skFitSpline and bSplineCurve .controlPoints

hervé_pipon

Hello,
I draw a spline on sketch1:

    skFitSpline(sketch1, "spline1", {

    "points" : [

    vector( 0 , 0) * centimeter,

    vector( 100, 100) * centimeter

    ],

    "startDerivative" : vector(150 , 0) * centimeter,

    "endDerivative" : vector(0 , 150) * centimeter,

    });

test: same with code formatting

<div>&nbsp; &nbsp; skFitSpline(sketch1, "spline1", {</div><div>&nbsp; &nbsp;&nbsp;"points" : [</div><div>&nbsp; &nbsp;&nbsp;vector( 0 , 0) * centimeter,</div><div>&nbsp; &nbsp;&nbsp;vector( 100, 100) * centimeter</div><div>&nbsp; &nbsp;&nbsp;],</div><div>&nbsp; &nbsp;&nbsp;"startDerivative" : vector(150 , 0) * centimeter,</div><div>&nbsp; &nbsp;&nbsp;"endDerivative" : vector(0 , 150) * centimeter,</div><div>&nbsp; &nbsp;&nbsp;});</div>

I use a Feature to print information  :
export const main = defineFeature(function(context is Context, id is Id, definition is map)

    precondition

    {

        annotation { "Name" : "Spline", "Filter" : EntityType.EDGE, "MaxNumberOfPicks" : 1 }

        definition.selectedEdge is Query;

    }

    {    

    var sketchPlane = evOwnerSketchPlane(context, { "entity" : definition.selectedEdge });

    var data = evCurveDefinition(context, {

    "edge" : qEntityFilter(definition.selectedEdge, EntityType.EDGE),

    "returnBSplinesAsOther":false

    });                    

    var P1 = worldToPlane(sketchPlane, data.controlPoints [0]);

    var P2 = worldToPlane(sketchPlane, data.controlPoints [1]);

    var P3 = worldToPlane(sketchPlane, data.controlPoints [2]);

    var P4 = worldToPlane(sketchPlane, data.controlPoints [3]);

    println(P1);

    println(P2);    

    println(P3);

    println(P4);

    ...

when I click on this spline it prints:

(0 meter, 0 meter)

(0.5340613126754761 meter, -1.8922261703604592e-31 meter) 

(0.9994866847991959 meter, 0.5380544066429138 meter)  

(1 meter, 1 meter)



we can approximate 

(0.5340613126754761 meter, -1.8922261703604592e-31 meter)  ~~ (0.534,0)

(0.9994866847991959 meter, 0.5380544066429138 meter)  ~~ (1, 0.538)

So we have :

P1 => vector( 0 , 0) * centimeter,

P4 => vector( 100, 100) * centimeter

but if I correctly understand
P2 has to be : P1 + startDerivative / 3 => (0.5, 0)     and in fact is   (0.534,0)

P3 has to be : P4 - endDerivative / 3 => (1 , 0.5)       and in fact is  (1, 0.538)

My question is:
    Why 0.534 or  0.538, and not 0.5 ?


If someone could explain me ?