Elasticity functions for Bezier and rectangular forms
- To: mathgroup at smc.vnet.net
- Subject: [mg132168] Elasticity functions for Bezier and rectangular forms
- From: "E. Martin-Serrano" <eMartinSerrano at telefonica.net>
- Date: Thu, 9 Jan 2014 01:50:10 -0500 (EST)
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- Delivered-to: l-mathgroup@wolfram.com
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Hi, (*I have the Bezier curve*) pts = {p[0], p[1], p[2], p[3]} = {{0, .65}, {1.8, 2.6}, {4, 2.5}, {4, 5}}; n = Length[pts] - 1; bcurve = Sum[Binomial[n, i]* (1 - t)^(n - i) *t ^i p[i] , {i, 0, n}]; (* the plot range for the resulting Bezier curve is obviously {p[0][[1]], p[3][[1]} -> {0,4} *) (*Then, I want to transform the above parametric Bezier curve into a rectangular {x,y} curve one by solving curve[[1]] x= x(t) for t and plugging the result t-> x(t) into curve[[2]] or y = y(t).*) sols= Solve[x == bcurve[[1]], t, Reals], bcurve[[2]]/.% yvalues = (% /. x -> #) & /@ Range[0, 4] (*For testing purposes, by visual inspection I discard directly the resulting yvalues which overflow the plot range interval {0,4} and select only those values of y which are members of the interval.*) #[[2]]&/@yvalues (*But that done, none of these selected {x,y} points belong to the actual Bezier curve bcurve yet.*) (*In other words the apparent direct procedure to convert a parametric curve into rectangular one does not seem to work here.*) (*Remark: I need the basic Bezier curve bcurve to be reshapable (dynamic) and be able to calculate the elasticity point function of each new resulting function as the Bezier curve bcurve gets reshaped, and for some reason I am not being able of getting directly the elasticity point function of bcurve = Sum[Binomial[n, i]* (1 - t)^(n - i) *t ^i p[i] , {i, 0, n}]; no problem for any other similar (or approximate) function given in rectangular form*) ; Any help will be welcome. E. Martin-Serrano P.S. For the sake of clarity I have enclosed the text in as in (*text*) and symbols or experssions within text as in symbol (when necessary). __________________________________________ This e-mail and the documents attached are confidential and intended solely for the addressee; it may also be privileged. If you receive this e-mail in error, please notify the sender immediately and destroy it. As its integrity cannot be secured on the Internet, no sender's liability can be triggered for the message content. Although the sender endeavors to maintain a computer virus-free network, he/she does not warrant that this transmission is virus-free and will not be liable for any damages resulting from any virus transmitted. Este mensaje y los ficheros adjuntos pueden contener informaci=F3n confidencial destinada solamente a la(s) persona(s) mencionadas anteriormente y su contenido puede estar protegido por secreto profesional y en cualquier caso el mensaje en su totalidad est=E1 amparado y protegido por la legislaci=F3n vigente que preserva el secreto de las comunicaciones, y por la legislaci=F3n de protecci=F3n de datos de car=E1cter personal. Si usted recibe este correo electr=F3nico por error, gracias por informar inmediatamente al remitente y destruir el mensaje. Al no estar asegurada la integridad de este mensaje sobre la red, el remitente no se hace responsable por su contenido. Su contenido no constituye ning=FAn compromiso para el remitente, salvo ratificaci=F3n escrita por ambas partes. Aunque se esfuerza al m=E1ximo por mantener su red libre de virus, el emisor no puede garantizar nada al respecto y no ser=E1 responsable de cualesquiera da=F1os que puedan resultar de una transmisi=F3n de virus.
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- Re: Elasticity functions for Bezier and rectangular forms
- From: Bob Hanlon <hanlonr357@gmail.com>
- Re: Elasticity functions for Bezier and rectangular forms
- From: Bob Hanlon <hanlonr357@gmail.com>
- Re: Elasticity functions for Bezier and rectangular forms
- From: Bob Hanlon <hanlonr357@gmail.com>
- Re: Elasticity functions for Bezier and rectangular forms