OpenCascade Technology Overview: Modeling Data
0 likes536 views
OpenCascade is a modeling library that provides tools for: 1. Generating geometric shapes through interpolation and approximation techniques. 2. Analyzing relationships between points, curves, and surfaces. 3. Constructing common geometric entities like lines, circles, and cylinders. 4. Representing shapes using B-splines and managing their topology.
OpenCascade Technology Overview: Modeling Data
- 2. Geometry Utilities • 由內插補間 (interpolation)與趨近 (approximation)兩種不 同方式產生幾何形狀 shapes. • 由演算法建立幾何形狀. • 一般曲線/曲面轉換為B-spline曲線/曲面. • 計算曲線/曲面上某點的座標. • 提供幾何之間的極端量測工具(最大/最小距離等).
- 3. Interpolation and Approximation • PEquation class (GProp package): 分析一群點集合, 判斷 coincident, collinear, coplanar. • GeomAPI/Geom2dAPI packages: 指定一組點集合, 透過 interpolation/approximation找出一條通過所有點的曲線/ 曲面. • _Interpolate class: interpolation, 內插補間. • _PointsToBSpline (_PointsToBSplineSurface) class: approximation, 趨近.
- 4. Low-Level Approximation • AppDef package: 處理多組點限制 (MultiPointConstraint class), 計算出每一組對應的趨近曲線 (Bezier/B-spline). • AppParCurves package: 處理多組參數幾何限制 (ConstraintCouple class), 計算出每組對應的趨近曲線 (Bezier/B-spline).
- 5. Direct Construction • gce, GC, GCE2d packages: 提供簡化版本的建立幾何形狀 物件 (lines, curves, circles)之演算法. • Geometric entities: line, circle, hyperbola, parabola, plane, cylinder, cone, … • gp_* class都有對應的 gce_* class. • Geometric entities by handle: arc of circle/ellipse/parabola/hyperbola, trimmed cylinder ... • GC, GCE2d packages提供建立對應的 Geom/Geom2d entities物件 之演算法. • GC_*/GCE2d_* classes都有對應的 Geom_*/Geom2d_* classes.
- 6. B-Spline Conversion • B-spline formulation: 可表示一般基本幾何 (fundamental/2D/3D geometry types). • 可將B-spline分割成數段B-splines, 提供更高維度的連續性 (degree continuity). • 3 packages for conversion: • Convert package: 將目標轉換為單一B-spline曲線/曲面. 目標含 bounded curve/surface (line, circle, cylinder, cone, … in gp package). • Geom2dConvert/GeomConvert package: 由 Geom2d/Geom curves/surfaces物件轉換為 B-splines; 將 B-spline轉換為同等的一 組相連 Bezier curves/surfaces; 將 B-spline分割成數段 arcs; grid of Bezier surfaces to one B-spline surface.
- 7. Curve Points and Extrema • Points on curve (GCPnt package): • Points equally spaced (_UniformAbscissa class). • Point from a given distance from another point (_AbscissaPoint class). • _UniformDeflection class: calculates points at maximum constant deflection between the curve and the polygon (results from computed points). (? • Extrema: 計算兩對象之間的極端量測 (minimum and maximum)結果. • Point – curve. • Point – surface. • Curve – curve. • Curve – surface. • Surface – surface.
- 8. Geometry • Geom/Geom2d packages, 定義空間中的幾何物體, 座標位 置, transformation. • Point, Cartesian point, vector, direction, curve, line, conic, elementary surface, bounded curve/surface, … • Curves/surfaces are parameterized. 可計算參數 (u, v)對應 的point, derivative. • 建立 Bezier/B-spline curve/surface; trimmed curve/surface; offset curve/surface; swept surface. • 透過 gp package實現: • 實作 elementary algebraic calculus and analytic geometry. • Transformation applied to Geom/Geom2d objects. • 描述 Geom/Geom2d object的elementary data structure.
- 9. Shape Properties • Local properties: BRepLProp package. • Local properties: point, derivative (~3rd degree), tangent, normal, curvature. • Degree of continuity (at junction point of concatenated edges/curves). • Geom2dLProp/GeomLProp packages provide local properties for curves/surfaces. • Global properties: BRepGProp package. • Global properties of a composite geometric system: mass, mass center, inertia, moment, gyration, … • Lines from edges; surfaces from faces; volumes from solids. • GProp_PGProps package: global properties for a set of points. • Analyzed edge/face BRepAdapter curve/surface. • Algorithms’interfaces to operate on analyzed targets. • GeomAdapter/Geom2dAdapter packages for interfaces on curve (or curve lying on surface), surface.
- 10. Topology • Topology以參數空間的方式來描述幾何物件 (location/restriction). • Abstract data structure for basic entity – shape (形狀). 形 狀可由以下元素組成: • Vertex, edge, wire, face, shell, solid, compound solid. • Face可由一組三角面集合來趨近其代表的 surface. • Packages描述資料結構: TopAbs (notion enumerations), TopLoc (coordinate system), TopoDS (data structure). • Packages提供操作工具: TopTools, TopExp (to explore/manipulate), BRepTools (to explore/manipulate/read/write BRep data structure).
- 11. Shape Location • TopLoc package. • TopLoc_Datum3D class: (a change of) elementary reference coordinate (right-handed transformation). • TopLoc_Location class: composited reference coordinate. • Coordinate = transformation (in gp_trsf package).
- 12. Naming Shape and Sub-shape • TopAbs package provide enumerations for concepts of topology. • 3 notions: TopAbs_ShapeEnum (type), TopAbs_Orientation, TopAbs_State. • TopAbs_ShapeEnum: COMPOUND, COMPSOLID, SOLID, SHELL, FACE, WIRE, EDGE, VERTEX, SHAPE. • Graph of objects with adjacency relationships.
- 13. Topological Orientation • TopAbs_Orientation, Notion of direction for a boundary shape limiting a geometric domain. • Curve limited by vertex; surface limited by edge; space limited by face. • Define 2 local regions: external and internal/default (區別外部與 內部). Orientation Description FORWARD The interior is the default region. REVERSED The interior is the region complementary to the default. INTERNAL The interior includes both regions. The boundary lies inside the material. A surface inside a solid. EXTERNAL The interior includes neither region. The boundary lies outside the material. An edge in a wire-frame.
- 14. Topological State • TopAbs_State, 描述 vertex(點)的所在位置區域. Position Description IN The point is interior. OUT The point is exterior. ON The point is on the boundary(within tolerance). UNKNOWN The state of the point is indeterminate.
- 15. Manipulate Shape • TopoDS package透過參數空間描述形狀: vertex (via localization), face and edge (via restriction). • Edges form wire; faces form shell; solids form composite solid … • TopoDS_TShape class: root shape description (manipulated by reference). • TopoDS_Shape class: describe reference to a shape (*_TShape), orientation and local reference coordinate (manipulated by value).
- 16. Shared Sub-Shape • Data structure contains 2 versions of a solid.
- 17. Exploration TopoDS_Shape • TopoDS_Shape derived Classes: *_Vertex, *_Edge, *_Face, *_Shell, *_Solid, … • No implicit cast. • TopoExp package: explores TopoDS_Shape data structure (TopoExp_Explorer class). • TopTools package: 實體化對應的 TCollection物件來完成 探索 shape功能 (array, sequence, map, …). • TopTools_*MapOfShape class: 透過 map儲存shape, 避免重複的 shared shapes.
- 18. Storage • BRepTools package can read/write a shape to/from a stream/file (ASCII format). • BinTools package can read/write a shape to/from a stream/file (binary format).