Any good ideas on how to get the "ideal line" of a track?

WhateverMan · 2016-04-15T11:12:46

So the aproach I', creating my track at the moment is simmilar to 3d lofting, the track is a list of Segments, each segment has sideA, sideB and a center node. ?I created an AI algorythm that almost mimics the racing line behaviour, but at straights it centers to the track which is not that "ideal". So I figured why not add an ideal line node to the segmet aswell, so the AI can actually follow these points. ?In real life I know how a raceline is formed, but I would like to create a script that auto populates these "ideal nodes". So ideas are welcome. ?Here's an image of showing what I'm after. So according to the image, to draw the racing line, it needs to start from the outside of the track, go inside near apex and exit outside again. I've got a feeling that this is achievable with a DotProduct trick. Am I right?

Math and Physics Programming

Started by WhateverMan April 10, 2016 08:39 PM

10 comments, last by l0calh05t 8 years, 10 months ago

WhateverMan

Author

151

April 13, 2016 03:13 PM

I Did some GeoGebra magic today and found some usefull information, tho I'm not entirely sure on how to get the same information in Coding wise. ?As I thought I have to make use of DotProduct and CrossProduct. With DotProduct I can easly create scalar projections of Perpendicular points Using this formula:

ap = p - a
?ab = b - a

sp = dot(ap,ab.normalized)

where:

ap is the vector from a to p
ab is the vector from a to b
sp is the scalar projection of p on ab (float)

to get the actual normal point on ab we can write
normalPoint = a + (ab.normalized * sp)

Now the Cross product is the bit I dont quite get yet, it always seems to be zero or simmilar to the normalPoint, any tips?

?On the chart, my simple questions are, how to find A1, B1 and T. (Basically they would be mapped on the waypoint node as "RacingLinePoint" but first the magic...

?Edit:
The radius of the racing line comes from this formula:
ArcR_radius =? (C1T / 2) + ((A1B1 * A1B1) / 8 * C1T)

The variables are on the graph..