info/BezierInfo-2
1
0
Fork 0
mirror of https://github.com/Pomax/BezierInfo-2.git synced 2025-08-20 07:21:43 +02:00
Code Issues Releases Wiki Activity

Edits to intersections section (#192)

Browse Source 
* Edits to intersections section

* One more
This commit is contained in:
Simon Cozens
2019-06-11 01:40:43 +01:00
committed by Pomax
parent 9114a00913
commit 1c3622c54d
1 changed files with 3 additions and 3 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
components/sections/intersections/content.en-GB.md
View File

@@ -6,7 +6,7 @@ We'll do this in steps, because it's a bit of a journey to get to curve/curve in
### Line-line intersections
if we have two line segments with two coordinates each, segments A-B and C-D, we can find the intersection of the lines these segments are an intervals on by linear algebra, using the procedure outlined in this [top coder](http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=geometry2#line_line_intersection) article. Of course, we need to make sure that the intersection isn't just on the lines our line segments lie on, but also on our line segments themselves, so after we find the intersection we need to verify it lies without the bounds of our original line segments.
If we have two line segments with two coordinates each, segments A-B and C-D, we can find the intersection of the lines these segments are an intervals on by linear algebra, using the procedure outlined in this [top coder](http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=geometry2#line_line_intersection) article. Of course, we need to make sure that the intersection isn't just on the lines our line segments lie on, but actually on our line segments themselves. So after we find the intersection, we need to verify that it lies without the bounds of our original line segments.
The following graphic implements this intersection detection, showing a red point for an intersection on the lines our segments lie on (thus being a virtual intersection point), and a green point for an intersection that lies on both segments (being a real intersection point).
@@ -16,7 +16,7 @@ The following graphic implements this intersection detection, showing a red poin
### Implementing line-line intersections
Let's have a look at how to implement a line-line intersection checking function. The basics are covered in the article mentioned above, but sometimes you need more function signatures, because you might not want to call your function with eight distinct parameters. Maybe you're using point structs or the line. Let's get coding:
Let's have a look at how to implement a line-line intersection checking function. The basics are covered in the article mentioned above, but sometimes you need more function signatures, because you might not want to call your function with eight distinct parameters. Maybe you're using point structs for the line. Let's get coding:
```
lli8 = function(x1,y1,x2,y2,x3,y3,x4,y4):
@@ -47,4 +47,4 @@ Curve/line intersection is more work, but we've already seen the techniques we n
<Graphic title="Quadratic curve/line intersections" setup={this.setupQuadratic} draw={this.draw}/>
<Graphic title="Cubic curve/line intersections" setup={this.setupCubic} draw={this.draw}/>
Curve/curve intersection, however, is more complicated. Since we have no straight line to align to, we can't simply align one of the curves and be left with a simple procedure. Instead, we'll need to apply two techniques we've not covered yet: de Casteljau's algorithm, and curve splitting.
Curve/curve intersection, however, is more complicated. Since we have no straight line to align to, we can't simply align one of the curves and be left with a simple procedure. Instead, we'll need to apply two techniques we've met before: de Casteljau's algorithm, and curve splitting.