// SPDX-License-Identifier: MIT
// Copyright (c) 2026 Incoprea
// Locate a point by approximate curve distance
// Not compiled or tested in-world
// Setup: Use a spare owned prim. Set control points and FRACTION in zero through one. Touch for owner-only results.
// Stop / restore: Disable/remove. No scene properties change.
// Notes: Twenty segments approximate distance; interpolating between samples introduces error. Useful for even travel, not exact arc-length inversion.
// License: see LICENSE in this distribution.
// Original Incoprea. MIT.
vector A=<0.0,0.0,0.0>;
vector B=<1.0,8.0,0.0>;
vector C=<3.0,-2.0,0.0>;
vector D=<10.0,0.0,0.0>;
float FRACTION=0.5;
vector curve(float t)
{
    float u=1.0-t;
    return u*u*u*A+3.0*u*u*t*B+3.0*u*t*t*C+t*t*t*D;
}
default
{
    touch_start(integer detectedCount)
    {
        if(llDetectedKey(0)!=llGetOwner())return;
        if(FRACTION<0.0||FRACTION>1.0)
        {
            llOwnerSay("Fraction must be0..1.");
            return;
        }
        list points=[A];
        list lengths=[0.0];
        float total;
        vector last=A;
        integer i;
        for(i=1;i<=20;++i)
        {
            vector p=curve((float)i/20.0);
            total+=llVecDist(last,p);
            points+=[p];
            lengths+=[total];
            last=p;
        }
        float wanted=total*FRACTION;
        integer at=1;
        while(at<20&&llList2Float(lengths,at)<wanted)++at;
        float low=llList2Float(lengths,at-1);
        float span=llList2Float(lengths,at)-low;
        float mix=0.0;
        if(span>0.000001)mix=(wanted-low)/span;
        vector first=llList2Vector(points,at-1);
        llOwnerSay("Approximate point="+(string)(first+(llList2Vector(points,at)-first)*mix));
    }
}