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Realism and Performance
Published in Aditi Majumder, M. Gopi, Introduction to Visual Computing, 2018
To detect collision between two objects, bounding volume intersection tests are first performed at the level 0 of the hierarchical bounding volume representation of the objects. No collision between the bounding volumes implies nocollision between the enclosed objects. If the bounding volumes collide, there is a possibility that the enclosed objects will collide. Note that the bounding volumes can collide in the empty regions of its volume. Therefore, a collision of bounding volumes does not always imply a collision of objects. If the bounding volumes intersect, pairwise intersection tests between the bounding volumes of the children nodes are performed. Therefore, the above process is repeated on the bounding volumes of the children nodes recursively. The trees are thus traversed in depth first search and a collision is detected when one primitive remains in each bounding volume and their intersection computation is essentially a triangle-triangle intersection computation to detect the point of collision.
On the Application of Fractal Interpolation Functions within the Reliability Engineering Framework
Published in Ioannis S. Triantafyllou, Mangey Ram, Statistical Modeling of Reliability Structures and Industrial Processes, 2023
Polychronis Manousopoulos, Vasileios Drakopoulos
The remaining data pointsP∖Q are approximated by the fractal interpolation function, since it does not necessarily pass through them. In order to optimize the closeness of fit, various methods have been proposed in the literature for determining the vertical scaling factors, the only free parameters for a given set P. In most of the cases, the vertical scaling factors are calculated so as to minimize an error measure. This is commonly the squared error between the ordinates of the original and the reconstructed points ∑m=0Mvm−Gum2, where Gum is the attractor ordinate at abscissa um, or the Hausdorff distance hP,G. For example, in [6] an algebraic and a geometric method is proposed for minimizing the squared error; the first one provides analytical calculation of the factors, while the second one exploits geometric properties of the data. In [7, 8] the use of bounding volumes, namely bounding rectangles and convex hulls, of data points subsets is suggested; in both cases the target is optimizing the fit of original and transformed bounding volumes instead of individual points. Alternative methods include, for example, the use of fractal dimension [9], where the target is the preservation of the fractal dimension of the data points and not the minimization of an error measure; the use of wavelets is proposed in [10], where the target is the detection of self-affinity and the related vertical scaling factors in the continuous wavelet transform of the data. An example is presented in Figure 7.2, where a set of 37 data points is interpolated by a fractal interpolation function using every 3rd points as interpolation points, i.e., 13 points in total; the vertical scaling factors are calculated by the analytic algorithm of [6]. We note that despite the use of only approximately 1/3 of the data points and the simple, symmetric definition of the interpolation intervals, the resulting interpolant approximates rather well the remaining data points.
Collision-free path planning based on new navigation function for an industrial robotic manipulator in human-robot coexistence environments
Published in Journal of the Chinese Institute of Engineers, 2020
Chun-Chieh Chan, Ching-Chih Tsai
Collision detection is also essential in a dynamic environment. However, collision detection that involves moving involves great computational complexity, so bounding volumes are used when checking for a collision because this allows a simple mathematical representation. Some studies (Ma, Manocha, and Wang 2018; Choi et al. 2009; Hwang, Ju, and Chen 2003; Balan and Bone 2006) use bounding volumes for real-time reciprocal collision detection.
Collision detection during planning for sheet metal bending by bounding volume hierarchy approaches
Published in International Journal of Computer Integrated Manufacturing, 2018
D. Raj Prasanth, M. S. Shunmugam
Collision detection as an independent problem has been well studied owing to its relevance in a wide variety of applications. A good review of the topic can be found in Jiménez, Thomas, and Torras (2001) and Ericson (2005). Primary areas of application include computer simulations and prototyping (Agarwal et al. 2004; Fukuhara et al. 2014; Chen and Wei 2016), 3D games (Jang and Han 2008), virtual reality (Mei and Lee 2016), augmented reality (Schmidt and Wang 2014; Mohammed, Schmidt, and Wang 2017), tool path planning (Ahmad, Tichadou, and Hascoet 2013; Yau et al. 2016) and robotics (Balan and Bone 2006; Cho and Song 2013; Erdösa et al. 2016). When two bodies are checked for collision, brute force checking of intersections among all pairs of primitives is prohibitively costly and is never used. Instead, specific techniques are devised to quickly identify and eliminate non-intersecting pairs. Only those pairs of objects that have greater chance of actually colliding are checked for actual pair-wise intersection. Irrespective of the domain used, collision detection solutions involve two stages. The two stages of collision detection are as follows: (a) elimination of non-intersecting pairs and (b) pair-wise intersection of filtered primitives. A lot of research has been done into identifying suitable algorithms for quick elimination of non-intersecting pairs. In 3D collision detection, the elimination of non-intersecting pairs is typically done by constructing some form of bounding volume. The bounding volume may be in the form of a sphere (Agarwal et al. 2004; Kim, Guibasand, and Shin 2005), axis-aligned bounding box (AABB) (van den Bergen 1998), oriented bounding box (OBB) (Gottschalk, Lin, and Manocha 1997), k-discrete oriented polytopes (k-DOPS) (Tang et al. 2011) or convex hulls. Although the sphere and AABB hierarchies are easy to compute, they do not provide the tight fits of OBB, k-DOPS or convex hulls. Therefore, the choice of bounding volume depends on the nature of the problem to be solved. Gottschalk, Lin, and Manocha (1997) brought out the advantage of pre-computed OBB hierarchies in detection of collision between two closely placed polygon soups. Almost at the same time, van den Bergen (1998) also highlighted the advantages of AABB hierarchies for a mix of rigid and deformable bodies.