To better guide the coating process of rectangular tiles on a ship hull, a computerized three-dimensional design method is proposed. Research was done on a tile generating algorithm, tile laying design flow, tiles gap...To better guide the coating process of rectangular tiles on a ship hull, a computerized three-dimensional design method is proposed. Research was done on a tile generating algorithm, tile laying design flow, tiles gap examination algorithm, and tiles slight displacement, as well as cutting and rotating algorithms.A three-dimensional design system was developed using an MDT platform. The application of this system indicates that using the design arrangement to coat tiles on a ship’s hull can result in enhanced coating quality.展开更多
A new 3D layout algorithm to lay rectangular tiles on the 3D hull surface model is proposed to improve the algorithm performance in accelerating layout process and enhancing design accuracy. Three times optimizations ...A new 3D layout algorithm to lay rectangular tiles on the 3D hull surface model is proposed to improve the algorithm performance in accelerating layout process and enhancing design accuracy. Three times optimizations are carried out upon the original basic algorithm, namely optimization of calculating range, separation of surface flattening computation from laying computation, and optimization of interior point distribution. By testing, the generated surface layout drawing by the refined system is fairly applicable to guide the actual tiles＇ coating process.展开更多
Rectangular tiles can be laid on a ship's hull for protection, but the sides of the tiles must be adjusted so adjacent tiles will conform to the curvature of the hull.A method for laying tiles along a reference li...Rectangular tiles can be laid on a ship's hull for protection, but the sides of the tiles must be adjusted so adjacent tiles will conform to the curvature of the hull.A method for laying tiles along a reference line was proposed, and an allowable range of displacement for the four vertices of the tile was determined.Deformations of each tile on a specific reference line were then obtained.It was found that the least deformation was required when the tiles were laid parallel to a line with the least curvature.After calculating the mean curvature on the surface, the surface was divided into three layout areas.A set of discrete points following the least deformation of the principal curvatures was obtained.A NURBS interpolation curve was then plotted as the reference line for laying tiles.The optimum size of the tiles was obtained, given the allowable maximum deformation condition.This minimized the number of bolts and the amount of stuffing.A typical aft hull section was selected and divided into three layout areas based on the distribution of curvature.The optimum sizes of rectangular tiles were obtained for every layout area and they were then laid on the surface.In this way the layout of the rectangular tiles could be plotted.展开更多
The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by p...The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these tiles about the first bisector. Only translations of the tiles are allowed in a tiling. If the sides of the dissected rectangle are coprime, we show the existence of tilings of all (skewed) quadrants that do not follow the rectangular (parallelogram) pattern. If one of the sides of the dissected rectangle is 2 and the other is odd, we also show tilings of rectangles by the tile set that do not follow the rectangular pattern. If one of the sides of the dissected rectangle is 2 and the other side is even, we show a new infinite family of tile sets that follows the rectangular pattern when tiling one of the quadrants. For this type of dis-section, we also show a new infinite family that does not follow the rectangular pattern when tiling rectangles. Finally, we investigate more general dissections of rectangles, with. Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.展开更多
Let and let be the set of four ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by . Our main result shows a remarkable property of this set of tiles: any tiling of the first quadran...Let and let be the set of four ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by . Our main result shows a remarkable property of this set of tiles: any tiling of the first quadrant by , n even, reduces to a tiling by and rectangles, each rectangle being covered by two ribbon L-shaped n-ominoes. An application of our result is the characterization of all rectangles that can be tiled by , n even: a rectangle can be tiled by , n even, if and only if both of its sides are even and at least one side is divisible by n. Another application is the existence of the local move property for an infinite family of sets of tiles: , n even, has the local move property for the class of rectangular regions with respect to the local moves that interchange a tiling of an square by n/2 vertical rectangles, with a tiling by n/2 horizontal rectangles, each vertical/horizontal rectangle being covered by two ribbon L-shaped n-ominoes. We show that none of these results are valid for any odd n. The rectangular pattern of a tiling of the first quadrant persists if we add an extra tile to , n even. A rectangle can be tiled by the larger set of tiles if and only if it has both sides even. We also show that our main result implies that a skewed L-shaped n-omino, n even, is not a replicating tile of order k2 for any odd k.展开更多
文摘To better guide the coating process of rectangular tiles on a ship hull, a computerized three-dimensional design method is proposed. Research was done on a tile generating algorithm, tile laying design flow, tiles gap examination algorithm, and tiles slight displacement, as well as cutting and rotating algorithms.A three-dimensional design system was developed using an MDT platform. The application of this system indicates that using the design arrangement to coat tiles on a ship’s hull can result in enhanced coating quality.
基金Supported by the Fundamental Research and Application Fund for Ship Industry (04J1.13.3)
文摘A new 3D layout algorithm to lay rectangular tiles on the 3D hull surface model is proposed to improve the algorithm performance in accelerating layout process and enhancing design accuracy. Three times optimizations are carried out upon the original basic algorithm, namely optimization of calculating range, separation of surface flattening computation from laying computation, and optimization of interior point distribution. By testing, the generated surface layout drawing by the refined system is fairly applicable to guide the actual tiles＇ coating process.
基金Supported by Technological Support Project of Equipment Pre-research under Grant No.62201080202
文摘Rectangular tiles can be laid on a ship's hull for protection, but the sides of the tiles must be adjusted so adjacent tiles will conform to the curvature of the hull.A method for laying tiles along a reference line was proposed, and an allowable range of displacement for the four vertices of the tile was determined.Deformations of each tile on a specific reference line were then obtained.It was found that the least deformation was required when the tiles were laid parallel to a line with the least curvature.After calculating the mean curvature on the surface, the surface was divided into three layout areas.A set of discrete points following the least deformation of the principal curvatures was obtained.A NURBS interpolation curve was then plotted as the reference line for laying tiles.The optimum size of the tiles was obtained, given the allowable maximum deformation condition.This minimized the number of bolts and the amount of stuffing.A typical aft hull section was selected and divided into three layout areas based on the distribution of curvature.The optimum sizes of rectangular tiles were obtained for every layout area and they were then laid on the surface.In this way the layout of the rectangular tiles could be plotted.
文摘The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these tiles about the first bisector. Only translations of the tiles are allowed in a tiling. If the sides of the dissected rectangle are coprime, we show the existence of tilings of all (skewed) quadrants that do not follow the rectangular (parallelogram) pattern. If one of the sides of the dissected rectangle is 2 and the other is odd, we also show tilings of rectangles by the tile set that do not follow the rectangular pattern. If one of the sides of the dissected rectangle is 2 and the other side is even, we show a new infinite family of tile sets that follows the rectangular pattern when tiling one of the quadrants. For this type of dis-section, we also show a new infinite family that does not follow the rectangular pattern when tiling rectangles. Finally, we investigate more general dissections of rectangles, with. Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.
文摘Let and let be the set of four ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by . Our main result shows a remarkable property of this set of tiles: any tiling of the first quadrant by , n even, reduces to a tiling by and rectangles, each rectangle being covered by two ribbon L-shaped n-ominoes. An application of our result is the characterization of all rectangles that can be tiled by , n even: a rectangle can be tiled by , n even, if and only if both of its sides are even and at least one side is divisible by n. Another application is the existence of the local move property for an infinite family of sets of tiles: , n even, has the local move property for the class of rectangular regions with respect to the local moves that interchange a tiling of an square by n/2 vertical rectangles, with a tiling by n/2 horizontal rectangles, each vertical/horizontal rectangle being covered by two ribbon L-shaped n-ominoes. We show that none of these results are valid for any odd n. The rectangular pattern of a tiling of the first quadrant persists if we add an extra tile to , n even. A rectangle can be tiled by the larger set of tiles if and only if it has both sides even. We also show that our main result implies that a skewed L-shaped n-omino, n even, is not a replicating tile of order k2 for any odd k.
