CATIA V4/V5 Interoperability Project 2 : Migration of V4 surface : Influence of the transfer s settings Genta Yoshioka

Transcription

1 CATIA V4/V5 Interoperability Project 2 : Migration of V4 surface : Influence of the transfer s settings Genta Yoshioka Version /08/2001 CATIA Interoperability Project Office CIPO IBM Frankfurt, Germany

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3 Generated Table of Content 1 INTRODUCTION USED HARDWARE AND SOFTWARE FOR TESTING DEFINITION OF SURFACE MIGRATION: INFLUENCE OF TRANSFER S SETTINGS OUTLINE OF SURFACE TRANSFER S ALGORITHM MULTI-PATCH SURFACE TRANSFER HOMOGENIZATION OF THE PATCH S DEGREES INFLUENCE OF THE INTERSECTION PROJECTION TOLERANCE IN V4 TO REACH CONTINUITY V4 settings Surface s case Curve s case INFLUENCE OF MAXIMUM DEFORMATION VALUE IN V5 TO OBTAIN C2 CONTINUITY V4/V5 SPACE Setting Deformation to obtain C2 continuity of surface Segmentation setting V4 SKIN S TRANSFER (*SKI) HOW TO CHECK THE POSITION OF TRANSFERRED CONTROL POINTS: TESTED CASES V4 MULTI-PATCH SURFACE AND MULTI-ARC CURVE V4 model for testing Summary of the test V4 SKIN (*SKI) AND COMPOSITE CURVE (*CCV) V4 model for testing Summary of the test CONCLUSIONS...14 A. APPENDIX: CURVE & SURFACE BASIC...15 CURVE...15 Bezier ARC : definition...15 Nurbs Curve: definition...15 SURFACE...16 Bezier Patch: definition...16 Nurbs surface: definition...16 Nurbs Curve/Surface: in V TRANSFER...17 Transfer Bezier to Nurbs (V4 data structure to V5 data structure)...17 Transfer Nurbs to Bezier (V5 data structure to V4 data structure)...17 B. APPENDIX: DEGREE OF V4 AND V5 SURFACE...18 The properties of V4 and V5 s surface s degree (order)...18 The maximum value of the order of a V4 and V5 surface...18 C. APPENDIX: V4 MULTI-PATCH SURFACE AND MULTI-ARC CURVE TESTS...19 D. APPENDIX: V4 SKIN (*SKI) AND COMPOSITE CURVE (*CCV) TESTS...24 p02s02-surfacemigrationsettingsv1-0.doc - 3 -

4 Generated Table of Figures Figure 1 Homogenization of the patch s degrees...6 Figure 2 V4 skin s transfer...6 Figure 3 V4 settings...7 Figure 4 V5 settings...8 Figure 5 Connect checker...9 Figure 6 Control point positioning...10 Figure 7 V4 model tested (multi-patch surface & multi-arc curve)...11 Figure 8 V4 model tested (*SKI & *CCV)...12 Figure 9 Bezier arc...15 Figure 10 Sample of Nupbs...17 Figure 11 Setting of the maximum order...18 Figure 12 Test result of multi-patch surface & multi-arc curve Case Figure 13 Test result of multi-patch surface & multi-arc curve Case Figure 14 Test result of multi-patch surface & multi-arc curve Case Figure 15 Test result of multi-patch surface & multi-arc curve Case Figure 16 Continuity check of test case Figure 17 Continuity check of test case p02s02-surfacemigrationsettingsv1-0.doc - 4 -

5 1 Introduction This document is based on the V4 and V5 integration tests carried out in the CATIA Interoperability Project Office (CIPO) at IBM Frankfurt, Germany. To fully understand this document the CATIA specialist requires knowledge of CATIA V4 product and Global understanding of V5. In case of any specific application related topics please consult the specialist in that area. 2 Used Hardware and Software for Testing All the tests in this Document has been done by the following Hardware and Software: Hardware: SUNIX: RS/ with GXT 3000 SNT: IntelliStation M-Pro I3D Wildcat Graphics Adapter Software: SUNIX AIX CATIA GA CATIA V5.7 GA+SP1 SNT MicrosoftNT V4 SP4 CATIA V5.7 SP1 and the new capabilities in Version 5. 3 Definition of Surface migration: Influence of transfer s settings The purpose of this paper is to document an understanding of how CATIA V4 model tolerances and CATIA V5 settings can influence transferring CATIA V4 patches, surfaces, skins, curves and composite curves into CATIA V5 surfaces, cells and curves. Test cases will be presented to support the findings. 4 Outline of surface transfer s algorithm The process to transfer a surface contains the following steps: First step : Homogenization the degrees in u and v parametric directions for each patch. Second step : continuity 1 check and correction between each patch. Third step : C2 continuity 2 check and optimization between continuity patches. 1 continuity: Point continuity p02s02-surfacemigrationsettingsv1-0.doc - 5 -

6 5 Multi-patch surface transfer 5.1. Homogenization of the patch s degrees When converting V4 multi-patch surface to V5, the degree of each patch increases up to the maximum order in u and v parametric directions among every patch. Therefore, even if the order of one patch in multi-surface were low, the order would be raised after conversion. You can check if control points are inserted for the transfer by utilizing the Apply Dress Up function. However, this growth of control points must be achieved without any deformation. Therefore, you can easily get the same original control points as V4 with Control Point function without any deformation. As shown below, the surface on the left side is a V4 multi-patch surface composed of 2 patches. The surface on the right is the same surface in V5 after the transfer. One V4 patch has only 3 control points in v direction while the other has 5 control points in the v direction. The corresponding patch after the transfer into V5 has 5 control points in v direction. Figure 1 Homogenization of the patch s degrees However, as shown below, the degree and control points of a V4 skin (*SKI), which are created from the same patches, are not changed by the transfer. Figure 2 V4 skin s transfer 2 C2 continuity: Curvature continuity p02s02-surfacemigrationsettingsv1-0.doc - 6 -

7 5.2. Influence of the Intersection Projection Tolerance in V4 to reach continuity V4 settings Surface s case Figure 3 V4 settings When converting a V4 surface, the Intersection Projection Tolerance value determines if control points of adjacent patches in a surface are changed or if the patches in a surface are exploded into individual surfaces. The Intersection Projection Tolerance is stored as part of the *.model file. If there is a gap and the is less than the Intersection Projection Tolerance, automatic correction to obtain the continuity is achieved. The control points corresponding to the boundaries of the patches are changed to a mean value. In this case the deviation is bounded within Intersection Projection Tolerance value. Control points: p1 (x1, y1, z1), p2 (x2, y2, z2) -> p_new ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2) On the other hand, if between the control points is greater than the Intersection Projection Tolerance, each control point is reserved and the patch is exploded into a cell of the surface. If the number of patches in a surface is Nu in u direction and Nv in v direction and there are gaps greater than Intersection Projection Tolerance among every patch, one surface with Nu*Nv cells are created. (The definition and explanation of a cell is discussed in another document). Control points: p1 (x1, y1, z1), p2 (x2, y2, z2) -> p1_new (x1, y1, z1), p2_new (x2, y2, z2) Curve s case When converting a V4 curve, if there is a gap with, automatic correction to obtain the continuity is achieved. Being different from surface s case, even if p02s02-surfacemigrationsettingsv1-0.doc - 7 -

8 deviation is greater than Intersection Projection Tolerance, this correction should be done. The control points corresponding to the boundaries of the arcs are changed to mean value as an identical value. In this case the deviation might be greater than Intersection Projection Tolerance value Influence of Maximum Deformation value in V5 to obtain C2 continuity V4/V5 SPACE Setting V5 setting is set in the Tools->Options->General->Compatibility->V4/V5 SPACE panel. Figure 4 V5 settings When a V4 surface is transferred, the Maximum Deformation value influences the surface result: Set value to (-1) : The value that is taken into account is the maximum value between the V5 tolerance value (10-3 ) and the Intersection Projection Tolerance value. Set value >= 0 : The entered value, in units of milimeters, is taken into account. Control Points are modified according to the Maximum Deformation value. If all control points have positive weight, the surface is contained within the bounding region, the region defined by the control polygon (Convex hull property; Please refer to Appendix.A). Therefore, it is guaranteed that the surface deviation is within the Maximum Deformation value Deformation to obtain C2 continuity of surface By suppressing internal knots, the internal continuity is optimized to reach C2 continuity. The deviation is less than the maximum value ( Maximum Deformation, V5 tolerance). On this step, the control points of surface are changed. If C2 continuity is not reached, the patch is exploded into the cell of surface. If the number of patches in the V4 surface is Nu in u direction and Nv in v direction and there are gaps greater than Intersection Projection Tolerance among every patch, one surface with Nu*Nv cells is created Segmentation setting When the setting Use of segmentation is inactive (the default), the surfaces are deformed until the nodes are C whenever it is possible. On the other hand, when Use of segmentation is active, the nodes are deformed until C2. p02s02-surfacemigrationsettingsv1-0.doc - 8 -

9 In this case, the number of patches inside the V4 surface and the number of segments inside the V5 surface is the same. For example, when Use of segmentation is active and Maximum Deformation is appropriately large, the number of patches in surface is Nu in u and Nv in v corresponds to the following. Every patch s order =2 or 3 -> One surface with Nu*Nv cells is created. Every patch s order >3 -> A mono-cell surface with Nu*Nv segments can be created. 6 V4 skin s transfer (*SKI) When converting a *SKI that is created from several single-patch *SURs, the transfer does not provide any deformation as the multi-patch surface. However, if the *SKI is created from multipatch surface, as mentioned previously, deformation will occur. For a V4 *SKI that is created from several single-patch *SURs : Any control points between *SURs in the *SKI are not changed The components of the *SKI, i.e. corresponding to *FAC, are transferred to a Cell in V5. Every transferred cell is joined even if there are gaps between cells. This is the same meaning as applying the Join function to all cells. The Connect checker is one way to check the continuity between cells. (The Connect checker showed the internal discontinuities of Join element since V5R7.) Figure 5 Connect checker p02s02-surfacemigrationsettingsv1-0.doc - 9 -

10 7 How to check the position of transferred control points: As mentioned previously, when surfaces are transferred, deformation can occur. In this case, the position of the control points is changed. Control Point functionality can be used to check if control points are changed. However, a long time is needed to do this because this operation must to be done to each control point. Figure 6 Control point positioning 8 Tested cases 8.1. V4 Multi-patch surface and Multi-arc curve V4 model for testing V4 models with the same geometry and with a different Intersection Projection tolerance are also transferred with the different Maximum Deformation value. The tested V4 models have the following characteristics: Multi-patch surface that is composed of two patches. Each patch is created by SURF1/CYLINDER Point deviation = 0.05 mm Tangent is the same at the connecting end points between 2 patches (C1 3 ). The model contains a boundary curve, i.e. *CRV, created by CURVE1/BOUNDARY from *SUR. One model s Intersection Projection tolerance is 0.001mm. The others are set to 0.1mm. 3 C1: Tangency continuity p02s02-surfacemigrationsettingsv1-0.doc

11 Figure 7 V4 model tested (multi-patch surface & multi-arc curve) Summary of the test This table shows a summary of the test results. Please refer to Appendix.C for more details. V4 Surface V4 Setting V5 Settings V5 Result Gap distance (mm) Inter. Proj. (mm) Max.Def. (mm) Segmentation Curve Surface Y Two-cell (C1) (0.001) Y Two-cell (C1) Y Mono-cell (C2) Two-cell (C1) (0.1) Y Mono-cell (C2) Mono-cell (C2) The results imply the following: No parameter influences the point continuity () on curves. Only the Intersection Projection tolerance influences the curvature continuity (C2) on curves. Intersection Projection tolerance influences the point continuity () on surfaces. Maximum Deformation setting influences the curvature continuity (C2) on surfaces. p02s02-surfacemigrationsettingsv1-0.doc

12 8.2. V4 skin (*SKI) and composite curve (*CCV) V4 model for testing V4 Skin with a gap (0.05mm) and V4 Skin with no gap are transferred to V5 with different V4 and V5 settings. The model with a gap has the same shape as the model used in multi-patch surface test in previous section, but it has a different topology. Tested V4 models have the following characteristics: *SKI is composed of 2 single patches *SUR. Each patch is created by SURF1/CYLINDER Point deviation = 0.0mm or mm Tangent is the same on the connecting end points between patches. The model contains a boundary curve, i.e. *CCV, created by CURVE1/BOUNDARY from the *SKI One model s Intersection Projection tolerance is 0.001mm. The others are set to 0.1mm. Dev=0 Dev=0.05 Figure 8 V4 model tested (*SKI & *CCV) p02s02-surfacemigrationsettingsv1-0.doc

13 Summary of the test This table shows the summary of the test results. Please refer to Appendix.D for more details. V4 Surface V4 Settings V5 Settings V5 Result Gap distance (mm) Inter. Proj. (mm) Max.Def. (mm) Y (0.001) Y Y Y (0.1) Y Y Y (0.001) Y Y Y (0.1) Y Y Segmentation Curve Surface Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) Two-cell (C1) The results imply the following: No parameter influences the continuity (, C1, C2) of curves. No parameter influences the continuity (, C1, C2) of surfaces p02s02-surfacemigrationsettingsv1-0.doc

14 9 Conclusions The Maximum Deformation value does not influence any deviation of curves Only the Intersection Projection tolerance influences the point continuity () and the curvature continuity (C2) of multi-arc curves. The Intersection Projection tolerance influences the point continuity () of multipatch surfaces. The Maximum Deformation value influences the curvature continuity (C2) of multipatch surfaces. p02s02-surfacemigrationsettingsv1-0.doc

15 A. Appendix: Curve & Surface basic Curve Bezier ARC : definition Bezier arc is fundamental data structure of a CATIA V4 curve and surface. A Bezier arc is defined by control points. The curve defined by Bezier is similar in shape to its control polygon. Therefore, it is easier to modify the curve by manipulating control points within the control polygon. Figure 9 Bezier arc The Bezier curve has the following: The order of bezier must be the same as the number of control points. The end point of arc and the end control point must be the same The end of arc and the end of control polygon must be tangent. The curvature at the end point is influenced by the second and the third control point Any control point influences the bending of the arc The arc is contained within bounding region of control polygon. (Convex hull property) Nurbs Curve: definition The Nurbs curve is the fundamental data structure of V5 curve. The Nurbs is the superset of Bezier, so it is possible to represent V4 Bezier curve exactly using Nurbs curve data structure. Nurbs can represent several segments (arcs) connected in one equation. The Nurbs curve has the following properties: Nurbs has additional parameter w corresponding to each control points, which is called weight. Nurbs is represented with Control points and Knot vectors. The number of knots is equal to the number of control points plus order. The number of control points is equal or greater than order. If all control points have positive weight, the curve is contained within bounding region of the control polygon. (Convex hull property) Rank of the continuity is equal to (order-2) except at the knot points: (ex: order=4 -> C2 continuity) p02s02-surfacemigrationsettingsv1-0.doc

16 Nurbs can represent conic curves (Circle, ellipse, parabola, and hyperbola) exactly. (w<1: ellipse, w=1: parabola, w>1: hyperbola) Surface Bezier Patch: definition The Bezier patch is the fundamental data structure of a CATIA V4 surface. A Bezier patch is defined by control points. The patch defined by Bezier is similar in shape to its control polygon. Therefore, it is easier to modify the surface by manipulating control points within the control polygon. The Bezier patch has the following: The order of bezier must be the same as the number of control points for each of the u and v parametric direction. The end point of the patch polygon controls the position of the boundary. The second control point determines the tangency of the surface at the boundary. The curvature at the boundary is influenced by the second and the third control point All control points influence the bending of the patch The surface is contained within the bounding region of control polygon. (Convex hull property) Nurbs surface: definition Nurbs is the fundamental data structure of V5 surface. The Nurbs is the superset of Bezier, so it is possible to represent V4 Bezier surface exactly using the Nurbs surface data structure. Nurbs can represent several segments (patches) connected in one equation. The Nurbs surface has the following properties: Nurbs has the additional parameter w corresponding to each control points, which is called weight. Nurbs is represented with Control points and Knot vectors. The number of knots is equal to the number of control points plus order. The number of control points is equal or greater than order. If all control points have positive weight, the surface is contained within bounding region of the control polygon. (Convex hull property) Rank of the continuity is equal to (order-2) except at the knot points for each of the u and v direction: (ex: order=4 -> C2 continuity) Nurbs can represent conic surfaces (cylinder, sphere, conical sweep, etc.) p02s02-surfacemigrationsettingsv1-0.doc

17 Nurbs Curve/Surface: in V5 Nurbs used and created in V5 have special properties in order to manipulate data more easily. Data structure used in FreeStyle Shaper (FSS) is Nupbs (Non Uniform Polynomial Base Spline) surface. Nupbs is the special case of Nurbs surface where all the weight of the control points equal to 1. When adding control points in FSS, the degree increases as well as Bezier curve in V4 When the order of one parametric direction (i.e. u or v) is increased by one in FSS, a control point is added on this direction for each segment A Nurbs curve in V5 has C2 continuity between several segments (patches). The Control Point function can control only Nupbs surface. Nurbs created in V5 are only Conical Surfaces. The Geometric information command always shows transferred V4 surface as Nupbs or as canonic surface for Cylinder, Sphere, etc. Figure 10 Sample of Nupbs Transfer Transfer Bezier to Nurbs (V4 data structure to V5 data structure) Bezier control points are transferred as Nurbs control points. Weight w is set to 1 for each control point. Order of the Nurbs curve is set to the number of control points of Bezier. On a Bezier with order =n, the transfer sets the knot vector to [n0 ; n1]. (ex order =3 -> knot vector[ ]) Transfer Nurbs to Bezier (V5 data structure to V4 data structure) Each segment of a Nurbs curve is affected by some subset of the control points. The transfer takes each segment and adds knots to both ends of the segment and generates a new set of control points until the ends of each segment have a number of knots equal to the order of the curve. The result is a Bezier representation for each segment. The assembly of segments looks like the original Nurbs curve. p02s02-surfacemigrationsettingsv1-0.doc

18 B. Appendix: Degree of V4 and V5 Surface The properties of V4 and V5 s surface s degree (order) The order (u, v) of V4 surface is determined by the number of control points in the parameter s direction because V4 surface data structure is Bezier. That is, the order is equal to the number of control points. On the other hand a V5 surface is Nurbs based. Therefore, the order (u, v) of surface is less than or equal to the number of control points in that direction. V4 surface s order = the number of control points. V5 surface s order <= the number of control points The maximum value of the order of a V4 and V5 surface In V5 the maximum order of surface ranges from 5 to 12. This order is set in Tools->Options- >Shape->Free style for the P2 mode. (In P1 mode, the Max order is set to 12 and cannot be modified). On the other hand the maximum order of V4 bezier surface is 16. This fact seems to be inconsistent between V4 and V5. But V5 has a capability to be able to manipulate a higher degree V4 surface whereas V5 cannot generate a high degree surface more than order 12. This indicates that you have to be careful when you decrease the order of a transferred V4 surface. It is impossible to recover high degree surface from low degree one once you decrease the degree of surface. Figure 11 Setting of the maximum order p02s02-surfacemigrationsettingsv1-0.doc

19 C. Appendix: V4 Multi-patch surface and Multi-arc curve tests Case 1 V4 settings V5 settings : Intersection Projection =0.001 : Maximum Deformation=0 with Segmentation Results: The surface is transferred into a 2-cell surface and the curve is transferred into a 2-cell boundary curve. There is a gap between 2-cell patch and no gap between 2-cell arcs. You can check that using Connect checker and Curve connect checker though no gap seems to exist between the cells of patches or arcs in visual check. It is also possible to check the gap using Disassemble. Arc boundary 2-cell surface 2-cell curve Before Disassemble After Disassemble Figure 12 Test result of multi-patch surface & multi-arc curve Case1 p02s02-surfacemigrationsettingsv1-0.doc

20 Case 2 V4 settings V5 settings : Intersection Projection =0.001 : Maximum Deformation=-1 with Segmentation Results: The surface is transferred into a 2-cell surface and the curve is transferred into a 2-cell boundary curve. It is the same result as in case 1 Before Disassemble After Disassemble Figure 13 Test result of multi-patch surface & multi-arc curve Case2 p02s02-surfacemigrationsettingsv1-0.doc

21 Case 3 V4 settings V5 settings : Intersection Projection =0.1 : Maximum Deformation=0 with Segmentation Results: The surface is transferred into a 2-cell surface and the curve is transferred into a mono-cell curve with 2-segments. There is no gap between the cells of patches in the transferred surface and the 2-arc boundary with a gap that is 0.05mm is transferred to mono-cell curve. You can check that no gap exists using Connect checker and Disassemble. You can check that the boundary curve has two segments using Geometric Information function. You can also check the control points and segmentation point using Apply Dress Up function and Control Points functions 2-cell surface mono-cell curve with 2 segments Before Disassemble After Disassemble p02s02-surfacemigrationsettingsv1-0.doc

22 Control points of mono-cell curve with 2 segments Figure 14 Test result of multi-patch surface & multi-arc curve Case3 p02s02-surfacemigrationsettingsv1-0.doc

23 Case 4 V4 settings V5 settings : Intersection Projection =0.1 : Maximum Deformation=0.001 with Segmentation Results: The surface is transferred into a mono-cell surface with 2 segments and the curve is transferred into a mono-cell curve with 2 segments. The 2 patches with a gap of 0.05mm are transferred to the mono-cell surface. The 2-arc curve that contains a gap of 0.05mm is transferred into a mono-cell curve. You can check that no gap exists using Connect checker and Disassemble. You can check that the boundary curve has two segments using Geometric Information function. The control points and segmentation point can be checked by using the Apply Dress Up and Control Points functions mono-cell surface with 2 segments mono-cell curve with 2 segments Control points of mono-cell curve with 2 seg Control points of mono-cell surface with 2 seg Figure 15 Test result of multi-patch surface & multi-arc curve Case4 p02s02-surfacemigrationsettingsv1-0.doc

24 D. Appendix: V4 Skin (*SKI) and Composite curve (*CCV) tests Case1: Gap distance = 0.0mm A *SKI with no gap is transferred into a 2-cell surface with C1 Continuity. The results are the same for any Maximum deformation and Intersection Projection tolerance value. No deformation occurs in this transfer. continuity check on surface C1 continuity check on surface C2 continuity check on surface continuity check on curve continuity check on curve C1 continuity check on curve Figure 16 Continuity check of test case1 p02s02-surfacemigrationsettingsv1-0.doc

25 Case2: Gap distance = 0.05mm A *SKI with a gap = 0.05mm is transferred to 2-cell surface with. The results are the same for any value of Maximum deformation or Intersection Projection tolerance No deformation occurs during this transfer. continuity check on surface continuity check on curve Before Disassemble After Disassemble Figure 17 Continuity check of test case2 p02s02-surfacemigrationsettingsv1-0.doc

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