Coll et al 2014b - Revision history

Cinmemj: Cinmemj moved page Draft Samper 249832658 to Coll et al 2014b

2018-03-13T12:06:18Z

Cinmemj moved page Draft Samper 249832658 to Coll et al 2014b

Cinmemj at 12:04, 13 March 2018

2018-03-13T12:04:12Z

Cinmemj at 11:45, 13 March 2018

2018-03-13T11:45:19Z

Cinmemj at 11:39, 13 March 2018

2018-03-13T11:39:56Z

Cinmemj at 11:35, 13 March 2018

2018-03-13T11:35:11Z

Cinmemj at 11:33, 13 March 2018

2018-03-13T11:33:32Z

Cinmemj at 11:31, 13 March 2018

2018-03-13T11:31:02Z

Cinmemj at 11:28, 13 March 2018

2018-03-13T11:28:06Z

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Cinmemj at 11:07, 13 March 2018

2018-03-13T11:07:41Z

Cinmemj at 11:03, 13 March 2018

2018-03-13T11:03:23Z

@@ Line 5,322: / Line 5,322: @@
 '''[[#citeF-66|[66]]]''' Barcelona Media. (2014) "www.barcelonamedia.org/seccio/bm-labs/laboratori-de-visualitzacio-virtual"
-=9 Profiling tables and complete data of examples=
+=A Profiling tables and complete data of examples=
 This annex compile all the results data from the examples shown in chapter&nbsp;[[#7 Examples|7]].
-==9.1 <span id='lb-9.1'></span>Validation example VE-T1==
+==A.1 <span id='lb-A.1'></span>Validation example VE-T1==
 <div id='img-135'></div>
@@ Line 5,441: / Line 5,441: @@
 |}
-==9.2 <span id='lb-9.2'></span>Validation example VE-T2==
+==A.2 <span id='lb-A.2'></span>Validation example VE-T2==
@@ Line 5,556: / Line 5,556: @@
 |}
-==9.3 <span id='lb-9.3'></span>Validation example VE-T3==
+==A.3 <span id='lb-A.3'></span>Validation example VE-T3==
@@ Line 5,671: / Line 5,671: @@
 |}
-==9.4 <span id='lb-9.4'></span>Validation example VE-F1==
+==A.4 <span id='lb-A.4'></span>Validation example VE-F1==
@@ Line 5,792: / Line 5,792: @@
 |}
-==9.5 <span id='lb-9.5'></span>Validation example VE-F2==
+==A.5 <span id='lb-A.5'></span>Validation example VE-F2==
@@ Line 5,910: / Line 5,910: @@
 |}
-==9.6 <span id='lb-9.6'></span>Validation example VE-W1==
+==A.6 <span id='lb-A.6'></span>Validation example VE-W1==
@@ Line 6,025: / Line 6,025: @@
 |}
-==9.7 <span id='lb-9.7'></span>Validation example VE-W2==
+==A.7 <span id='lb-A.7'></span>Validation example VE-W2==
@@ Line 6,143: / Line 6,143: @@
 |}
-==9.8 <span id='lb-9.8'></span>Validation example VE-W3==
+==A.8 <span id='lb-A.8'></span>Validation example VE-W3==
@@ Line 6,255: / Line 6,255: @@
 |}
-==9.9 <span id='lb-9.9'></span>Validation example VE-C1==
+==A.9 <span id='lb-A.9'></span>Validation example VE-C1==
@@ Line 6,370: / Line 6,370: @@
 |}
-==9.10 <span id='lb-9.10'></span>Validation example VE-C2==
+==A.10 <span id='lb-A.10'></span>Validation example VE-C2==
@@ Line 6,485: / Line 6,485: @@
 |}
-==9.11 <span id='lb-9.11'></span>Validation example VE-C3==
+==A.11 <span id='lb-A.11'></span>Validation example VE-C3==
@@ Line 6,600: / Line 6,600: @@
 |}
-==9.12 <span id='lb-9.12'></span>Validation example VE-I1==
+==A.12 <span id='lb-A.12'></span>Validation example VE-I1==
@@ Line 6,715: / Line 6,715: @@
 |}
-==9.13 <span id='lb-9.13'></span>Validation example VE-E1==
+==A.13 <span id='lb-A.13'></span>Validation example VE-E1==
@@ Line 6,784: / Line 6,784: @@
 |}
-==9.14 <span id='lb-9.14'></span>Validation example VE-S1==
+==A.14 <span id='lb-A.14'></span>Validation example VE-S1==
@@ Line 6,962: / Line 6,962: @@
 |}
-==9.15 <span id='lb-9.15'></span>Validation example VE-S2==
+==A.15 <span id='lb-A.15'></span>Validation example VE-S2==
@@ Line 7,146: / Line 7,146: @@
 |}
-==9.16 Racing car==
+==A.16 Racing car==
@@ Line 7,259: / Line 7,259: @@
 |}
-==9.17 Barcelona model==
+==A.17 Barcelona model==

@@ Line 3,612: / Line 3,612: @@
 The data of the generated mesh is detailed in Table&nbsp;[[#table-8|8]].
@@ Line 3,842: / Line 3,840: @@
 The data of the generated mesh is detailed in Table&nbsp;[[#table-11|11]].
@@ Line 3,942: / Line 3,938: @@
 | colspan="2" | '''Figure 94:''' Mesh generated of the model of <math>VE-W3</math>. '''(a)''' Zoom view of a part of the model. '''(b)''' Zoom of a selection of inner tetrahedra.
 |}
@@ Line 4,021: / Line 4,015: @@
 The data of the generated mesh is detailed in Table&nbsp;[[#table-13|13]].
@@ Line 4,117: / Line 4,109: @@
 The data of the generated mesh is detailed in Table&nbsp;[[#table-14|14]].
@@ Line 4,187: / Line 4,177: @@
 The data of the generated mesh is detailed in Table&nbsp;[[#table-15|15]].
@@ Line 4,261: / Line 4,249: @@
 The data of the generated mesh of this validation example is detailed in Table&nbsp;[[#table-16|16]].
@@ Line 4,358: / Line 4,344: @@
 The data of the generated mesh is detailed in Table&nbsp;[[#table-17|17]].
@@ Line 4,453: / Line 4,437: @@
 The characteristics of each configuration are depicted in Table&nbsp;[[#table-18|18]].
@@ Line 4,541: / Line 4,523: @@
 The characteristics of each configuration are detailed in Table&nbsp;[[#table-19|19]]. The minimum dihedral angle of the tetrahedra generated is higher than <math display="inline">5</math> degrees in all the configurations.

← Older revision		Revision as of 11:39, 13 March 2018
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	The data of the generated mesh is detailed in Table [[#table-10\|10]].		The data of the generated mesh is detailed in Table [[#table-10\|10]].
−
−	~~[h!]~~

← Older revision		Revision as of 11:35, 13 March 2018
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	The data of the generated mesh is detailed in Table [[#table-9\|9]].		The data of the generated mesh is detailed in Table [[#table-9\|9]].
−
−	~~[h!]~~
−

	{\| class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;"		{\| class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;"

@@ Line 3,597: / Line 3,597: @@
 |-
 |[[Image:draft_Samper_249832658-monograph-wing_profile_final_mesh_v2.png|300px|(a)]]
-|[[Image:draft_Samper_249832658-monograph-wing_profile_zoom_mesh_v2.png|420px|(b)]]
+|[[Image:draft_Samper_249832658-monograph-wing_profile_zoom_mesh_v2.png|300px|(b)]]
 |- style="text-align: center; font-size: 75%;"
 | (a)
 | (b)
 |-
-| colspan="2"|[[Image:draft_Samper_249832658-monograph-wing_profile_zoom_mesh_v3.png|420px|(c)]]
+| colspan="2"|[[Image:draft_Samper_249832658-monograph-wing_profile_zoom_mesh_v3.png|300px|(c)]]
 |- style="text-align: center; font-size: 75%;"
 |  colspan="2" | (c)

← Older revision	Revision as of 12:06, 13 March 2018
(No difference)

← Older revision		Revision as of 11:31, 13 March 2018
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	A mesh with a mesh size of <math display="inline">0.1</math> has been generated using the presented algorithm. The final mesh is shown in Figure [[#img-79\|79]]. It can be appreciated that the topology of the model is preserved. The data of the generated mesh is detailed in Table [[#table-7\|7]].		A mesh with a mesh size of <math display="inline">0.1</math> has been generated using the presented algorithm. The final mesh is shown in Figure [[#img-79\|79]]. It can be appreciated that the topology of the model is preserved. The data of the generated mesh is detailed in Table [[#table-7\|7]].
−
−	~~[h!]~~
−

	{\| class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;"		{\| class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;"

@@ Line 1,593: / Line 1,593: @@
 A 2D example of the algorithm is depicted in Table [[#5.2.4 Meshing algorithm|5.2.4]], where each step is illustrated by a figure. The model is formed by two surfaces in contact (drawn in orange and blue), and it contains only two mesh size points (represented by a cross in the figures) in the input data.
-[c] p
+{| class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;
+|style="width: 65%;"|1- ''Process input data and create the octree root''. The crosses are the mesh size points. The arrow beside each mesh size point represents its associated size. The octree root is the black square, and the <math display="inline">Bbox_{m}^{+}</math> of the model is drawn with dotted lines. <math display="inline">S_{max}</math> in this example coincides with <math display="inline">S_2</math>, as it is the largest size coming from the generalized mesh size points, and it is smaller than <math display="inline">s_{box}</math>.
-.55 1- ''Process input data and create the octree root''. The crosses are the mesh size points. The arrow beside each mesh size point represents its associated size. The octree root is the black square, and the <math display="inline">Bbox_{m}^{+}</math> of the model is drawn with dotted lines. <math display="inline">S_{max}</math> in this example coincides with <math display="inline">S_2</math>, as it is the largest size coming from the generalized mesh size points, and it is smaller than <math display="inline">s_{box}</math>.
+|[[Image:draft_Samper_249832658-monograph-embedded_algorithm_1.png|300px|Figures/chapter_octree/embedded_algorithm_1]]
+|-
-.33 [[Image:draft_Samper_249832658-monograph-embedded_algorithm_1.png|300px|Figures/chapter_octree/embedded_algorithm_1]]
+|2- ''Refine the octree accomplishing the size refinement criteria''. In this example the size transition factor is equal to one (the transition corresponds to the constrained two to one condition) to make the figure clearer.
+|[[Image:draft_Samper_249832658-monograph-embedded_algorithm_2.png|300px|Figures/chapter_octree/embedded_algorithm_2]]
-.55 2- ''Refine the octree accomplishing the size refinement criteria''. In this example the size transition factor is equal to one (the transition corresponds to the constrained two to one condition) to make the figure clearer.
+|-
+|3- ''Classify the input boundary entities into the octree''. It is important to note that, until now, the input boundaries only have been considered to build the bounding box of the model, but they have not been implied in the octree refinement process.
-.33 [[Image:draft_Samper_249832658-monograph-embedded_algorithm_2.png|300px|Figures/chapter_octree/embedded_algorithm_2]]
+|[[Image:draft_Samper_249832658-monograph-embedded_algorithm_3.png|300px|Figures/chapter_octree/embedded_algorithm_3]]
+|-
-.55 3- ''Classify the input boundary entities into the octree''. It is important to note that, until now, the input boundaries only have been considered to build the bounding box of the model, but they have not been implied in the octree refinement process.
+|4- ''Create and color the linear octree nodes and compute the distances to the input boundaries''. The nodes of the figure are painted with the corresponding color: orange or blue if they are inside the corresponding surface, black if they are onto the input boundaries, and white if the are outside the domain.
+|[[Image:draft_Samper_249832658-monograph-embedded_algorithm_4.png|300px|Figures/chapter_octree/embedded_algorithm_4]]
-.33 [[Image:draft_Samper_249832658-monograph-embedded_algorithm_3.png|300px|Figures/chapter_octree/embedded_algorithm_3]]
+|-
+|5- ''Apply the tetrahedra pattern''. It can be appreciated in this figure that the final tetrahedra (triangles in this 2D case) are not body-fitted, as they do not preserve the original shape of the domain.
-.55 4- ''Create and color the linear octree nodes and compute the distances to the input boundaries''. The nodes of the figure are painted with the corresponding color: orange or blue if they are inside the corresponding surface, black if they are onto the input boundaries, and white if the are outside the domain.
+|[[Image:draft_Samper_249832658-monograph-embedded_algorithm_5.png|300px|Figures/chapter_octree/embedded_algorithm_5]]
+|}
-.33 [[Image:draft_Samper_249832658-monograph-embedded_algorithm_4.png|300px|Figures/chapter_octree/embedded_algorithm_4]]
-−
-.55 5- ''Apply the tetrahedra pattern''. It can be appreciated in this figure that the final tetrahedra (triangles in this 2D case) are not body-fitted, as they do not preserve the original shape of the domain.
-−
-.33 [[Image:draft_Samper_249832658-monograph-embedded_algorithm_5.png|300px|Figures/chapter_octree/embedded_algorithm_5]]
 Steps followed by the embedded meshing algorithm applied to a 2D example with two surfaces and two mesh size points.

@@ Line 1,273: / Line 1,273: @@
 A graphical interpretation of these cases in a 2D example is illustrated in Table&nbsp;[[#4.3.1 Pathological situations|4.3.1]]. As a 2D cases, only two surrounding segments take sense for a MIP.
-[c] p
+{| class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;
+|style="width: 65%;"| Case I: there are three interfacing surfaces (<math display="inline">A</math>, <math display="inline">B</math> and zero) involved in the intersection points of the surrounding segments. <math display="inline">M</math> intersection type.
-.55 Case I: there are three interfacing surfaces (<math display="inline">A</math>, <math display="inline">B</math> and zero) involved in the intersection points of the surrounding segments. <math display="inline">M</math> intersection type.
+| [[Image:draft_Samper_249832658-monograph-ray_pathological_M_segments.png|300px|Figures/chapter_coloring/ray_pathological_M_segments]]
+|-
-.35 [[Image:draft_Samper_249832658-monograph-ray_pathological_M_segments.png|300px|Figures/chapter_coloring/ray_pathological_M_segments]]
+|Case II: all the intersected entities have the same interfacing surfaces (<math display="inline">A</math> and zero), and there is one surrounding segment with no intersection. <math display="inline">T</math> intersection type.
+|[[Image:draft_Samper_249832658-monograph-ray_pathological_T_segments.png|300px|Figures/chapter_coloring/ray_pathological_T_segments]]
-.55 Case II: all the intersected entities have the same interfacing surfaces (<math display="inline">A</math> and zero), and there is one surrounding segment with no intersection. <math display="inline">T</math> intersection type.
+|-
+|Case IIIa: each of the surrounding segments intersects the boundaries in one point and all the interfacing surfaces are the same (<math display="inline">A</math> and zero). <math display="inline">C</math> intersection type.
-.35 [[Image:draft_Samper_249832658-monograph-ray_pathological_T_segments.png|300px|Figures/chapter_coloring/ray_pathological_T_segments]]
+|[[Image:draft_Samper_249832658-monograph-ray_pathological_C_segments.png|300px|Figures/chapter_coloring/ray_pathological_C_segments]]
+|-
-.55 Case IIIa: each of the surrounding segments intersects the boundaries in one point and all the interfacing surfaces are the same (<math display="inline">A</math> and zero). <math display="inline">C</math> intersection type.
+|Case IIIb: all the surrounding segments can create a MIP (its intersection points are closer than <math display="inline">tol_c</math>) and all the interfacing surfaces are the same (<math display="inline">A</math> and zero). <math display="inline">W</math> intersection type.
+| [[Image:draft_Samper_249832658-monograph-ray_pathological_W_segments.png|300px|Figures/chapter_coloring/ray_pathological_W_segments]]
-.35 [[Image:draft_Samper_249832658-monograph-ray_pathological_C_segments.png|300px|Figures/chapter_coloring/ray_pathological_C_segments]]
+|-
+|Case IIIc: Some surrounding segment has more than one intersection point. <math display="inline">T</math> intersection type.
-.55  Case IIIb: all the surrounding segments can create a MIP (its intersection points are closer than <math display="inline">tol_c</math>) and all the interfacing surfaces are the same (<math display="inline">A</math> and zero). <math display="inline">W</math> intersection type.
+| [[Image:draft_Samper_249832658-monograph-ray_pathological_T2_segments.png|300px|Figures/chapter_coloring/ray_pathological_T2_segments]]
+|}
-.35 [[Image:draft_Samper_249832658-monograph-ray_pathological_W_segments.png|300px|Figures/chapter_coloring/ray_pathological_W_segments]]
-−
-.55 Case IIIc: Some surrounding segment has more than one intersection point. <math display="inline">T</math> intersection type.
-−
-.35 [[Image:draft_Samper_249832658-monograph-ray_pathological_T2_segments.png|300px|Figures/chapter_coloring/ray_pathological_T2_segments]]
 Different cases for surrounding segments for identification of intersection types corresponding to a MIP (white dot) in a 2D example.