将二次曲线转换为三次曲线

问题描述

查看，我终于明白为什么编程老师总是告诉我数学如此重要。不幸的是，我没有听。

任何人都可以提供一个更具体的 - 例如计算机语言 - y公式，用于将二次曲线转换为立方曲线？理解可能存在一些舍入误差，这很好。

给定一个由变量表示的四条曲线：

  StartX，StartY 
 ControlX，ControlY 
 EndX，EndY 
  

并且希望StartX，StartY和EndX，EndY保持不变，但现在Control1X，Control1Y和Control2X，Control2Y是一个三次曲线。

它是...

pre $ Control1X = StartX +（.66 *（ControlX - StartX））
Control2X = EndX +（.66 *（ControlX - EndX））


使用相同的基本函数来计算Control1Y和Control2Y？

解决方案

你的代码是正确的，除了你应该使用 2.0 / 3.0 而不是 0.66 。

Looking at Convert a quadratic bezier to a cubic?, I can finally understand why programming teachers always told me that math was so important. Sadly, I didn't listen.

Can anyone provide a more concrete - e.g., computer-language-y - formula for converting a quadratic curve to a cubic? Understanding that there's some rounding errors possible, which is fine.

Given a quad curve represented by variables:

StartX, StartY
ControlX, ControlY
EndX, EndY

And desiring StartX, StartY and EndX, EndY to remain the same, but to now have Control1X, Control1Y and Control2X, Control2Y of a cubic curve.

Is it...

Control1X = StartX + (.66 * (ControlX - StartX))
Control2X = EndX + (.66 * (ControlX - EndX))

With the same essential functions used to calculate Control1Y and Control2Y?

解决方案

Your code is right except that you should use 2.0/3.0 instead of 0.66.

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