I'm using bezier curves as paths for my spaceships to travel along when they are coming into dock at a station. I have a simple algorithm to calculate where the ship should be at time t along a cubic bezier curve:
public class BezierMovement{
public BezierMovement(){
// start docking straight away in this test version
initDocking();
}
private Vector3 p0;
private Vector3 p1;
private Vector3 p2;
private Vector3 p3;
private double tInc = 0.001d;
private double t = tInc;
protected void initDocking(){
// get current location
Vector3 location = getCurrentLocation();
// get docking point
Vector3 dockingPoint = getDockingPoint();
// ship's normalised direction vector
Vector3 direction = getDirection();
// docking point's normalised direction vector
Vector3 dockingDirection = getDockingDirection();
// scalars to multiply normalised vectors by
// The higher the number, the "curvier" the curve
float curveFactorShip = 10000.0f;
float curveFactorDock = 2000.0f;
p0 = new Vector3(location.x,location.y,location.z);
p1 = new Vector3(location.x + (direction.x * curveFactorShip),
location.y + (direction.y * curveFactorShip),
location.z + (direction.z * curveFactorShip));
p2 = new Vector3(dockingPoint.x + (dockingDirection.x * curveFactorDock),
dockingPoint.y + (dockingDirection.y * curveFactorDock),
dockingPoint.z + (dockingDirection.z * curveFactorDock));
p3 = new Vector3(dockingPoint.x, dockingPoint.y, dockingPoint.z);
}
public void incrementPosition() {
bezier(p0, p1, p2, p3, t, getCurrentLocation());
// make ship go back and forth along curve for testing
t += tInc;
if(t>=1){
tInc = 0-tInc;
} else if(t<0){
tInc = 0-tInc;
}
}
protected void bezier(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, double t, Vector3 outputVector){
double a = (1-t)*(1-t)*(1-t);
double b = 3*((1-t)*(1-t))*t;
double c = 3*(1-t)*(t*t);
double d = t*t*t;
outputVector.x = a*p0.x + b*p1.x + c*p2.x + d*p3.x;
outputVector.y = a*p0.y + b*p1.y + c*p2.y + d*p3.y;
outputVector.z = a*p0.z + b*p1.z + c*p2.z + d*p3.z;
}
}
The curve start point is the spaceship location, and end point is the entrance to the docking bay (red dots on diagram). The spaceship has a normalised vector for its direction, and the docking bay has another normalised vector to indicate the direction the ship must be traveling in so as to be aligned straight on to the docking bay when it arrives (the yellow lines on the diagram)
The green line is a possible path of the spaceship, and the purple circle, the spaceship's radius. Finally, the black box is the bounding box for the station.
I have two problems:
- The spaceship is supposed to only be able to turn at r radians per second
- The spaceship can't fly through the station
I assume that this translates into:
a). Finding the "curve factors" (control point lengths) that will give a path where the ship doesn't have to turn too tightly
b). Finding the spaceship location/direction from which it can't avoid colliding with the station (and creating a path to guide it out of that state, so it can get on with part a))
However, with both of these, I haven't had much luck finding a solution. I already have code to detect intersections between vectors, boxes, points and spheres, but not bezier curves yet. I also have functions to let me find the distance between two points.
Any help would be most appreciated
Thanks, James
