Interpolation between two 3D points?
- by meds
I'm working with some splines which define a path a character follows (you can see a gameplay video here to get a better understanding of what's going on: http://www.youtube.com/watch?v=BndobjOiZ6g). Basically the characters 'forward' look direction is set to the 'forward' direction of the spline and when players tilt their phone left and right the character is strafed along its 'right' coordinate.
The issue with this is (rather obviously) in performance, interpolating over a spline to find the nearest position and tangent relative to the player is an incredibly costly operation. To get by this I cache a finite number of positions in what I call 'SplineDetails', the class is as follows:
public class SplineDetails
{
public SplineDetails()
{
Forward = Vector3.forward;
Position = Vector3.one * float.MaxValue;
Alpha = -1;
}
public float Alpha; // [0,1] measured along length of spline where 0 is the initial point and 1 is the end point of the spline
public Vector3 Position; // the point of the spline at this alpha
public Vector3 Forward; // the forward tangent of the spline at this alpha
}
I populate this with say 30 coordinates and I can give a rough estimate of a coordinate and 'forward' based on a position past in. It's not as accurate but it's much faster.
But now I'd like to make the system work better by estimating positions and 'forward' directions by interpolating between two of the cached points though I'm stuck trying to figure out some logic.
My first problem is, how can I determine between which two points the object is? Given each point can be placed at different intervals along the spline it could mean that two points in front or behind the object can be closer to the object.
The other problem is to figure out the proportion between the two paths it's between, i.e. if there is a point a at coordinate (0,0,0) and point b at coordinate (1,0,0) if the object is at position (0.5,0,0) then the result it should give is '0.5' (as it is equal distance away from point a and point b). That's a simple example, but what if the object is at coordinate (0.5,3,0) for example?
