Harmonic parameterization by electrostatics

Abstract

In this article, we introduce a method to apply ideas from electrostatics to parameterize the open space around an object. By simulating the object as a virtually charged conductor, we can define an object-centric coordinate system which we call Electric Coordinates. It parameterizes the outer space of a reference object in a way analogous to polar coordinates. We also introduce a measure that quantifies the extent to which an object is wrapped by a surface. This measure can be computed as the electric flux through the wrapping surface due to the electric field around the charged conductor. The electrostatic parameters, which comprise the Electric Coordinates and flux, have several applications in computer graphics, including: texturing, morphing, meshing, path planning relative to a target object, mesh parameterization, designing deformable objects, and computing coverage. Our method works for objects of arbitrary geometry and topology, and thus is applicable in a wide variety of scenarios.

An Energy-Driven Motion Planning Method for Two Distant Postures

“…Their method assumes that some body parts can always be de-correlated, which is not always the case in motions such as Yoga and Contortion. Wang et al [10], [11] suggest control methods to interact with deformable objects. They deal with a high number of degrees of freedom but the character control is too simple to handle impending penetrations.…”

Dexterous reaching, grasp transfer and planning using electrostatic representations

“…We briefly review the electrostatic parametrisation proposed by Wang et al [26], which computes an objectcentric curvilinear coordinate system that resembles polar coordinates. Such a coordinate system is useful for defining reaching and grasping motion with respect to the object as it gives a relative spatial relationship between a point and a charged object.…”

“…We look up the electric coordinates for points p i (q) in the 3D grid at runtime. The electric field computational complexity is O(L) (where L is the number of triangles comprising the object), as defined by the superposition principle and discussed in [26]. This lookup grid reduces the computational complexity of the potential calculation for a single point from O(L) to an O(1) lookup and trilinear interpolation.…”

“…W ,L are the number of hand surface triangles and the number of object triangles respectively. The flux function between a charged (object) and an uncharged (hand) triangle, f flux , is described in [25] and further explained in [26] (Appendix A.3).…”

“…In this paper, we propose to solve these problems by using a novel representation that borrows the concepts from electrostatics [26] that looks to define the spatial relationship between the hand and the object, as well as the envelopment of the hand around the object. Firstly, by virtually charging the object, we compute an object-centric coordinate system that we call electric coordinates.…”