Finding a point of a triangle from two known points, one angle and two lengths

[jasmines]

Hi,

 

I'm a programmer and was just playing about with some AI for a game.

 

There is

 

a moving object

 

http://www.ahappydea...oduct_31869.htm

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which has a target point it is travelling to. It will travel to this point directly except it may need to evade a circular area. I'm trying to find the point to use as an intermediary target to evade the circle.

 

Attached is an image which shows the situation.

 

On that image:

• Point a is the target of the object
• Point b is the object itself
• Point c is the center point of the circle to avoid
• Point d is the point we're trying to find
• Points a, c and d are known
• The length of the dotted line dc is known

The circle is probably not necessary.

 

In my head ab and cd are perpendicular (??).

 

The angle inside point c (ie the angle opposite ab within the triangle abc) is known. I'll call this theta just for a moment.

 

In the triangle bcd the angle inside c (ie the angle opposite db) is half theta.

 

I keep drawing lots of pretty pictures but haven't actually got anywhere with the problem! I could probably work it out if ab was parallel to the y axis (2d space) but I cannot guarantee that it will be so there's my problem!

 

Any thoughts on the above?

 

Thanks in advance,

Kazatan

</b></b> Attached Images

[michel123456]

 

It will travel to this point directly except it may need to evade a circular area. I'm trying to find the point to use as an intermediary target to evade the circle.

 

trying to understand your preoccupation... you are at point b, you want to reach a, but you have first to escape the circle as soon as possible, is that correct?

 

The circle is probably not necessary.

 

???

 

In my head ab and cd are perpendicular (??).

 

Why? If I understand correctly, the line a-d must be tangent to the circle.

 

The angle inside point c (ie the angle opposite ab within the triangle abc) is known. I'll call this theta just for a moment.

 

O.K.

 

In the triangle bcd the angle inside c (ie the angle opposite db) is half theta.

I have a serious doubt.

Edited September 2, 2011 by michel123456