Accelerated Proximity Queries for Haptic Rendering of Deformable Models Nico Galoppo * Miguel A. Otaduy † Paul Mecklenburg * Markus Gross † Ming C. Lin * (*) University of North Carolina at Chapel Hill, USA (†) ETH Zurich, Switzerland E-mail: {nico,prm,lin}@cs.unc.edu, {otaduy,grossm}@inf.ethz.ch Abstract We present a fast proximity query algorithm for hap- tic display of complex deformable models using a lay- ered representation. Assuming that each solid model can be represented as a rigid core covered by a layer of deformable material, the deformation field of the sur- face can be expressed as a function in the parametric domain of the rigid core. Our 2-stage collision query algorithm starts by performing an approximate object- space collision detection between low-resolution polyg- onal proxies. We then refine the query result by comput- ing a directional penetration depth field using a local height-field representation of the deformable layers to detect the interference between the high-resolution sur- face geometry. We have developed a proof-of-concept demonstration using commodity graphics processors and been able to perform fast proximity queries between two highly complex deformable models in less than 2 msecs. 1 Introduction Haptic rendering of forces and torques between in- teracting objects, also known as 6 degree-of-freedom (DoF) haptics, has been demonstrated to improve task performance in applications such as molecular dock- ing, nanomanipulation, medical training, and mechani- cal assembly in virtual prototyping. Haptic display of complex interaction between two deformable models is considered especially challenging, due to the com- putational complexity involved in computing contact response and performing proximity queries, including collision detection, separation distance, and penetration depth, between two deformable models at force update rates. In this short paper, we will focus on the prob- lem of proximity queries between two highly complex Figure 1: Soft Object Interaction in a Dynamic Scene. Deformable objects roll and collide in the play- ground. deformable models. We assume that real-world de- formable solids can be modeled as a rigid core covered by a layer of deformable material [2] and that the defor- mation field of the surface can be expressed as a func- tion in the parametric domain of the rigid core. Exam- ples include animated characters, furniture, toys, tires, etc. We reformulate the problem of collision detection on a 2D parametric atlas to reduce the extremely high geometric complexity due to contacts between high- resolution deformable surfaces. We exploit our layered representation in a scalable and output-sensitive two-stage collision detection algo- rithm. This novel formulation of the problem is espe- cially well suited for realization on commodity single- instruction multiple-data (SIMD) or parallel architec- tures, such as multi-core architecture, graphics proces- sor units (GPUs), Cell processors, and physics process- ing units (PPUs). We show a proof-of-concept demon- stration using GPUs (See Fig. 1).