C ++如何计算两个3D点之间的弧线

Question

I read through the forum and as I am sure this question has been asked before, but I couldn't really find what I was looking for.

My problem is the following:

I have an AI-Character moving along a spline. Should that path be blocked, the character should move in an arc around it and then continue on it's path.

For arguments sake lets assume that the spline has a length of 7000 units.

Therefore, I have two 3D (x,y,z) vectors. The first vector is the current position of the AI-bot and the second vector the position past the obstacle. For the time being lets just say: current spline position + 400 units; later on I could do a line trace to get the dimension of the obstacle etc. but for now I don't care about it.

Now I would like to compute an alternative path to avoid aforementioned obstacle - hence compute the arc between these two points - How do I do this? I am really terrible at maths but looked at projectile trajectory because I thought that it would be sort of the same, just was unable to really understand it :<

Answer 1

It doesn't have to be an arc. You can solve this problem recursively in a very simple way.

Consider you're at position A, and the obstacle is at position B. You can do the following moves:

• From current position to A+V(B[x]+height(B),0,0)
• From current position to A+V(0,B[y]+width(B),0)
• From current position to A+V(B[x]-height(B),0,0)

where V is a vector with components V(x,y,z), width(B) is the width of the obstacle and B[x] is the x component of the position of B. This way you moved around it along a rectangle. You can now smoothen the path by subdividing that rectangle in halves. 3 subdivisions are enough to make this smooth enough. To subdivide, take the middle point the first path, and draw a line to the middle of the second path. The same you do from the second path to the third one, and now your rectangle becomes an octagon. If that's not smooth enough, do a few more steps. This will create a new spline that you can use.

Answer 2

I would look at a combination of splines and the EQS system. The spline defines the ideal path to follow. The EQS system finds locations near or on the path, while still doing obstacle avoidance. EQS can return all valid destinations so you can manually order them by custom critera.

Actors set on a spline do work, but there's a whole bunch o' mess when making them stop following a spline, creating a new one at the correct point, attaching the actor the new spline, and so on.

Answer 3

I arrived at this conclusion yesterday after exactly going the messy way of adding spline points etc. The only problem i see is that I find the EQS system very difficult to understand. Not following the examples as such, but modifying it in the way I need it. Lets see, i keep you posted.