摘要 :
Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper pre...
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Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper presents an algorithm for medial axis transform computation from a perspective of minimum distance between the points in a two-dimensional shape and its boundary. The minimum distance is given by a resultant distance function which is a superposition of the individual distance function between a point within a shape and each boundary point. By elaborating the resultant distance function, the medial axis transform will be obtained naturally. The distance function is modeled as a solid cone and the superposition is equivalent to the union Boolean set operation. The implementation of the approach is simplified using a solid modeling kernel. Several examples of two-dimensional shapes with free form boundaries are raised to illustrate the concept and algorithm.
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摘要 :
Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper pre...
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Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper presents an algorithm for medial axis transform computation from a perspective of minimum distance between the points in a two-dimensional shape and its boundary. The minimum distance is given by a resultant distance function which is a superposition of the individual distance function between a point within a shape and each boundary point. By elaborating the resultant distance function, the medial axis transform will be obtained naturally. The distance function is modeled as a solid cone and the superposition is equivalent to the union Boolean set operation. The implementation of the approach is simplified using a solid modeling kernel. Several examples of two-dimensional shapes with free form boundaries are raised to illustrate the concept and algorithm.
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摘要 :
Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper pre...
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Although medial axis transform is introduced as a shape description for many engineering applications, the computational algorithm is still challenging. This is especially true for the shape with free form boundary. This paper presents an algorithm for medial axis transform computation from a perspective of minimum distance between the points in a two-dimensional shape and its boundary. The minimum distance is given by a resultant distance function which is a superposition of the individual distance function between a point within a shape and each boundary point. By elaborating the resultant distance function, the medial axis transform will be obtained naturally. The distance function is modeled as a solid cone and the superposition is equivalent to the union Boolean set operation. The implementation of the approach is simplified using a solid modeling kernel. Several examples of two-dimensional shapes with free form boundaries are raised to illustrate the concept and algorithm.
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摘要 :
The Medial Axis Transform surface, (or MAT or MS) is proving to be a useful tool for several applications and geometric reasoning tasks. However, calculation of the MAT is a time-consuming task and the benefits of the mathematical...
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The Medial Axis Transform surface, (or MAT or MS) is proving to be a useful tool for several applications and geometric reasoning tasks. However, calculation of the MAT is a time-consuming task and the benefits of the mathematical-based tool are offset by the cost of the calculation. This paper presents a method for medial surface calculation which uses subdivision to simplify the problem and hence speed up the calculation, a so-called 'divide-and-conquer' approach. The basis for this is a modification of the dual structure of the original object. As the calculation proceeds this structure is broken up into sub-pieces each representing a simpler sub-part of the MAT. Perhaps more importantly, this method creates a correct node decomposition of the dual structure. The paper goes on to demonstrate some applications of the results for geometric tasks, specifically offsetting and model subdivision, which are normally expensive but are simpler based on the MAT calculation results.
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摘要 :
Currently engineering analysis is regarded as an integrated part of design process and medial axis (MA) is often utilized. However, the generation of MA of complicated models is computation intensive since it is always generated f...
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Currently engineering analysis is regarded as an integrated part of design process and medial axis (MA) is often utilized. However, the generation of MA of complicated models is computation intensive since it is always generated from scratch even if a tiny modification is imposed. A novel local adaptation-based approach to generating the MA for efficient engineering analysis is proposed in this study. With this method, the MA of a resultant model constructed from two other models via a Boolean operation or parameter modification is generated by adapting the MAs of the operand models in a certain way, instead of regenerating the MA from scratch. First, several new properties of the MA which are the fundamental basis of the proposed method are investigated. Then, the boundaries that will vanish from or be added into the resultant model during the Boolean operation or parameter modification are found, and the region in which the MA segments (MASs) need to be regenerated is determined. Finally, the new MASs are generated for the region using an improved tracing method. The final MA of the resultant model is thus constructed by combining the newly generated MASs with the reserved MASs of the operated model(s). Some examples are given to illustrate the high computational efficiency of the proposed method for engineering analysis.
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摘要 :
Currently engineering analysis is regarded as an integrated part of design process and medial axis (MA) is often utilized. However, the generation of MA of complicated models is computation intensive since it is always generated f...
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Currently engineering analysis is regarded as an integrated part of design process and medial axis (MA) is often utilized. However, the generation of MA of complicated models is computation intensive since it is always generated from scratch even if a tiny modification is imposed. A novel local adaptation-based approach to generating the MA for efficient engineering analysis is proposed in this study. With this method, the MA of a resultant model constructed from two other models via a Boolean operation or parameter modification is generated by adapting the MAs of the operand models in a certain way, instead of regenerating the MA from scratch. First, several new properties of the MA which are the fundamental basis of the proposed method are investigated. Then, the boundaries that will vanish from or be added into the resultant model during the Boolean operation or parameter modification are found, and the region in which the MA segments (MASs) need to be regenerated is determined. Finally, the new MASs are generated for the region using an improved tracing method. The final MA of the resultant model is thus constructed by combining the newly generated MASs with the reserved MASs of the operated model(s). Some examples are given to illustrate the high computational efficiency of the proposed method for engineering analysis.
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摘要 :
Currently engineering analysis is regarded as an integrated part of design process and medial axis (MA) is often utilized. However, the generation of MA of complicated models is computation intensive since it is always generated f...
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Currently engineering analysis is regarded as an integrated part of design process and medial axis (MA) is often utilized. However, the generation of MA of complicated models is computation intensive since it is always generated from scratch even if a tiny modification is imposed. A novel local adaptation-based approach to generating the MA for efficient engineering analysis is proposed in this study. With this method, the MA of a resultant model constructed from two other models via a Boolean operation or parameter modification is generated by adapting the MAs of the operand models in a certain way, instead of regenerating the MA from scratch. First, several new properties of the MA which are the fundamental basis of the proposed method are investigated. Then, the boundaries that will vanish from or be added into the resultant model during the Boolean operation or parameter modification are found, and the region in which the MA segments (MASs) need to be regenerated is determined. Finally, the new MASs are generated for the region using an improved tracing method. The final MA of the resultant model is thus constructed by combining the newly generated MASs with the reserved MASs of the operated model(s). Some examples are given to illustrate the high computational efficiency of the proposed method for engineering analysis.
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摘要 :
The medial axis (MA) of a planar region is the locus of those maximal disks contained within its boundary. This entity has many CAD/CAM applications. Approximations based on the Voronoi diagram are efficient for linear-arc boundar...
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The medial axis (MA) of a planar region is the locus of those maximal disks contained within its boundary. This entity has many CAD/CAM applications. Approximations based on the Voronoi diagram are efficient for linear-arc boundaries, but such constructions are more difficult if the boundary is free. This paper proposes an algorithm for free-form boundaries that uses the relation between MA and offsets. It takes the curvature information from the boundary in order to find the self-intersections of successive offset curves. These self-intersection points belong to the MA and can be interpolated to obtain an approximation in Bezier form. This method also approximates the medial axis transform by using the offset distance to each self-intersection.
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摘要 :
The medial axis (MA) of a planar region is the locus of those maximal disks contained within its boundary. This entity has many CAD/CAM applications. Approximations based on the Voronoi diagram are efficient for linear-arc boundar...
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The medial axis (MA) of a planar region is the locus of those maximal disks contained within its boundary. This entity has many CAD/CAM applications. Approximations based on the Voronoi diagram are efficient for linear-arc boundaries, but such constructions are more difficult if the boundary is free. This paper proposes an algorithm for free-form boundaries that uses the relation between MA and offsets. It takes the curvature information from the boundary in order to find the self-intersections of successive offset curves. These self-intersection points belong to the MA and can be interpolated to obtain an approximation in Bezier form. This method also approximates the medial axis transform by using the offset distance to each self-intersection.
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In this paper we present a simple and fast approach for MAT generation in discrete form. It is used for manufacturability analysis in the part modelling stage of injected parts. The method is a volume thinning method based on stra...
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In this paper we present a simple and fast approach for MAT generation in discrete form. It is used for manufacturability analysis in the part modelling stage of injected parts. The method is a volume thinning method based on straight skeleton computation, modified and applied in 3D on B-rep models in STL. The volume thinning of the B-rep model is based on its boundary surfaces offset towards the model interior. The surfaces' offset is done with an adequately proposed offset distance which makes some of the non adjacent offset model surfaces overlap (they 'meet' in mid-surface or MAT). Offset surfaces are used to reconstruct the topology of a new B-rep model (offset model). Overlapping surfaces in the offset model are detected, separated and aggregated to MAT. For adequate MAT precision and adequate MAT radius function, we propose to treat B-rep model concave edges (vertices) as cylinders (spheres) of zero-radius and offset them in an adequate way. On these bases, we present an iterative algorithm in which MAT is constructed in an incremental way by consecutive volume thinning of the obtained offset models. MAT construction is finished when an empty offset model is obtained. An algorithm has been created and implemented in Visual C++. Some of the obtained results are presented in this paper.
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