Post by thread:[OT]: graphics: how many Bezier controls to make 1

Hi, I am doing something that requires an animation curve which must be sinusoidal. I can only use Bezier curves to set up the graph. I have come up with a solution that uses two Bezier curves to make a 1/2 sinus but the result is not 'sinusoidal' enough. The Bezier control I am using uses the pivot + 2 points input method (the 2 control points are on a line that passes through the pivot point on the curve being traced). Am I trying something impossible here ? Assuming that I'd use enough <any> curves I could approximate a sinus, no ? thanks, Peter -- http://www.piclist.com hint: PICList Posts must start with ONE topic: "[PIC]:" PIC only "[EE]:" engineering "[OT]:" off topic "[AD]:" ad's

Obviously, with enough Bezier's you can make a 'practically perfect' sine curve. Just imagine that you make your Bezier's straight lines and then use a piecewise linear approximation to the sine. Ugly, but it proves the point. The neat thing about Bezier's is you have quite a bit of control about the shape, if you can figure out the correct control points. This should let you get the same accuracy with far fewer segments than straight lines would allow for. Good luck figuring out the math. Bob Ammerman RAm Systems (contract development of high performance, high function, low-level software) {Original Message removed}

To my knowledge, beziers are based on a largely polynomial equation. If you want to produce a sinewave using a bezier, the closer you want to be, the more beziers (or the more complex each bezier needs to be) According to Don Lancaster, a Bezier curve is a type of cubic spline. He has quite a bit of information on cubic splines and bezier curves here: http://www.tinaja.com/cubic01.html This page includes a PDF in which "Jim Fitzsimmons TEX tutorial shows an eight step approximation to a full sinewave that uses Bezier cubic splines. Each spline curve fits 45 degrees and exactly matches value and slope at end points." here: http://www.tinaja.com/glib/bezsine.pdf It seems as though Don's column is no longer included in poptronics (the incestuous marriage of Electronics Now and Popular Electronics). Anyone know and care to comment why? -Adam "Peter L. Peres" wrote: {Quote hidden}> > Hi, > > I am doing something that requires an animation curve which must be > sinusoidal. I can only use Bezier curves to set up the graph. I have come > up with a solution that uses two Bezier curves to make a 1/2 sinus but the > result is not 'sinusoidal' enough. The Bezier control I am using uses the > pivot + 2 points input method (the 2 control points are on a line that > passes through the pivot point on the curve being traced). > > Am I trying something impossible here ? Assuming that I'd use enough <any> > curves I could approximate a sinus, no ? > > thanks, > > Peter > > -- > http://www.piclist.com hint: PICList Posts must start with ONE topic: > "[PIC]:" PIC only "[EE]:" engineering "[OT]:" off topic "[AD]:" ad's -- http://www.piclist.com hint: PICList Posts must start with ONE topic: "[PIC]:" PIC only "[EE]:" engineering "[OT]:" off topic "[AD]:" ad's

At 08:36 AM 10/10/00 -0500, you wrote: >What program are you trying to draw in? I would approach this by drawing an >EXACT sinusoid in a real CAD program like AutoCad, then porting it to the >other graphics program. Or, in Adobe Illustrator 7.0+, just open the below very simple file as a parsed EPS, lock it, then trace over it with Bezier curves to your required accuracy. Best regards, ---- %! % draw half a sine wave 72 72 dup scale % make it 1" x 1" /inc 0.1 def % increment in degrees /x 0 def /y 0 def /stx 1 def /sty 1 def stx sty moveto 0 inc 180 { /x exch def /y x sin def x 180 div stx add y sty add lineto } for 0 setlinewidth stroke %showpage =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Spehro Pefhany --"it's the network..." "The Journey is the reward" spam_OUTspeffTakeThisOuTinterlog.com Info for manufacturers: http://www.trexon.com Embedded software/hardware/analog Info for designers: http://www.speff.com Contributions invited->The AVR-gcc FAQ is at: http://www.bluecollarlinux.com =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -- http://www.piclist.com hint: The list server can filter out subtopics (like ads or off topics) for you. See http://www.piclist.com/#topics

>good luck with the math Gee, thanks ;-). Except there is no math, this is a graphical input system and I need to drag & twist until the curve looks sinus and then the program animates using the curve. This is not my idea, I assure you. There may be another way to do it but I haven't figured it out yet. I have gotten reasonably nice results with only 2 Beziers, with the pivots at the peaks of the 1/2 sinus. I have tried a third at the zero crossing but it made things worse. Oh, well. Peter -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

>what program It's an animation program that was never meant to be used the way I am using it ;-). Your idea is good but if there had been a way to do that I would not have posted the question ... and yet there might be a way. I'll try to get hold of the people who wrote this thing. thanks, Peter -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

>EPS sinus algorythm Thank you for the algorythm, but that is not an option. Anyway nice of you to post Fort^H^H^H^H Post Script source files inline. It reminds people of things ;-) Peter PS: My latest saying: Unix has a lot of four letter commands with twenty page apologies. -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

I imagine the system will import postscript files. If so, then you can make it into a math problem. Figure out the bezier(s) mathematically, describe them in postscript, and import them into your program. If your program doesn't import postscript (or HPGL, or another generic ascii vector language), then bang your head against a wall repeatedly, and chant, "It's not worth the pain! It's not worth the pain!" -Adam "Peter L. Peres" wrote: {Quote hidden}> > >good luck with the math > > Gee, thanks ;-). Except there is no math, this is a graphical input system > and I need to drag & twist until the curve looks sinus and then the > program animates using the curve. This is not my idea, I assure you. There > may be another way to do it but I haven't figured it out yet. > > I have gotten reasonably nice results with only 2 Beziers, with the pivots > at the peaks of the 1/2 sinus. I have tried a third at the zero crossing > but it made things worse. Oh, well. > > Peter > > -- > http://www.piclist.com hint: The PICList is archived three different > ways. See http://www.piclist.com/#archives for details. -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! use listservKILLspammitvma.mit.edu?body=SET%20PICList%20DIGEST

At 09:52 AM 10/12/00 -0400, you wrote: >I imagine the system will import postscript files. If so, then you can make it >into a math problem. Figure out the bezier(s) mathematically, describe them in >postscript, and import them into your program. > >If your program doesn't import postscript (or HPGL, or another generic ascii >vector language), then bang your head against a wall repeatedly, and chant, >"It's not worth the pain! It's not worth the pain!" Yes, using the simple program I posted to generate an almost perfect sine as short line segments and tracing over it, I was able to nicely describe a 1/2 sine-wave in Illustrator using about 8 bezier curves, in about 2 minutes. Error was maybe 0.1%. The coefficients could be extracted from the generated Postscript code (the .ai file is a kind of Postscript with some predefined shortcuts) but that would take a lot more time (for me anyway) and there are doubtless some strange scale factors that would be involved. As far as actually optimizing bezier curves to match a sine wave, this could be done either mathematically (maybe!) or numerically, and I'd suggest the latter. Any kind of program that will do multi-dimensional optimization should be able to do it. I'd still start with Illustrator to pick a good starting point for where the Bezier curves should begin and end. Best regards, =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Spehro Pefhany --"it's the network..." "The Journey is the reward" .....speffKILLspam.....interlog.com Info for manufacturers: http://www.trexon.com Embedded software/hardware/analog Info for designers: http://www.speff.com Contributions invited->The AVR-gcc FAQ is at: http://www.bluecollarlinux.com =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! use EraseMElistservspam_OUTTakeThisOuTmitvma.mit.edu?body=SET%20PICList%20DIGEST