Approximation by planar elastic curves

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient-driven optimization is then used to find the approximating elastic curve.Comment: 18 pages, 10 figures. Version2: new section 5 added (conclusions and discussions

B\'ezier curves that are close to elastica

We study the problem of identifying those cubic B\'ezier curves that are close in the L2 norm to planar elastic curves. The problem arises in design situations where the manufacturing process produces elastic curves; these are difficult to work with in a digital environment. We seek a sub-class of special B\'ezier curves as a proxy. We identify an easily computable quantity, which we call the lambda-residual, that accurately predicts a small L2 distance. We then identify geometric criteria on the control polygon that guarantee that a B\'ezier curve has lambda-residual below 0.4, which effectively implies that the curve is within 1 percent of its arc-length to an elastic curve in the L2 norm. Finally we give two projection algorithms that take an input B\'ezier curve and adjust its length and shape, whilst keeping the end-points and end-tangent angles fixed, until it is close to an elastic curve.Comment: 13 pages, 15 figure

Fairing of Discrete Planar Curves by Discrete Euler's Elasticae

After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing process via a $L^2\!$-distance minimization to avoid the numerical instabilities. The optimization problem is solved via a gradient-driven optimization method (IPOPT). This problem is non-convex and the result strongly depends on the initial guess, so that we use a discrete analogue of the algorithm provided by Brander et al., which gives an initial guess to the optimization method

Integrated Fabrication Approach of Complex, Architectural Forms Made from Foamed Polystyrene Using Industrial Robots

Integrisanjem višerazličitih oblasti arhitekture, poznavanja svojstava materijala, fabrikacije, zajedno sa primenom digitalnih alata, postalo je moguće lakše I efikasnije fabrikovati složene arhitektonske forme. Primena penastog polistirena u arhitektonskoj fabrikaciji je pogodna zbog dobrih svojstava polistirena, prevashodno njegove lake obradivosti. Upotrebom zagrejane žice za obradu materijala I industrijskog robota kao mašine za fabrikaciju, u ovom istraživanju su pokazana tri projektantska scenarija, koja predlažu automatizovan proces fabrikovanja složenih arhitektonskih formi različitih veličina od penastog polistirena I primenom različitih strategija za fabrikaciju. Rezultati su predstavljeni u vidu fabrikovanih prototipova.  Theintegrationofmultipledifferentfields-architecture,materialproperties,fabrication,combinedwiththeapplicationofdigitaltoolshasmadethefabricationofcomplexarchitecturalformseasyandefficient.Theapplicationoffoamedpolystyreneinarchitecturalfabricationissuitableduetothegoodpropertiesoffoamedpolystyrene,especiallytheeaseofmillingorcuttingthematerial.Inthisresearch,theapplicationofahot-wireasatoolandanindustrialrobotasafabricationmachinehasenabledthreedifferentdesignscenarios,whichsuggestanautomatedfabricationprocessforcomplexarchitecturalformsofdifferentsizes,madefrompolystyreneandbysuingdifferentfabricationstrategies.Theresultsarepresentsin a form of fabricated prototypes