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Re: Howto sample a curve?

by Aleksandar Mancic :: Rate this Message:

There is only one problem with such approach - you essentially get a 2D curve plotted on a 3D plane, so it's still a 2D Bezier but with, well, a twist :D That's why I've created the Bezier3D class - to get a full 3D Bezier, however, since it uses Line3D class to plot itself segmentation cannot be avoided. So, it all depends what you need.

I'll be releasing my Graphics3D addon for PV3D in a week or two that should be able to do all the Drawing API functions in 3D, allowing you to plot your points on all 3 axes. Till then use whatever suits you best :)

Cheers...

James Hay wrote:

I actually built a curve3D class that works in exactly the same way as the lines3D class but uses the curveTo() method of the flash drawing api so that you can get smooth curves instead of creating curves from seperate straight lines. Worked a treat!

Jimmy.

On Thu, May 22, 2008 at 9:38 PM, Aleksandar Mancic <sxdesign@...> wrote:

Ooops, forgot to attach the Bezier3D class :blush:

There you go...

Aleksandar Mancic wrote:

If you need a PV3D curve, you can use the attached Bezier3D class. It uses multiple Line3D instances (default segmentation is 10) to simulate a quadric bezier curve, giving you pretty much the drawing API's curveTo() functionality in 3D. Usage is, i hope, quite self-explanatory :D

It will also explain you how segmentation is done - just look at the build() method. If you want to change the shape of Bezier3D run-time (changing properties than calling rebuild() method), you should also edit Lines3D class from PV3D and replace it's removeLine() method because it doesn't remove vertices when removing a line. Replace the removeLine() method with something like:

public function removeLine(line:Line3D):void
{
var lineindex : int = lines.indexOf(line);
if(lineindex>-1)
{
var vertices:Array = geometry.vertices;
var c_v0:int = vertices.indexOf(line.v0);
if(c_v0 != -1) vertices.splice(c_v0, 1);
var c_v1:int = vertices.indexOf(line.v1);
if(c_v1 != -1) vertices.splice(c_v1, 1);

lines.splice(lineindex,1); }
else if(Papervision3D.VERBOSE)
{
trace("Papervision3D Lines3D.removeLine : WARNING removal of non-existant line attempted. ");

}
}

That should do the trick... Until I finish my Graphics3D extension for PV3D :)

Cheers...

Tim Knip wrote:

Hi list,

I have a curved line (curveTo)...

How to get straight line-segments following this curve?
Where start- and endpoints of the segments lie on the curve .

Say I have a circle created from 4 curveTo's. How do I create like 16
straight line segments?

Thanks!
Tim

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/*
* Copyright 2008 (c) Aleksandar Mancic, sx@...
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/

/**
* Bezier3D
* Bezier3D for Papervision3D Public Alpha 2.0 - Great White
*
* @author Aleksandar Mancic
* @version 0.0.2
*/

package com.topflashers.ext.pv3d.core.geom.renderables {
import org.papervision3d.core.geom.Lines3D;
import org.papervision3d.core.geom.renderables.Line3D;
import org.papervision3d.core.geom.renderables.Vertex3D;
import org.papervision3d.materials.special.LineMaterial;

public class Bezier3D {

private var _lines:Array;

private var _instance:Lines3D;
private var _material:LineMaterial;

public function Bezier3D(instance:Lines3D, material:LineMaterial, size:Number, segments:int, start:Vertex3D, end:Vertex3D, control:Vertex3D) {

this._instance = instance;
this._material = material;
this.size = size;
this.segments = segments;
this.start = start;
this.end = end;
this.control = control;

rebuild();
}

private var _size:Number = 1;
public function get size():Number {
return _size;
}
public function set size(value:Number):void {
if(value == _size) return;
_size = value;
}

private var _segments:int = 10;
public function get segments():int {
return _segments;
}
public function set segments(value:int):void {
if(value == _segments) return;
_segments = Math.max(1, value);
}

private var _start:Vertex3D;
public function get start():Vertex3D {
return _start;
}
public function set start(value:Vertex3D):void {
if(value === _start) return;
_start = value;
}

private var _end:Vertex3D;
public function get end():Vertex3D {
return _end;
}
public function set end(value:Vertex3D):void {
if(value === _end) return;
_end = value;
}

private var _control:Vertex3D;
public function get control():Vertex3D {
return _control;
}
public function set control(value:Vertex3D):void {
if(value === _control) return;
_control = value;
}

public function rebuild():void {
clear();
build();
}

public function clear():void {
if(_lines && _lines.length) {
var c_len:int = _lines.length;
for(var i:int=0; i<c_len; i++) _instance.removeLine(_lines[i]);
}
_lines = [];
}

private function build():void {
var c_seg:Number, c_dseg:Number, c_sqdseg:Number, c_dbseg:Number, c_pseg:Number;
for(var i:int=0; i<_segments; i++) {
c_seg = i / _segments;
c_dseg = 1 - c_seg;
c_sqdseg = c_dseg * c_dseg;
c_dbseg = 2 * c_seg * c_dseg;
c_pseg = c_seg * c_seg;

var c_p1:Vertex3D = new Vertex3D();
c_p1.x = c_sqdseg * _start.x + c_dbseg * _control.x + c_pseg * _end.x;
c_p1.y = c_sqdseg * _start.y + c_dbseg * _control.y + c_pseg * _end.y;
c_p1.z = c_sqdseg * _start.z + c_dbseg * _control.z + c_pseg * _end.z;

c_seg = (i+1) / _segments;
c_dseg = 1 - c_seg;
c_sqdseg = c_dseg * c_dseg;
c_dbseg = 2 * c_seg * c_dseg;
c_pseg = c_seg * c_seg;

var c_p2:Vertex3D = new Vertex3D();
c_p2.x = c_sqdseg * _start.x + c_dbseg * _control.x + c_pseg * _end.x;
c_p2.y = c_sqdseg * _start.y + c_dbseg * _control.y + c_pseg * _end.y;
c_p2.z = c_sqdseg * _start.z + c_dbseg * _control.z + c_pseg * _end.z;

var c_line:Line3D = new Line3D(_instance, _material, _size, c_p1, c_p2);
_lines.push(c_line);
_instance.addLine(c_line);
}
}
}
}
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