CNF:CNF Adaptivity - Revision history

Spyridon97: /* Simple Definition */

2020-07-23T23:31:19Z

Simple Definition

← Older revision		Revision as of 18:31, 23 July 2020
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	= Simple Definition =		= Simple Definition =
	The input image is used as a background(BG) mesh while refining the mesh. Before the beginning of the refinement, the input image is analyzed, and the ~~global constraints~~ of ~~maximum~~-element-edge-~~size~~ and element-~~weight~~-~~range are computed~~. The refinement algorithm queries the sizing function (SF) to verify whether each element satisfies the ~~global and~~ user ~~constraints~~. Each time SF is called upon an element, it will check if ~~its size~~ meets the ~~global (maximum~~-element-edge-~~size)~~ and ~~user (min~~-edge~~) constraints~~. Consequently, it will create a set SP of sampling points out of the element. This set consists of the element’s vertices, barycenter, and midpoints of vertices and barycenter. The sampling points that are preserved out of SP are those that lie within the BG mesh. Using the BG mesh, a set V of the values of SP is created. Subsequently, the ~~quantity~~ max(V) - min(V) is evaluated. If ~~abs(max(V)~~ - ~~min(V))~~/~~element~~-weight-range exceeds the user constraint weight-limit, the element is split.		The input image is used as a background(BG) mesh while refining the mesh. Before the beginning of the refinement, the input image is analyzed, and the image-weight-range along with the diagonal of the image is computed, The diagonal is used to define the minimum-element-edge-length and maximum-element-edge-length multiplied by the user-defined min-edge and max-edge diagonal percentages. The refinement algorithm queries the sizing function (SF) to verify whether each element satisfies the user constrains. Each time SF is called upon an element, it will check if it meets the size constraints minimum-element-edge-length and maximum-element-edge-size. Consequently, it will create a set SP of sampling points out of the element. This set consists of the element’s vertices, barycenter, and midpoints of vertices and barycenter. The sampling points that are preserved out of SP are those that lie within the BG mesh. Using the BG mesh, a set V of the values of SP is created. Subsequently, the element-weight-range = abs(max(V) - min(V)) is evaluated. If element-weight-range/image-weight-range exceeds the user constraint weight-limit, the element is split.

	=Results=		=Results=

Spyridon97 at 18:58, 19 June 2020

2020-06-19T18:58:45Z

← Older revision		Revision as of 13:58, 19 June 2020
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	[[Image:AdaptivityAlgorithm.png\|500px]]		[[Image:AdaptivityAlgorithm.png\|500px]]

	# Simple Definition		= Simple Definition =
	The input image is used as a background(BG) mesh while refining the mesh. Before the beginning of the refinement, the input image is analyzed, and the global constraints of maximum-element-edge-size and element-weight-range are computed. The refinement algorithm queries the sizing function (SF) to verify whether each element satisfies the global and user constraints. Each time SF is called upon an element, it will check if its size meets the global (maximum-element-edge-size) and user (min-edge) constraints. Consequently, it will create a set SP of sampling points out of the element. This set consists of the element’s vertices, barycenter, and midpoints of vertices and barycenter. The sampling points that are preserved out of SP are those that lie within the BG mesh. Using the BG mesh, a set V of the values of SP is created. Subsequently, the quantity max(V) - min(V) is evaluated. If abs(max(V) - min(V))/element-weight-range exceeds the user constraint weight-limit, the element is split.		The input image is used as a background(BG) mesh while refining the mesh. Before the beginning of the refinement, the input image is analyzed, and the global constraints of maximum-element-edge-size and element-weight-range are computed. The refinement algorithm queries the sizing function (SF) to verify whether each element satisfies the global and user constraints. Each time SF is called upon an element, it will check if its size meets the global (maximum-element-edge-size) and user (min-edge) constraints. Consequently, it will create a set SP of sampling points out of the element. This set consists of the element’s vertices, barycenter, and midpoints of vertices and barycenter. The sampling points that are preserved out of SP are those that lie within the BG mesh. Using the BG mesh, a set V of the values of SP is created. Subsequently, the quantity max(V) - min(V) is evaluated. If abs(max(V) - min(V))/element-weight-range exceeds the user constraint weight-limit, the element is split.

Spyridon97 at 18:58, 19 June 2020

2020-06-19T18:58:32Z

← Older revision		Revision as of 13:58, 19 June 2020
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	=Algorithm=		=Algorithm=
	[[Image:AdaptivityAlgorithm.png\|500px]]		[[Image:AdaptivityAlgorithm.png\|500px]]

			# Simple Definition
			The input image is used as a background(BG) mesh while refining the mesh. Before the beginning of the refinement, the input image is analyzed, and the global constraints of maximum-element-edge-size and element-weight-range are computed. The refinement algorithm queries the sizing function (SF) to verify whether each element satisfies the global and user constraints. Each time SF is called upon an element, it will check if its size meets the global (maximum-element-edge-size) and user (min-edge) constraints. Consequently, it will create a set SP of sampling points out of the element. This set consists of the element’s vertices, barycenter, and midpoints of vertices and barycenter. The sampling points that are preserved out of SP are those that lie within the BG mesh. Using the BG mesh, a set V of the values of SP is created. Subsequently, the quantity max(V) - min(V) is evaluated. If abs(max(V) - min(V))/element-weight-range exceeds the user constraint weight-limit, the element is split.

	=Results=		=Results=

Spyridon97: Spyridon97 moved page Internal:CNF Adaptivity to CNF:CNF Adaptivity

2020-06-19T18:39:06Z

Spyridon97 moved page Internal:CNF Adaptivity to CNF:CNF Adaptivity

← Older revision	Revision as of 13:39, 19 June 2020
(No difference)

Spyridon97: Spyridon97 moved page CNF Adaptivity to Internal:CNF Adaptivity

2020-04-30T20:09:44Z

Spyridon97 moved page CNF Adaptivity to Internal:CNF Adaptivity

← Older revision	Revision as of 15:09, 30 April 2020
(No difference)

Spyridon97: Spyridon97 moved page Adaptivity to CNF Adaptivity

2020-04-30T20:04:42Z

Spyridon97 moved page Adaptivity to CNF Adaptivity

← Older revision	Revision as of 15:04, 30 April 2020
(No difference)

Spyridon97 at 20:04, 30 April 2020

2020-04-30T20:04:08Z

← Older revision		Revision as of 15:04, 30 April 2020
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			=Introduction=
	In [9], the ''CRTC ''developed ''PODM'', which is a parallel Image to Mesh conversion algorithm with quality and fidelity guarantees. Using ''PODM'', ''JLab'' acquired the ability to convert their phase-space distribution images to meshes and then utilize them for Monte Carlo Simulations. Nonetheless, ''JLab ''requested that their phase-space distribution images should be converted to adaptive meshes, which means adapting the tessellation procedure to the n-dimensional features of their distribution.		In [9], the ''CRTC ''developed ''PODM'', which is a parallel Image to Mesh conversion algorithm with quality and fidelity guarantees. Using ''PODM'', ''JLab'' acquired the ability to convert their phase-space distribution images to meshes and then utilize them for Monte Carlo Simulations. Nonetheless, ''JLab ''requested that their phase-space distribution images should be converted to adaptive meshes, which means adapting the tessellation procedure to the n-dimensional features of their distribution.

	In [10], CERN dealt with an equivalent problem and developed a general-purpose, self-adapting Monte Carlo (MC) event generator (simulator) Foam algorithm. Leveraging this algorithm, ''the CRTC ''developed an algorithm to support adaptive tessellation in N-D with user-defined parameters (minimum element size, element weight limit) and integrated it into its Mesh Generators, ''Tesselate 2D'' and'' PODM 3D''. Similarly, this algorithm is separated into two stages. The first stage is the initialization of the adaptive function which in a sense extracts the n-dimensional features of the distribution image and saves its attributes. The second and most crucial stage is the check if the adaptive function needs to be applied to a specific element, and only then the element is split. First, it computes the necessary parameters of the geometry of the element, and then, if it meets those and user-defined parameters, the element is split. The check of the adaptive function is made if and only if the tested element meets all the Delaunay refinement rules of its Mesh Generator.		In [10], CERN dealt with an equivalent problem and developed a general-purpose, self-adapting Monte Carlo (MC) event generator (simulator) Foam algorithm. Leveraging this algorithm, '' the CRTC '' developed an algorithm to support adaptive tessellation in N-D with user-defined parameters (minimum element size, element weight limit) and integrated it into its Mesh Generators, ''Tesselate 2D'' and'' PODM 3D''. Similarly, this algorithm is separated into two stages. The first stage is the initialization of the adaptive function which in a sense extracts the n-dimensional features of the distribution image and saves its attributes. The second and most crucial stage is the check if the adaptive function needs to be applied to a specific element, and only then the element is split. First, it computes the necessary parameters of the geometry of the element, and then, if it meets those and user-defined parameters, the element is split. The check of the adaptive function is made if and only if the tested element meets all the Delaunay refinement rules of its Mesh Generator.

			=Algorithm=
	[[Image:AdaptivityAlgorithm.png\|500px]]		[[Image:AdaptivityAlgorithm.png\|500px]]

	# ~~Modify Adaptivity Report in~~ a ~~way that can be included in the report of January~~		=Results=
			# Podm Result of Gagic Data image with volume grading on and δ=6, minimum Volume Size = 0.5, limit = 0.1✔
			## 2D (Triangle): [[File:NT_X_min_0.5_limit_2e-3_interpolated.png\|500px\|Nt2DAdaptivity]] (Done by Christos)
			## 3D (PODM): [[File:NtAdaptivity.png\|500px\|Nt3DAdaptivity]] (Done with Christos)
			# Produce an Animated Adaptive Procedure video http://www.cs.odu.edu/crtc/videos/PODM3D.html ✔
			## [[File:InputImage.png\|250px\|InputImage]] -> Input Image:
			## [[File:ImageSegmentation.png\|250px\|ImageSegmentation]] -> Image Segmentation
			## [[File:AdaptiveMeshing.gif\|250px\|AdaptiveMeshing]] -> Meshing Procedure. This is a gif which is visible here: https://crtc.cs.odu.edu/images/8/89/AdaptiveMeshing.gif
			## [[File:AdaptedMesh.png\|250px\|AdaptedMesh]] -> Adapted mesh
			## [[File:LinearInterpolation.png\|250px\|LinearInterpolation]] -> Linear Interpolation

Spyridon97 at 22:19, 3 November 2019

2019-11-03T22:19:14Z

← Older revision		Revision as of 17:19, 3 November 2019
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	[[Image:AdaptivityAlgorithm.png\|500px]]		[[Image:AdaptivityAlgorithm.png\|500px]]

			# Modify Adaptivity Report in a way that can be included in the report of January

Spyridon97 at 21:47, 3 November 2019

2019-11-03T21:47:32Z

← Older revision		Revision as of 16:47, 3 November 2019
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	In [9], the ''CRTC ''developed ''PODM'', which is a parallel Image to Mesh conversion algorithm with quality and fidelity guarantees. Using ''PODM'', ''JLab'' acquired the ability to convert their phase-space distribution images to meshes and then utilize them for Monte Carlo Simulations. Nonetheless, ''JLab ''requested that their phase-space distribution images should be converted to adaptive meshes, which means adapting the tessellation procedure to the n-dimensional ~~shape~~ of their distribution.		In [9], the ''CRTC ''developed ''PODM'', which is a parallel Image to Mesh conversion algorithm with quality and fidelity guarantees. Using ''PODM'', ''JLab'' acquired the ability to convert their phase-space distribution images to meshes and then utilize them for Monte Carlo Simulations. Nonetheless, ''JLab ''requested that their phase-space distribution images should be converted to adaptive meshes, which means adapting the tessellation procedure to the n-dimensional features of their distribution.

	In [10], CERN dealt with an equivalent problem and developed a general-purpose, self-adapting Monte Carlo (MC) event generator (simulator) Foam algorithm. Leveraging this algorithm, ''the CRTC ''developed an algorithm to support adaptive tessellation in N-D with user-defined parameters (minimum element size, element weight limit) and integrated it into its Mesh Generators, ''Tesselate 2D'' and'' PODM 3D''. Similarly, this algorithm is separated into two stages. The first stage is the initialization of the adaptive function which in a sense ~~explores~~ the n-dimensional ~~shape~~ of the distribution image and saves its attributes. The second and most crucial stage is the check if the adaptive function needs to be applied to a specific element, and only then the element is split. First, it computes the necessary parameters of the geometry of the element, and then, if it meets those and user-defined parameters, the element is split. The check of the adaptive function is made if and only if the tested element meets all the Delaunay refinement rules of its Mesh Generator.		In [10], CERN dealt with an equivalent problem and developed a general-purpose, self-adapting Monte Carlo (MC) event generator (simulator) Foam algorithm. Leveraging this algorithm, ''the CRTC ''developed an algorithm to support adaptive tessellation in N-D with user-defined parameters (minimum element size, element weight limit) and integrated it into its Mesh Generators, ''Tesselate 2D'' and'' PODM 3D''. Similarly, this algorithm is separated into two stages. The first stage is the initialization of the adaptive function which in a sense extracts the n-dimensional features of the distribution image and saves its attributes. The second and most crucial stage is the check if the adaptive function needs to be applied to a specific element, and only then the element is split. First, it computes the necessary parameters of the geometry of the element, and then, if it meets those and user-defined parameters, the element is split. The check of the adaptive function is made if and only if the tested element meets all the Delaunay refinement rules of its Mesh Generator.

	[[Image:AdaptivityAlgorithm.png\|500px]]		[[Image:AdaptivityAlgorithm.png\|500px]]

	~~#replace volume check with edge length check~~
	~~# braces instead of parenthesis and comma instead of +~~
	~~# max value = - infinity~~
	~~# value = query (input image, sample point)~~
	~~# remove abs value~~

Spyridon97 at 13:09, 29 October 2019

2019-10-29T13:09:42Z

← Older revision		Revision as of 08:09, 29 October 2019
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	#replace volume check with edge length check		#replace volume check with edge length check
			# braces instead of parenthesis and comma instead of +
			# max value = - infinity
			# value = query (input image, sample point)
			# remove abs value