ABSTRACT Thesis (M.Phil.)--University of Hong Kong, 2001. Includes bibliographical references (le... more ABSTRACT Thesis (M.Phil.)--University of Hong Kong, 2001. Includes bibliographical references (leaves 67-68) Mode of access: World Wide Web.
We present an efficient and robust method based on the culling approach for computing the minimum... more We present an efficient and robust method based on the culling approach for computing the minimum distance between two Bézier curves or Bézier surfaces. Our contribution is a novel dynamic subdivision scheme that enables our method to converge faster than previous methods based on binary subdivision.
Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we p... more Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present ex...
In this paper, we describe an exact method for detecting collision between two moving ellipsoids ... more In this paper, we describe an exact method for detecting collision between two moving ellipsoids under pre-specified rational motions. Our method is based on an algebraic condition that determines the separation status of two static ellipsoids -- the condition itself is described by the signs of roots of the characteristic equation of the two ellipsoids. To deal with moving ellipsoids, we derive a bivariate function whose zero-set possesses a special topological structure. By analyzing the zero-set of this function, we are able to tell whether or not two moving ellipsoids under prespecified rational motions are collision-free; and if not, we can determine the intervals in which they overlap.
The area coverage problem of mobile sensor networks has attracted much attention recently, as mob... more The area coverage problem of mobile sensor networks has attracted much attention recently, as mobile sensors find many important applications in remote and hostile environments. However, the deployment of mobile sensors in a non-convex domain is nontrivial due to the more general shape of the domain and the attenuation of sensing capabilities caused by the boundary walls or obstacles. We consider the problem of exploration and coverage by mobile sensors in an unknown non-convex domain. We propose the definition of “visibility-based Voronoi diagram ” and extend the continuous-time Lloyd’s method, which only works for convex domains, to deploy the mobile sensors in the unknown environments in a distributed manner. Our simulations show the effectiveness of the proposed algorithms.
Smooth surfaces are approximated by discrete triangle meshes for applications in computer graphic... more Smooth surfaces are approximated by discrete triangle meshes for applications in computer graphics. Various discrete operators have been proposed for estimating differential quantities of triangle meshes, such as curvatures, for geometric processing tasks. Since a smooth surface can be approximated by many different triangle meshes, we propose to investigate which triangle mesh yields an estimation of differential quantities with optimal accuracy and how to compute such an optimal triangle mesh approximating the given smooth surface. Specifically, we study a special type of triangle meshes, called shapepreserving meshes, that preserve the local shapes of the smooth surface they represent, and characterize optimal shape-preserving meshes. We present an efficient method for computing the so called optimal shape-preserving meshes, and prove the convergence of several discrete differential operators on optimal shape-preserving meshes, an important property that does not hold for general...
The area coverage problem of mobile sensor networks has attracted much attention recently, as mob... more The area coverage problem of mobile sensor networks has attracted much attention recently, as mobile sensors find many important applications in remote and hostile environments. However, the deployment of mobile sensors in a non-convex domain is nontrivial due to the more general shape of the domain and the attenuation of sensing capabilities caused by the boundary walls or obstacles. We consider the problem of exploration and coverage by mobile sensors in an unknown non-convex domain. We propose the definition of “visibility-based Voronoi diagram” and extend the continuoustime Lloyd’s method, which only works for convex domains, to deploy the mobile sensors in the unknown environments in a distributed manner. Our simulations show the effectiveness of the proposed algorithms. Keywords-mobile sensor networks; sensor deployment; sensor coverage; distributed control
We present an exact algebraic algorithm for real-time continuous collision detection (CCD) for mo... more We present an exact algebraic algorithm for real-time continuous collision detection (CCD) for moving ellipsoids under affine deformations. An efficient collisio n test is first developed for two static ellipsoids, which takes less than 1 microsecond. Using this practical result a nd the properties of our algebraic condition, we produce a real-time solution to the CCD problem that computes the exact collision time intervals.
We present an accurate and efficient algorithm for continuous collision detection between two mov... more We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids under rational Euclidean or affine motion. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then, we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop an efficient algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with practical examples.
We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The ... more We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.
The directional contact range of two convex polyhedra is the range of positions that one of the p... more The directional contact range of two convex polyhedra is the range of positions that one of the polyhedron may locate along a given straight line so that the two polyhedra are in collision. Using the contact range, one can quickly classify the positions along a line for a polyhedron as “safe” for free of collision with another polyhedron, or “unsafe” for the otherwise. This kind of contact detection between two objects is important in CAD, computer graphics and robotics applications. In this paper we propose a robust and efficient computation scheme to determine the directional contact range of two polyhedra. We consider the problem in its dual equivalence by studying the Minkowski difference of the two polyhedra under a duality transformation. The algorithm requires the construction of only a subset of the faces of the Minkowski difference, and resolves the directional range efficiently. It also computes the contact configurations when the boundaries of the polyhedra are in contact.
Collision detection is an essential problem in many applications in computer graphics, CAD/CAM, a... more Collision detection is an essential problem in many applications in computer graphics, CAD/CAM, and robotics. In this paper, a new method, called CD-Dual, for detecting collision between two convex polyhedra is proposed. The idea is based on a local search among the faces on the Minkowski difference (M) of the polyhedra. The local search is guided by a simple signed distance function defined on the dual polyhedron of M. Due to the convexity of the dual polyhedron, it is guaranteed that the result of the local search will lead to a vertex on the dual polyhedron that attains the global maximum signed distance, and this distance tells whether the two polyhedra overlap.
ABSTRACT Thesis (M.Phil.)--University of Hong Kong, 2001. Includes bibliographical references (le... more ABSTRACT Thesis (M.Phil.)--University of Hong Kong, 2001. Includes bibliographical references (leaves 67-68) Mode of access: World Wide Web.
We present an efficient and robust method based on the culling approach for computing the minimum... more We present an efficient and robust method based on the culling approach for computing the minimum distance between two Bézier curves or Bézier surfaces. Our contribution is a novel dynamic subdivision scheme that enables our method to converge faster than previous methods based on binary subdivision.
Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we p... more Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present ex...
In this paper, we describe an exact method for detecting collision between two moving ellipsoids ... more In this paper, we describe an exact method for detecting collision between two moving ellipsoids under pre-specified rational motions. Our method is based on an algebraic condition that determines the separation status of two static ellipsoids -- the condition itself is described by the signs of roots of the characteristic equation of the two ellipsoids. To deal with moving ellipsoids, we derive a bivariate function whose zero-set possesses a special topological structure. By analyzing the zero-set of this function, we are able to tell whether or not two moving ellipsoids under prespecified rational motions are collision-free; and if not, we can determine the intervals in which they overlap.
The area coverage problem of mobile sensor networks has attracted much attention recently, as mob... more The area coverage problem of mobile sensor networks has attracted much attention recently, as mobile sensors find many important applications in remote and hostile environments. However, the deployment of mobile sensors in a non-convex domain is nontrivial due to the more general shape of the domain and the attenuation of sensing capabilities caused by the boundary walls or obstacles. We consider the problem of exploration and coverage by mobile sensors in an unknown non-convex domain. We propose the definition of “visibility-based Voronoi diagram ” and extend the continuous-time Lloyd’s method, which only works for convex domains, to deploy the mobile sensors in the unknown environments in a distributed manner. Our simulations show the effectiveness of the proposed algorithms.
Smooth surfaces are approximated by discrete triangle meshes for applications in computer graphic... more Smooth surfaces are approximated by discrete triangle meshes for applications in computer graphics. Various discrete operators have been proposed for estimating differential quantities of triangle meshes, such as curvatures, for geometric processing tasks. Since a smooth surface can be approximated by many different triangle meshes, we propose to investigate which triangle mesh yields an estimation of differential quantities with optimal accuracy and how to compute such an optimal triangle mesh approximating the given smooth surface. Specifically, we study a special type of triangle meshes, called shapepreserving meshes, that preserve the local shapes of the smooth surface they represent, and characterize optimal shape-preserving meshes. We present an efficient method for computing the so called optimal shape-preserving meshes, and prove the convergence of several discrete differential operators on optimal shape-preserving meshes, an important property that does not hold for general...
The area coverage problem of mobile sensor networks has attracted much attention recently, as mob... more The area coverage problem of mobile sensor networks has attracted much attention recently, as mobile sensors find many important applications in remote and hostile environments. However, the deployment of mobile sensors in a non-convex domain is nontrivial due to the more general shape of the domain and the attenuation of sensing capabilities caused by the boundary walls or obstacles. We consider the problem of exploration and coverage by mobile sensors in an unknown non-convex domain. We propose the definition of “visibility-based Voronoi diagram” and extend the continuoustime Lloyd’s method, which only works for convex domains, to deploy the mobile sensors in the unknown environments in a distributed manner. Our simulations show the effectiveness of the proposed algorithms. Keywords-mobile sensor networks; sensor deployment; sensor coverage; distributed control
We present an exact algebraic algorithm for real-time continuous collision detection (CCD) for mo... more We present an exact algebraic algorithm for real-time continuous collision detection (CCD) for moving ellipsoids under affine deformations. An efficient collisio n test is first developed for two static ellipsoids, which takes less than 1 microsecond. Using this practical result a nd the properties of our algebraic condition, we produce a real-time solution to the CCD problem that computes the exact collision time intervals.
We present an accurate and efficient algorithm for continuous collision detection between two mov... more We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids under rational Euclidean or affine motion. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then, we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop an efficient algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with practical examples.
We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The ... more We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.
The directional contact range of two convex polyhedra is the range of positions that one of the p... more The directional contact range of two convex polyhedra is the range of positions that one of the polyhedron may locate along a given straight line so that the two polyhedra are in collision. Using the contact range, one can quickly classify the positions along a line for a polyhedron as “safe” for free of collision with another polyhedron, or “unsafe” for the otherwise. This kind of contact detection between two objects is important in CAD, computer graphics and robotics applications. In this paper we propose a robust and efficient computation scheme to determine the directional contact range of two polyhedra. We consider the problem in its dual equivalence by studying the Minkowski difference of the two polyhedra under a duality transformation. The algorithm requires the construction of only a subset of the faces of the Minkowski difference, and resolves the directional range efficiently. It also computes the contact configurations when the boundaries of the polyhedra are in contact.
Collision detection is an essential problem in many applications in computer graphics, CAD/CAM, a... more Collision detection is an essential problem in many applications in computer graphics, CAD/CAM, and robotics. In this paper, a new method, called CD-Dual, for detecting collision between two convex polyhedra is proposed. The idea is based on a local search among the faces on the Minkowski difference (M) of the polyhedra. The local search is guided by a simple signed distance function defined on the dual polyhedron of M. Due to the convexity of the dual polyhedron, it is guaranteed that the result of the local search will lead to a vertex on the dual polyhedron that attains the global maximum signed distance, and this distance tells whether the two polyhedra overlap.
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Papers by Yi-king Choi