Interpolation/Spline/Vectors

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Summary

Function: vector pSpline( list v, float t, integer Loop );

B-Spline Interpolation between four vector points in a list of vectors that define a path.
Returns a vector

• list v
• float t Ranges between [0, 1]
• integer Loop Whether the list is a curved line or loops into a closed shape.

Specification

vector pSpline(list v, float t, integer Loop) {
    integer l = llGetListLength(v); t *= l-1;
    integer f = llFloor(t); t -= f;
    float t2 = t * t; float t3 = t2 * t;
    return (
      ( (-t3 + (3.*t2) - (3.*t) + 1.) * llList2Vector(v, pIndex(f-1,l,Loop)) )
    + ( ((3.*t3) - (6.*t2) + 4.) * llList2Vector(v, pIndex(f,l,Loop)) )
    + ( ((-3.*t3) + (3.*t2) + (3.*t) + 1.) * llList2Vector(v, pIndex(f+1,l,Loop)) )
    + ( t3 * llList2Vector(v, pIndex(f+2,l,Loop)) )
    ) / 6.0;
}
integer pIndex( integer Index, integer Length, integer Loop) {
    if(Loop) return Index % Length;
    if(Index < 0) return 0;
    if(Index > --Length) return Length;
    return Index;
}
// Released into public domain. By Nexii Malthus.

Examples

//Quick Dirty Example By To-mos Codewarrior (tomos.halsey)
integer LINK_cube;integer LINK_1;
integer LINK_2;   integer LINK_3;
integer LINK_4;   integer LINK_5;
integer LINK_6;   integer LINK_7;
 
vector pos_1;vector pos_2;
vector pos_3;vector pos_4;
vector pos_5;vector pos_6;
vector pos_7;
 
getlinks()
{
    integer total=llGetNumberOfPrims()+1;
    string name;
    while((total--)-1)
    {
        name=llGetLinkName(total);
        if(name == "Cube")LINK_cube = total;
        if(name == "1")   LINK_1 = total;
        if(name == "2")   LINK_2 = total;
        if(name == "3")   LINK_3 = total;
        if(name == "4")   LINK_4 = total;
        if(name == "5")   LINK_5 = total;
        if(name == "6")   LINK_6 = total;
        if(name == "7")   LINK_7 = total;
    }
}
 
getPositions()
{
    pos_1 = llList2Vector(llGetLinkPrimitiveParams(LINK_1, [PRIM_POS_LOCAL]), 0);
    pos_2 = llList2Vector(llGetLinkPrimitiveParams(LINK_2, [PRIM_POS_LOCAL]), 0);
    pos_3 = llList2Vector(llGetLinkPrimitiveParams(LINK_3, [PRIM_POS_LOCAL]), 0);
    pos_4 = llList2Vector(llGetLinkPrimitiveParams(LINK_4, [PRIM_POS_LOCAL]), 0);
    pos_5 = llList2Vector(llGetLinkPrimitiveParams(LINK_5, [PRIM_POS_LOCAL]), 0);
    pos_6 = llList2Vector(llGetLinkPrimitiveParams(LINK_6, [PRIM_POS_LOCAL]), 0);
    pos_7 = llList2Vector(llGetLinkPrimitiveParams(LINK_7, [PRIM_POS_LOCAL]), 0);
}
 
vector bSpline(list v, float t, integer Loop) {
    integer l = llGetListLength(v); t *= l-1;
    integer f = llFloor(t); t -= f;
    float t2 = t * t; float t3 = t2 * t;
    vector out=(
      ( (-t3 + (3.*t2) - (3.*t) + 1.) * llList2Vector(v, pIndex(f-1,l,Loop)) )
    + ( ((3.*t3) - (6.*t2) + 4.) * llList2Vector(v, pIndex(f,l,Loop)) )
    + ( ((-3.*t3) + (3.*t2) + (3.*t) + 1.) * llList2Vector(v, pIndex(f+1,l,Loop)) )
    + ( t3 * llList2Vector(v, pIndex(f+2,l,Loop)) )
    ) / 6.0;
    llSetText(
        "time: "+(string)t+"\n"+
        "vector pos: "+(string)out
    ,<1.0,1.0,1.0>,1.0);
    return out;
}
integer pIndex( integer Index, integer Length, integer Loop) {
    if(Loop) return Index % Length;
    if(Index < 0) return 0;
    if(Index > --Length) return Length;
    return Index;
}
 
interpolate()
{
    getPositions();
 
    float t;
    for(t = 0; t < 1; t += 0.001)
    {
        llSetLinkPrimitiveParamsFast(LINK_cube, [PRIM_POS_LOCAL,bSpline([pos_1,pos_2,pos_3,pos_4,pos_5,pos_6,pos_7,pos_7,pos_7],t,0)]);
    }
}
 
default
{
    state_entry()
    {getlinks();}
 
    touch_start(integer num)
    {interpolate();}
}