4. Product Data 4.1 Geometrical Data Requirements and Methods to Manage Geometrical Data for Engineering Applications Overview • Geometric Modeling – Applications – Historical roots of Technical Modeling • Overview of Geometrical Models – Criteria – Wire-frame Models – CSG – Voxel/Octrees – Triangle Meshes (Polygon Meshes) – B-Rep • The Boundary Representation-Model – Basics – Primitives and Basic Data Structures – Modeling Kernels and File Formats – B-REP Data in Databases Schallehn: Data Management for Engineering Applications Historical Roots of Technical Modeling • Historical roots date back more than 2000 years – Sketches and informal drawings used in ancient Egypt and Greece (Euclid, 300BC) to medieval times – Move from agricultural to industrial age increased importance of sharing information for technical development and documentation – Around the 19th century patents (protection of intellectual property) required formalization of technical • Manual Technical Drawing on paper standard way for technical modeling until the 1980s – Formalized process with commonly used conventions for representing 3D geometries represents “visual language” – Projection methods (orthogonal, parallel, perspective) to map 3D geometries to 2D – Data representing concrete measures with special syntax as dimension values or parameters and legends • First Computer Aided Design (CAD) developed in the 1960’s – Became industrial practice in the 1980s – Required digital representation of geometries Schallehn: Data Management for Engineering Applications Historical Technical Drawings Technical drawing describing details of Drawing of a US patent (cigarette a helicopter by Leonardo da Vinci rolling machine)from 1881 [Source: wikipedia.org] Schallehn: Data Management for Engineering Applications Technical Drawings [Source: wikipedia.org] Schallehn: Data Management for Engineering Applications CAD Systems [Source: wikipedia.org] Schallehn: Data Management for Engineering Applications Geometric Modeling Geometric modeling refers to methods and data structures suitable to represent the shape and topology of geometric objects as data for computer applications. • In Engineering also referred to as Solid Modeling highlighting physical properties of solid objects • Geometric model has central importance for product lifecycle – Based on specifications and requirements from – Result of initial design steps and step-wise refinements – Input for further steps in product development like FEA, simulation, mockups, production planning, manufacturing, etc. Schallehn: Data Management for Engineering Applications Computer Graphics vs. CAD • Computer Graphics – General term for methods to create images from data – Comprises geometric modeling methods (representing geometry) + rendering (creating image) – Geometric modeling focuses on efficiency of computations – Two main branches • Real-time rendering for fast graphics generation in interactive applications (games, virtual worlds, CAD, etc.) • Photo-realistic rendering for application requiring high (realistic) image quality (CGI in movies, computer arts, etc.) • Computer Aided Design – Focus on formal representation of geometrical data – Geometric models focus on expressiveness, completeness and correctness of geometry – Uses methods from computer graphics (real-time rendering) for interaction • CAD model needs to be mapped to rendering model Schallehn: Data Management for Engineering Applications Geometry vs. Topology • Terms for different aspects of representing local and global properties of objects Geometry: describes local features (dimensions, relations between dimensions, primitive type, etc.) of each element of an object. Topology: describes transformations (position in space via translation, rotation, etc.) of elements and how they are connected to form complex shapes. Schallehn: Data Management for Engineering Applications Classification of Geometric Modeling • Over time and for different applications various methods were developed, which differ regarding key criteria – Supported Dimensionality – Supported Primitives (Geometry) – Supported Construction (Topology) – Supported Level of Detail/Approximation – Intended Applications Schallehn: Data Management for Engineering Applications Criteria: Dimensionality • 2D – Derived from paper 2D drafting – Adapted in early CAD systems, today not often practiced – Commonly used in some applications (electronic circuit design, architecture) • 3D – Constructions represented as 3D shapes – Current standard in CAD • 2½D – Data represented as 2D + “3D interpretation” – Sweeping methods for interpretaion, e.g. • Extrusion (along a trajectory) • Rotation Schallehn: Data Management for Engineering Applications Criteria: Primitives • Points and curves – Points, lines, line loops – Freeform curves like Splines and NURBS • Polygons – Triangles of special importance as most simple face type (used to construct or approximate any polygon or surface) • 3D objects – Basic 3D objects like prisms, spheres, cuboids, etc. • Space partitions – Part of space according to a 3D grid partitioning the room Schallehn: Data Management for Engineering Applications Criteria: Construction Methods • Basic topology – Transformations: translation, rotation, scaling, etc. – Connection of vertexes, edges, faces • Set operations on primitives – Union or intersection (symmetric) – Relative complement/subtraction (asymmetric) • Sweeping – 2½D construction methods like extrusion, rotation etc. Schallehn: Data Management for Engineering Applications Criteria: Approximation/Level of Detail • Exact Geometry – Often can be represented applying freeform curves (2D) and freeform surfaces (3D), e.g. using NURBS – Support for intuitive design • Approximated Geometry – Often implemented in terms of tessellation: representing a complex surface with simple polygons (e.g. triangle meshes) – Level of detail can be set according to requirements – More efficient for rendering [Source: wikipedia.org] Schallehn: Data Management for Engineering Applications Intended Applications • Interactive work on geometries – Requires intuitive methods and expressiveness – Examples: • CAD (development) • Game content development • CGI/special FX development • Rendering – Requires simple structures and efficient algorithms – Examples • Games • CAD (interaction, display) • Interactive virtual worlds • Capturing real-word geometries – As objects semantics are unknown, low-level representation required – Examples • 3D scanners or printers • X-ray computed tomography (CT) • Motion Capturing Schallehn: Data Management for Engineering Applications Overview of Modeling Methods • Wire-frame Models • Constructive Solid Geometry (CSG) • Voxel/Octrees • Triangle Meshes (Polygon Meshes) • B-Rep Schallehn: Data Management for Engineering Applications Wire-Frame Models Schallehn: Data Management for Engineering Applications Wire-Frame Characteristics Supported Dimensionality • 2D • 2½D • 3D Supported Primitives • Lines • Curves (splines, ellipses etc.) Construction Methods • Edges of physical objects represented by lines and curves Level of Detail • Precise description of edges possible • Information about surfaces and volumes lost Intended Application • Interactive Modeling: early CAD, simple visualizations • Rendering: early computer graphics Schallehn: Data Management for Engineering Applications Wire-Frame Usage • Rendering of 3D models applies – Projection methods (perspective, orthogonal, parallel) – Hidden edges can be removed, colored or dashed (requires information about surfaces) • Disadvantages – Semantic loss (information about surfaces and volumes) – Leads to ambiguities in interpretation Schallehn: Data Management for Engineering Applications Constructive Solid Geometry (CSG) Schallehn: Data Management for Engineering Applications [Source: wikipedia.org] CSG Characteristics Supported Dimensionality • 3D Supported Primitives • Parametrizable 3D basic shapes: cuboids, spheres, prisms, etc. • In some approaches: parametrizable free-form shapes Construction Methods • Boolean set operations • Basic transformations: translation, rotation Level of Detail • Many geometries can represented correctly • If no free-form shapes are supported, according geometries have to be approximated Intended Application • Interactive Modeling: CAD, modeling for games etc. Schallehn: Data Management for Engineering Applications CSG Usage • Rich semantics allow intuitive creation of 3D models • Disadvantages – Rendering and some verifications/evaluation of geometric models require complex computations – Construction of a shape by Boolean operators is ambiguous – Some geometries (e.g. free-form surfaces such as used for automotive design etc.) had to be approximated with basic primitives in early approaches • CSG combined with other methods (e.g. B-Rep) to support interactive modeling • Rarely used as stand-alone geometric model in CAD Schallehn: Data Management for Engineering Applications Voxel-based Models [Source: Tobias Wüstefeld, http://www.bilderzucht.de] Schallehn: Data Management for Engineering Applications Voxel Characteristics Supported Dimensionality • 3D Supported Primitives • Volume elements = Voxel = “3D pixel” • Space partitioned according to grid Construction Methods - Level of Detail • Approximation according to grid properties (resolution) Intended Application • Capturing or creating real-world geometries: 3D scanners, 3D printers Schallehn: Data Management for Engineering Applications Octrees • Problem of voxel-based 3D data: huge amounts