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An Implicit-Based Haptic Rendering TechniqueLaehyun Kim Anna Kyrikou Gaurav S. Sukhatme Mathieu DesbrunUniversity of Southern California,{laehyunk, kyrikou, gaurav, desbrun}@usc.eduAbstractWe present a novel haptic rendering technique. Build-ing on previous work, we propose a haptic model basedon a volumetric description of the geometry of an ob-ject. Unlike previousvolumetric approaches, we also finda virtual contact point on the surface in order to derivea penalty force that is consistent with the real geome-try of the object, without introducing force discontinuity.We also demonstrate that other surface properties such asfriction and texture can be added elegantly. The resultingtechnique is fast (a constant 1000 Hz refresh rate) and canhandle large geometry models on low-end computers.1 IntroductionA haptic display device is a force output device as wellas a point input device in 3-D space. It renders the virtualobject tangible and provides an intuitive interface with avirtual environment. When the user touches a virtual ob-ject, the haptic rendering algorithm generates an adequateforce field to simulate the presence of the object and sur-face properties such as friction and texture.The haptic rendering methods can be classified intoroughly two groups according to the surface representa-tion they use: geometric haptic algorithms [23, 19, 13,20] used to render surface data and volume haptic algo-rithms [1, 9, 11] used for volumetric data.Our novel haptic rendering algorithm takes advantage ofboth the geometric (B-rep) and the implicit (V-rep) sur-face representations for a given 3D object. The geomet-ric model can effectively represent the interface betweenthe object in 3D and the rest of the scene, while an im-plicit surface representation has many properties whichcan highly benefit to the haptic rendering algorithm. Thenovelty of our technique therefore lies in exploiting bothrepresentations to derive a fast and accurate haptic ren-dering technique.We will proceed with a short discussion on previous re-lated work in section 2. Some background informationabout implicit surfaces will be presented in section 3. Insection 4, we will describe the force field generation andsurface properties such as friction and haptic texture. Insection 5 we will present applications for both geometricand implicit representation based model. We concludewith some results and future perspectives of this algo-rithm in section 6.2 Related WorkTraditional haptic rendering methods are based on geo-metric surface representations which mainly consist oftriangle meshes. One interesting approach for the ge-ometric models is the penalty-based method [13, 14]which suffers from a strong force discontinuity and push-through for thin and small objects [23, 19]. In orderto overcome these limitations, Zilles and Salisbury [23]introduced a constraint-based “god-object” method inwhich the movement of a god-object (a virtual contactpoint on the surface) is constrained to stay on the object’ssurface. Ruspini et al. [19] proposed another constraint-based and simulation method for additional surface prop-erties such as friction and haptic texture. They used animplementation of Force Shading [18] in which a surfacenormal is obtained by interpolating the normals from thevertices of the mesh.Force discontinuityFigure 1: Force discontinuity in constraint-based ap-proachThe constraint-based approach, however, still suffersfrom force discontinuity(see Figure 1) and does not scalewell with the complexity of the object’s surface. ForceShading solves the force discontinuity problem, but in-troduces a feeling of rounded surfaces due to the discrep-ancy between the haptic force field and the actual normalfield of the surface [8, 19] as sketched in Figure 2a.Note that haptic rendering algorithms for geometric mod-els are not applicable to volumetric data without a priorconversion, using a Marching Cubes algorithm [12] forinstance. However, the resultant geometric models usu-(a) (b)Figure 2: Comparison of two haptic methods withoutforce discontinuity (a) Force shading method (b) Our ap-proachally contain a large number of polygons, which makes itimpractical.In the volume haptic rendering, instead, the force fieldis computed directly from the volume data. A hapticrendering algorithm for volumetric data was first intro-duced by Iwata and Noma [9]. They used the gradientof the potential value to calculate the force. However,in this volume haptic rendering technique and those thatfollowed[1, 11], the amount of force was linearly propor-tional to the potential value. This approximationdoes nottake into account the distance to a virtual contact point onthe surface - or in other words, it is a good approximationonly when the haptic device is extremely close to the realsurface. As a result, the haptic surface does not match thevisible surface, as sketched in Figure 3a.2.1 ContributionsWe employ an implicit surface representation to hapti-cally render a geometric model to take advantage of theimplicit representation as well as the geometric repre-sentation. In our algorithm, the user ”sees” a geomet-ric model and ”feels” an implicit surface which wrapsaround the geometric model (Figure 4).Our approach avoids the force discontinuity around vol-umetric boundaries (edges and vertices) in a geometricmodel without a feeling of rounded surfaces (Figure 2b)using an interpolation function in a volumetric model,which was first introduced by Avila [1].Another contribution is that we use a simple variationof Avila’s volume haptic method [1] to obtain the cor-rect force magnitude. In previous volume haptic algo-rithms [1, 11], the force magnitude is a function of thepotential value. This approximation may not allow theuser to feel stiff objects (Figure 3a). In order to solvethe problem, we find a virtual contact point on the sur-face to render the surface more accurately and robustly(Figure 3b).Haptic texturing, in our algorithm, is implemented bymapping a texture pattern directly into the implicit rep-resentation unlike previous haptic texturing methods [2,13, 20] which modulate the friction or perturb the surfacenormal. As a result, the geometry of the implicit surfaceis changed and it can express texture geometry explicitly(a) (b)Figure 3: computing the force magnitude (a) approxima-tion in previous methods (b) our approachwithout additional computations.Furthermore, our algorithm is fast and stable, and can beused for huge models


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