info/BezierInfo-2
1
0
Fork 0
mirror of https://github.com/Pomax/BezierInfo-2.git synced 2025-08-30 11:40:27 +02:00
Code Issues Releases Wiki Activity

spell check

Browse Source
This commit is contained in:
Pomax
2020-09-26 15:55:13 -07:00
parent 6d3f6c4de4
commit 5fe5878eaa
17 changed files with 121 additions and 121 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
docs/chapters/curvefitting/content.en-GB.md
View File

@@ -249,7 +249,7 @@ Now, given the above derivative, we can rearrange the terms (following the rules
Here, the "to the power negative one" is the notation for the [matrix inverse](https://en.wikipedia.org/wiki/Invertible_matrix). But that's all we have to do: we're done. Starting with **P** and inventing some `t` values based on the polygon the coordinates in **P** define, we can compute the corresponding Bézier coordinates **C** that specify a curve that goes through our points. Or, if it can't go through them exactly, as near as possible.
So before we try that out, how much code is involved in implementing this? Honestly, that answer depends on how much you're going to be writing yourself. If you already have a matrix maths library available, then really not that much code at all. On the other hand, if you are writing this from scratch, you're going to have to write some utility functions for doing your matrix work for you, so it's really anywhere from 50 lines of code to maybe 200 lines of code. Not a bad price to pay for being able to fit curves to prespecified coordinates.
So before we try that out, how much code is involved in implementing this? Honestly, that answer depends on how much you're going to be writing yourself. If you already have a matrix maths library available, then really not that much code at all. On the other hand, if you are writing this from scratch, you're going to have to write some utility functions for doing your matrix work for you, so it's really anywhere from 50 lines of code to maybe 200 lines of code. Not a bad price to pay for being able to fit curves to pre-specified coordinates.
So let's try it out! The following graphic lets you place points, and will start computing exact-fit curves once you've placed at least three. You can click for more points, and the code will simply try to compute an exact fit using a Bézier curve of the appropriate order. Four points? Cubic Bézier. Five points? Quartic. And so on. Of course, this does break down at some point: depending on where you place your points, it might become mighty hard for the fitter to find an exact fit, and things might actually start looking horribly off once there's enough points for compound [floating point rounding errors](https://en.wikipedia.org/wiki/Round-off_error#Floating-point_number_system) to start making a difference (which is around 10~11 points).