操作看一下:下面的图形都是可交互的,因此你可以通过上下键来增加或减少插值距离,来观察图形的变化。我们从三个点构成的两条线段开始。通过对各条线段进行线性插值得到两个点,对点之间的线段再进行线性插值,产生一个新的点。最终这些点——所有的点都可以通过选取不同的距离插值产生——构成了贝塞尔曲线