in [OOP]

From: CTips on 11 Jun 2005 15:08 Jeff Brooks wrote: > In my design I don't have a class hierarchy of curves (curves, and lines > are not shapes). A series of simple curves can make up any complex curve > so I never need to extend curve. Not true. Consider a curve in polar coordiates: C=(r,t) = (f(t), t) where f is some function which we are interested in. Let us assume that this is equivalent to a series of simple curves. Depending on what you mean by series, either you mean a piecewise approxiamtion, or a linear combination. Either way, your claim is that C can be represented by some combination of simple curves Si. Thus C = Combine(Si) Either the set of simple curves is infinite [and therefore useless in this context], or you've just discovered a way to represent _any_ function as a combination of a finite set of basis functions [and you should probably write it up - you're a shoo-in for a Fields medal]. So: are you sure you don't need a hierarchy of curves?
From: Jeff Brooks on 11 Jun 2005 19:46 CTips wrote: > zing! > :) > > But its a bit of a waste of effort. Once he made the preposterous claim > that any curve can be approximated with a combination of simpler curves, > it was already clear that he doesn't understand the field. I tried to > demonstrate the fallacy using a reductio-ad-absrudum argument, but it > seems that he's never been exposed to power-series and transforms of any > form, and the argument escaped him. Lol. If you understood the field you would know that even a series of lines can approximate a curve. A series of points can approximate a line, etc. A good example of this is your monitor. A monitor can't draw lines it can only draw small squares called pixels. Using a series of these pixels a line can be approximated, so can a curve, etc. Your original argument didn't prove anything. Finding a curve that won't work doesn't prove that there isn't a type of curve that does work. I suggest you study up on logic so in the future your "logical" arguments don't work against you. Power-series, and transforms have nothing to do with your original challenge. Bringing them up has no impact on the fact that I succeed at your challenge. If you want to see bezier curves in action look at the text on your screen. Both adobe, and truetype fonts use bezier curves, and lines to describe the shape of the text. The mathematical model is approximated on the screen via pixels. Jeff Brooks
From: Jeff Brooks on 11 Jun 2005 16:15 CTips wrote: > Jeff Brooks wrote: > >> In my design I don't have a class hierarchy of curves (curves, and >> lines are not shapes). A series of simple curves can make up any >> complex curve so I never need to extend curve. > > Not true. It is true. > Consider a curve in polar coordiates: > C=(r,t) = (f(t), t) > where f is some function which we are interested in. I'm not going to consider a curve based on your definition because your definition is flawed in this context. I suggest you look up "bezier curve". > Let us assume that this is equivalent to a series of simple curves. > Depending on what you mean by series, either you mean a piecewise > approxiamtion, or a linear combination. Either way, your claim is that C > can be represented by some combination of simple curves Si. Thus > C = Combine(Si) > > Either the set of simple curves is infinite [and therefore useless in > this context], or you've just discovered a way to represent _any_ > function as a combination of a finite set of basis functions [and you > should probably write it up - you're a shoo-in for a Fields medal]. > > So: are you sure you don't need a hierarchy of curves? Yes. Jeff Brooks
From: Patrick May on 11 Jun 2005 16:33 "topmind" <topmind (a)technologist.com> writes:> > You may investigate this by looking at the source code of this > > particular program. You can download it at www.fitnesse.org. [ . . . ] > Regarding your wiki example, I actually wrote my own wiki about 5 > months ago. Outstanding, you finally have the opportunity to demonstrate the advantages of your preferred programming approach over OO in the context of a real application. Robert Martin has already provided a link to his implementation -- let's see yours. Sincerely, Patrick ------------------------------------------------------------------------ S P Engineering, Inc. | The experts in large scale distributed OO | systems design and implementation. pjm (a)spe.com | (C++, Java, ObjectStore, Oracle, CORBA, UML)
From: Willem on 11 Jun 2005 16:50
Jeff wrote: ) CTips wrote: )> Jeff Brooks wrote: )>> In my design I don't have a class hierarchy of curves (curves, and )>> lines are not shapes). A series of simple curves can make up any )>> complex curve so I never need to extend curve. )> )> Not true. ) ) It is true. ) ) ... ) ) I'm not going to consider a curve based on your definition because your ) definition is flawed in this context. I suggest you look up "bezier curve". So you don't see any need to be able to draw a circle ? SaSW, Willem -- Disclaimer: I am in no way responsible for any of the statements made in the above text. For all I know I might be drugged or something.. No I'm not paranoid. You all think I'm paranoid, don't you ! #EOT |