// SPDX-License-Identifier: MIT
// Copyright (c) 2026 Incoprea
// Predict first contact of two moving circular bounds
// Not compiled or tested in-world
// Setup: Use a spare owned prim. Set relative POSITION/VELOCITY and nonnegative radii. Touch for owner-only calculation output.
// Stop / restore: Remove/disable. Does not sense, collide with, or modify actual objects.
// Notes: The supplied vectors should be planar for circles; the same equation also models spheres. No live entities are tracked.
// License: see LICENSE in this distribution.
// Original Incoprea. MIT. Ideal geometry only.
vector POSITION=<8.0,2.0,0.0>;
vector VELOCITY=<-2.0,0.0,0.0>;
float R1=1.0;
float R2=1.5;
default
{
    touch_start(integer detectedCount)
    {
        if(llDetectedKey(0)!=llGetOwner())return;
        if(R1<0.0||R2<0.0)
        {
            llOwnerSay("Invalid radius.");
            return;
        }
        float radius=R1+R2;
        float c=POSITION*POSITION-radius*radius;
        if(c<=0.0)
        {
            llOwnerSay("Already touching or overlapping.");
            return;
        }
        float a=VELOCITY*VELOCITY;
        if(a<0.000001)
        {
            llOwnerSay("No relative motion.");
            return;
        }
        float b=2.0*(POSITION*VELOCITY);
        float disc=b*b-4.0*a*c;
        if(disc<0.0)
        {
            llOwnerSay("No contact on trajectories.");
            return;
        }
        float t=(-b-llSqrt(disc))/(2.0*a);
        if(t<0.0)
        {
            llOwnerSay("Contact lies in the past.");
            return;
        }
        llOwnerSay("First contact in "+(string)t+" seconds.");
    }
}