そこで本研究では、FFD の格子を自動生成し、オリジ ナルの FFD の柔軟性を保ちつつ、ユーザによる 3 次元 モデルの変形を支援する手法を提案する。我々の手法 は、まずモデルのバウンディングボックスを生成し、 それを初期格子とする。その初期格子から階層的に新 たな格子を生成することで、多重解像度格子という格 子集合を作り出し、ユーザがその中から目的に沿った 適切な格子、すなわち大域的な変形のための少数の制 御点を持つ格子や、局所的な変形のための変形対象領 域の形状をよく近似する格子を選択できるようにする。 さらに、変形前の格子だけでなく、ユーザによって変 形された格子から新たな格子の生成を行うことで、階 層的変形を行うことができる。階層的変形を用いるこ とで、格子をバウンディングボックスから再定義する ことなく、大域的な変形から局所的な変形、またはそ の逆といったようにモデルを階...

In this work, we show that the eigenvalues of the problem  (∆2 + V (x) + λ)u(x) = 0 x ∈ Ω u(x) = ∆u(x) = 0 x ∈ ∂Ω are generically simple in the set of C4 regular regions of Rn, n ≥ 2. In fact, we prove that there exists a residual set of regions C4 diffeomorphic to a given Ω such that all the eigenvalues for a supported plate equation are simple.

With the increasing complexity of photo-realistic scenes, the question of building and placing objects in three-dimensional scenes is becoming ever more di cult. While the question of placement of rigid objects has captured the attention of researchers in the past, this work presents an intuitive and interactive scheme to properly place deformable objects with the aid of free-form deformation t...

Etiolated mung bean hypocotyl segments were incubated in 0.25 m mannitol solutions with indoleacetic acid. They were then deformed mechanically with a longitudinal tensile force at a constant strain rate. The magnitudes of the mechanical forces were comparable to those of the hydrostatic forces existing in normally growing tissues. Each segment was repeatedly deformed and returned to zero force...

Given the set of square matrices M ⊂ Mn+m(C) that keep the subspace W = Cnx{0} ⊂ C invariant, we obtain the implicit form of a miniversal deformation of a matrix a ∈ M, and we compute it explicitely when this matrix is marked (this is, if there is a permutation matrix p ∈ Mn+m(C) such that p−1ap is a Jordan matrix). We derive some applications to tackle the classical Carlson problem.

deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. the governing differential equations and c...