elastic stretching or bending

[rui_fartaria]

Hello,
I could not find anything in the forum or manual about this.

Are there any transforms implemented that allow to stretch or bend a polyline according to an elastic function across the line.

What I mean is, I want to to be able to pick the end of the line and drag it so that the full polyline is transformed with decreasing intensity as distance increases (along the line) from the end of the line.

Also, this would be valid for any point of the polyline.

Thank you in advance for your attention.

[Husky]

Hi

Are there any transforms implemented that allow to stretch or bend a polyline according to an elastic function across the line.

You can't "bend" a polyline but you can "bend" a spline ...

What I mean is, I want to to be able to pick the end of the line and drag it so that the full polyline is transformed with decreasing intensity as distance increases (along the line) from the end of the line.

You can design a polyline with a start width of ... let say zero and an end width of 25. If you then drag the end it will behave like a rubber line ...

[rui_fartaria]

HI,
I was trying to experiment with the behaviour you explained (progressive width) but could not see it. Only the last segment moved. Not the whole polyline.

I will have to implement this myself. If I succeed i'll try to make it available as a script/macro.

Thanks.

[CVH]

Very interesting,
Keep us posted.
Regards,
CVH

[rui_fartaria]

What I have so far....

paste this into the ecmascript console or run it as a script.

it will:
1. create a horizontal polyline from x=0 to x=100 with 100 vertices
2. will "bend" left tip with offset (20,20)
2. will "bend" rigth tip with offset (-20,20)

This bending model uses exponential decay. I've been experimenting with others but this is the best I found for my objectives. If anyone can tell about any literature on this (plastic bending mathematical models) I would very much appreciate it.

Final result should be:
https://pasteboard.co/JkXBUm8.png

The script:

Code: Select all

function makeExponentialDecay(factor) {
    return function (length) {
        var r = Math.exp(-factor*length);
        return r < 0.001 ? 0.0 : r;
    }
}

function makeExponentialDecayFullLine(lineLength) {
    var factor = 3 * Math.log(10) / lineLength;  // weight = 1.0E-3 at farthest point
    return makeExponentialDecay(factor);
}


// /**
//  * @param {RPolyLineEntity} polyLineEntity 
//  * @param {number} ivertex 
//  * @param {function (length)} weightsFunc 
//  * @param {RVector} offset 
//  */
function polylinePlasticBending(polyLineEntity, ivertex, weightsFunc, offset) { 
    var nvertex = polyLineEntity.countVertices();
    if (ivertex !== 0 && ivertex !== nvertex-1 ) {
        throw "Not implemented!";
    }

    var vertices = polyLineEntity.getData().getVertices();
    var lengths = [];
    var i;
    for (i=0; i<nvertex-1; i++) {
        lengths.push(polyLineEntity.getSegmentAt(i).getLength());
    }

    for (i=nvertex-1; i>=0; i--) {
        polyLineEntity.removeLastVertex();
    }

    if (ivertex === 0) {
        // first vertex
        var weight = weightsFunc(0.0);
        var newVertex = vertices[0].operator_add(offset.operator_multiply(weight));
        polyLineEntity.appendVertex(newVertex);

        var d0 = 0.0;
        for (i=1; i<nvertex; i++) {
            d0 += lengths[i-1];
            var weight = weightsFunc(d0);
            var newVertex = vertices[i].operator_add(offset.operator_multiply(weight));
            polyLineEntity.appendVertex(newVertex);
        }
    } else if (ivertex === nvertex-1) {
        var d0 = 0.0;
        for (i=0; i<nvertex-1; i++) d0 += lengths[i];

        // first vertex
        var weight = weightsFunc(d0);
        var newVertex = vertices[0].operator_add(offset.operator_multiply(weight));
        polyLineEntity.appendVertex(newVertex);
        
        for (i=1; i<nvertex; i++) {
            d0 -= lengths[i-1];
            var weight = weightsFunc(d0);
            var newVertex = vertices[i].operator_add(offset.operator_multiply(weight));
            polyLineEntity.appendVertex(newVertex);
        }
    } else {
        throw "Not implemented!";
    }

    var op = new RModifyObjectOperation(polyLineEntity);    
    var transaction = this.getDocumentInterface().applyOperation(op);

    return transaction;
}


//  *** begin operations

var doc = this.getDocument();
var di = this.getDocumentInterface();

var vertices = [];
for (i=0;i<100;i++) vertices.push([i*1,0,0]);
addPolyline(vertices, false);

// find out ID of polyline, that was added to the document:
var ids = doc.queryAllEntities();
for (var i=0; i<ids.length; ++i) {
    var id = ids[i];
    var entity = doc.queryEntity(id);
    if (isPolylineEntity(entity)) {
        plp = entity;
        break;
    }
}

var transaction = polylinePlasticBending(plp, 0, makeExponentialDecayFullLine(plp.getLength()), new RVector(20,20,0));
// find out ID of polyline, that was added to the document:
var ids = transaction.getAffectedObjects();
for (var i=0; i<ids.length; ++i) {
    var id = ids[i];
    var entity = doc.queryEntity(id);
    if (isPolylineEntity(entity)) {
        plp = entity;
        break;
    }
}
var r = polylinePlasticBending(plp, plp.countVertices()-1, makeExponentialDecayFullLine(plp.getLength()), new RVector(-20,20,0));