Fleshing: Spine‐driven Bending with Local Volume Preservation

Several design and animation techniques use a one‐dimensional proxy C (a spine curve in 3D) to control the deformation or behavior of a digital model of a 3D shape S. We propose a modification of these “skinning” techniques that ensures local volume preservation, which is important for the physical plausibility of digital simulations. In the proposed “fleshing” techniques, as input, we consider a smooth spine C0, a model S0 of a solid that lies “sufficiently close” to C0, and a deformed version C1 of C0 that is “not overly bent”. (We provide a precise characterization of these restrictions.) As output, we produce a bijective mapping M, that maps any point X of S onto a point M(X) of M(S). M satisfies two properties: (1) The closest projection of X on C0 and of M(X) on C1 have the same arc length parameter. (2) U and M(U) have the same volume, where U is any subset of S. We provide three different closed form expressions for radial, normal and binormal fleshing and discuss the details of their practical real‐time implementation.

[1]  John P. Lewis,et al.  Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation , 2000, SIGGRAPH.

[2]  Alexis Angelidis,et al.  Eurographics/ Acm Siggraph Symposium on Computer Animation (2007) Kinodynamic Skinning Using Volume-preserving Deformations , 2022 .

[3]  Steve Capell,et al.  Physically based rigging for deformable characters , 2005, SCA '05.

[4]  Ming C. Lin,et al.  Fast volume-preserving free form deformation using multi-level optimization , 1999, SMA '99.

[5]  Mark A. Ganter,et al.  Skeleton-based modeling operations on solids , 1997, SMA '97.

[6]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[7]  Ignacio Llamas,et al.  Simulation of bubbles in foam with the volume control method , 2007, ACM Trans. Graph..

[8]  Hans-Peter Seidel,et al.  Vector field based shape deformations , 2006, ACM Trans. Graph..

[9]  Geoff Wyvill,et al.  Swirling-sweepers: Constant-volume modeling , 2006, Graph. Model..

[10]  Jarek Rossignac,et al.  Curvature-based offset distance: Implementations and applications , 2012, Comput. Graph..

[11]  Jirí Zára,et al.  Skinning with dual quaternions , 2007, SI3D.

[12]  Hwan Pyo Moon.  Equivolumetric offset surfaces , 2009, Comput. Aided Geom. Des..

[13]  A. Requicha,et al.  Piecewise-circular curves for geometric modeling , 1987 .

[14]  David Salomon,et al.  Computer Graphics and Geometric Modeling , 1999, Springer New York.

[15]  Marie-Paule Cani,et al.  Exact volume preserving skinning with shape control , 2009, SCA '09.

[16]  Hwan Pyo Moon.  Equivolumetric offsets for 2D machining with constant material removal rate , 2008, Comput. Aided Geom. Des..

[17]  Marie-Paule Cani,et al.  Local Volume Preservation for Skinned Characters , 2008, Comput. Graph. Forum.

[18]  Leif Kobbelt,et al.  Multiresolution Surface Representation Based on Displacement Volumes , 2003, Comput. Graph. Forum.

[19]  Ignacio Llamas,et al.  Simulation of bubbles in foam with the volume control method , 2007, SIGGRAPH 2007.

[20]  Geoff Wyvill,et al.  Swirling-sweepers: constant-volume modeling , 2004, 12th Pacific Conference on Computer Graphics and Applications, 2004. PG 2004. Proceedings..

[21]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[22]  Robert L. Foote,et al.  The Volume Swept Out by a Moving Planar Region , 2006 .

[23]  Gregory S. Chirikjian,et al.  Closed-Form Primitives for Generating Locally Volume Preserving Deformations , 1995 .

[24]  Rida T. Farouki,et al.  Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves , 2003, Comput. Aided Geom. Des..