... of the overall surface morphology. By representing the surface shape using circle packing and leveraging conformal mapping, the framework enables smooth deformation between 2D and 3D shapes while maintaining local geometry and global morphology. The morphing surface design problem is recast as designing circular...

... on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The original governing equations defined on the 3D manifold can now be properly modified and solved on a 2D domain. The objective function, constraint, and velocity field are also equivalently...

... Abstract This paper presents a method to determine optimum topologies of two dimensional elastic planar structures by using conformal mappings. We use the conformal mappings which is known to be effective in two dimensional fluid mechanics, electromagnetics and elasticity by complex coordinate...

... be captured mathematically by using intermediate test specimens. In an effort to improve ESM, conformal mapping has been hypothesized to be an important technique for scaling and analysis. This paper explores the technique of Conformal Mapping as a potential equivalence procedure based on the principle of ESM...

... Coordinate Transformation Conformal Mapping Optimum Topology Laplace Equation This paper presents a new method to determine an optimum topology of plate structure using coordinate transformation by conformal mapping. We have already proposed a method to determine an optimum topology...