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Table 1 The node-based optimization problem for inverse form finding [5]

From: A non-invasive node-based form finding approach with discretization-independent target configuration

Objective function

\(\delta \big (\mathbf {X}^\mathrm{D},\mathbf {x}_\mathrm{tg}^\mathrm{D}\big )=\sum _{D=1}^{n_\mathrm{dsgn}} \tfrac{1}{2} \Vert {\varvec{d}^D}\Vert _2^2\)

Design variables

Material positions \(\varvec{X}^D\) of the design nodes

State equation

Deformation map \(\varvec{\varphi }:\mathbf {X}^\mathrm{D}\in \mathcal {B}_0^\mathrm{h}\rightarrow \mathbf {x}^\mathrm{D} \in \mathcal {B}_{t}^\mathrm{h}\)