The document discusses various techniques for achieving visual realism in 3D modeling and visualization. It describes methods for projecting 3D objects into 2D views, including orthographic projection, isometric projection, and perspective projection. Techniques for removing hidden lines and surfaces like backface elimination are covered. The document also discusses algorithms for hidden surface removal including the depth/priority, painter's, area-oriented, and scanline algorithms. Applications of visualization like robot simulations, CNC programming, and scientific computing are also mentioned.
This document discusses techniques for hidden line removal (HLR) in 3D modeling. HLR involves determining which lines or edges of a 3D model are hidden from a given viewpoint and not drawing them. The document introduces various HLR techniques such as the minimax test, containment test, surface test, computing silhouettes, edge intersection, segment comparison, and homogeneity test. It also describes common HLR algorithms like the priority, area-oriented, and overlay algorithms. The priority algorithm assigns depth priorities to surfaces and removes hidden lines based on depth. The area-oriented algorithm identifies silhouette polygons and uses quantitative hiding to determine line visibility. The overlay algorithm approximates curved surfaces with planar grids to enable standard HLR techniques.
This document discusses techniques for achieving visual realism in 3D computer graphics. It covers hidden line removal, hidden surface removal, and hidden solid removal algorithms. Hidden line removal algorithms like the priority and area-oriented algorithms aim to correctly display occluded lines. Hidden surface algorithms like the z-buffer, Warnock's area coherence, and painter's priority approaches determine which surfaces are visible. Ray tracing is introduced as a hidden solid removal technique that traces the path of light in a scene to realistically render 3D objects.
This document discusses various standards used in computer-aided design (CAD) and computer-aided manufacturing (CAM). It outlines the need for graphics standards to enable portability and device independence. It then describes several key CAD standards, including those for graphics (GKS, PHIGS), data exchange (IGES, STEP, DXF), and communication (LAN, WAN). It provides more detail on specific standards like IGES, STEP, DXF, and VRML. The document emphasizes that standards are crucial to integrating design and manufacturing processes for maximum efficiency.
Surface modeling represents the surfaces of 3D objects and can be used to model complex shapes like vehicles, ships, and aircraft wings. There are two main types of surface modeling: parametric surfaces and implicit surfaces. Parametric surfaces use a set of equations to define the x, y, and z coordinates as functions of parameters u and v. Common parametric surface types include planes, ruled surfaces, surfaces of revolution, and tabulated cylinders. Implicit surfaces use a single polynomial equation to define the surface. Surface modeling provides more realistic representations than wireframe models and can be used for applications like finite element analysis, machining tool paths, and rendering models.
This document discusses techniques for achieving visual realism in geometric modeling. It covers topics like hidden line removal, hidden surface determination, shading models, transparency, reflection, and camera models. The goal of visual realism is to generate images that capture effects of light interacting with physical objects similarly to how we see the real world. This involves modeling objects and lighting conditions, determining visible surfaces, assigning color to pixels, and creating animated sequences. Realistic images find applications in simulation, design, entertainment, research, and control.
This document discusses various techniques for achieving visual realism in 3D computer graphics, including hidden surface removal algorithms, shading methods, and color models. It describes algorithms for hidden line elimination, hidden surface removal, and hidden solid removal. It also covers shading techniques like constant intensity shading, Gouraud shading, and Phong shading. Finally, it discusses color models such as RGB, CMY, HSV, and HSL that can be used for computer graphics applications.
The document discusses different methods for modeling solid objects in 3D, including constructive solid geometry (CSG) and boundary representation (B-Rep). CSG uses boolean operations on primitive solids, represented as a tree structure, while B-Rep defines solids by their enclosing faces, edges and vertices with topological connectivity. Both have advantages such as unambiguous definitions but also challenges around complexity, storage or modeling restrictions. Hybrid approaches combine benefits of both methods.
This document discusses techniques for hidden line removal (HLR) in 3D modeling. HLR involves determining which lines or edges of a 3D model are hidden from a given viewpoint and not drawing them. The document introduces various HLR techniques such as the minimax test, containment test, surface test, computing silhouettes, edge intersection, segment comparison, and homogeneity test. It also describes common HLR algorithms like the priority, area-oriented, and overlay algorithms. The priority algorithm assigns depth priorities to surfaces and removes hidden lines based on depth. The area-oriented algorithm identifies silhouette polygons and uses quantitative hiding to determine line visibility. The overlay algorithm approximates curved surfaces with planar grids to enable standard HLR techniques.
This document discusses techniques for achieving visual realism in 3D computer graphics. It covers hidden line removal, hidden surface removal, and hidden solid removal algorithms. Hidden line removal algorithms like the priority and area-oriented algorithms aim to correctly display occluded lines. Hidden surface algorithms like the z-buffer, Warnock's area coherence, and painter's priority approaches determine which surfaces are visible. Ray tracing is introduced as a hidden solid removal technique that traces the path of light in a scene to realistically render 3D objects.
This document discusses various standards used in computer-aided design (CAD) and computer-aided manufacturing (CAM). It outlines the need for graphics standards to enable portability and device independence. It then describes several key CAD standards, including those for graphics (GKS, PHIGS), data exchange (IGES, STEP, DXF), and communication (LAN, WAN). It provides more detail on specific standards like IGES, STEP, DXF, and VRML. The document emphasizes that standards are crucial to integrating design and manufacturing processes for maximum efficiency.
Surface modeling represents the surfaces of 3D objects and can be used to model complex shapes like vehicles, ships, and aircraft wings. There are two main types of surface modeling: parametric surfaces and implicit surfaces. Parametric surfaces use a set of equations to define the x, y, and z coordinates as functions of parameters u and v. Common parametric surface types include planes, ruled surfaces, surfaces of revolution, and tabulated cylinders. Implicit surfaces use a single polynomial equation to define the surface. Surface modeling provides more realistic representations than wireframe models and can be used for applications like finite element analysis, machining tool paths, and rendering models.
This document discusses techniques for achieving visual realism in geometric modeling. It covers topics like hidden line removal, hidden surface determination, shading models, transparency, reflection, and camera models. The goal of visual realism is to generate images that capture effects of light interacting with physical objects similarly to how we see the real world. This involves modeling objects and lighting conditions, determining visible surfaces, assigning color to pixels, and creating animated sequences. Realistic images find applications in simulation, design, entertainment, research, and control.
This document discusses various techniques for achieving visual realism in 3D computer graphics, including hidden surface removal algorithms, shading methods, and color models. It describes algorithms for hidden line elimination, hidden surface removal, and hidden solid removal. It also covers shading techniques like constant intensity shading, Gouraud shading, and Phong shading. Finally, it discusses color models such as RGB, CMY, HSV, and HSL that can be used for computer graphics applications.
The document discusses different methods for modeling solid objects in 3D, including constructive solid geometry (CSG) and boundary representation (B-Rep). CSG uses boolean operations on primitive solids, represented as a tree structure, while B-Rep defines solids by their enclosing faces, edges and vertices with topological connectivity. Both have advantages such as unambiguous definitions but also challenges around complexity, storage or modeling restrictions. Hybrid approaches combine benefits of both methods.
This document summarizes different types of surfaces that are important from a CAD/CAM perspective. It discusses analytic surfaces like planes, ruled surfaces, tabulated surfaces, and surfaces of revolution which are defined by equations. It also discusses synthetic surfaces like Hermite bi-cubic surfaces, Bezier surfaces, B-spline surfaces, Coons surfaces, fillet surfaces, and offset surfaces which are defined by a set of data points and approximated with polynomials. The document provides examples and definitions of each surface type.
Unit 4-ME8691 & COMPUTER AIDED DESIGN AND MANUFACTURINGMohanumar S
This document provides information on numerical control systems and computer numerical control (CNC) systems. It defines numerical control and describes traditional NC, CNC, and DNC systems. It discusses the basic components of NC systems including software, machine control units, and machine tools. It also covers CNC machine construction, driving systems, tooling systems, applications, advantages, and disadvantages of NC and CNC machines. Finally, it discusses topics like part programming fundamentals, coordinate systems, canned cycles, and micromachining.
The document discusses assembly modeling and provides information on various topics related to assembly modeling including interference checking, tolerance analysis, mass property calculations, and mechanism simulation. It describes the bottom-up and top-down approaches to assembly, with bottom-up involving creating individual parts independently and inserting them into the assembly, while top-down involves creating an assembly layout sketch first before finalizing individual parts. It also discusses how tolerances are specified in parts and how greater tolerances increase costs.
Unit 3-ME8691 & COMPUTER AIDED DESIGN AND MANUFACTURINGMohanumar S
This document discusses various CAD standards including:
1. Graphical standards like GKS and OpenGL that define graphics primitives and device independence.
2. Data exchange standards like IGES and STEP that define neutral formats for transferring geometric and non-geometric CAD data between systems.
3. Communication standards like LAN and WAN that define how CAD data is transferred over networks between systems.
The goals of CAD standards are to enable interoperability and portability of CAD data across different software and hardware platforms. They aim to support the complete transfer of product description data.
Assembly modeling allows components to be brought together to define a more complex product representation. It facilitates collaboration between different teams to ensure the assembly works together. An assembly contains component objects that can be individual parts or subassemblies. There are two main approaches to assembly modeling - bottom-up builds the assembly from individual pre-made parts, while top-down designs parts within the assembly context. Mating conditions like concentric or parallel define relationships between components.
Introduction, Conventional and Revised with CAD/CAM Product cycle, Application of computers to the design process, comparison of capabilities of designers and computers, Reasons for implementing CAD, Benefits of CAD, CAD workstation,
The document discusses various computer-aided design (CAD) standards used for data exchange, including graphics standards like GKS and OpenGL, as well as data exchange standards like IGES, DXF, and STEP. It provides details on the purpose and requirements of each standard, explaining concepts like layers, entities, and file structure. The key standards discussed are IGES for shape data exchange, DXF for CAD file interchange, and STEP for comprehensive product data across the design and manufacturing lifecycle.
This document discusses different types of surface models used in computer graphics, including:
- Plane, ruled, surface of revolution, tabulated, bilinear, Coons patch, and bicubic surfaces. Plane and ruled surfaces are linear, while surfaces of revolution and tabulated surfaces are axisymmetric. Bilinear surfaces are generated by interpolating 4 endpoints and are useful for finite element analysis. Coons patches interpolate 4 edge curves. Bicubic surfaces use parametric curves and interpolation of control points to define smooth surfaces.
This document provides an overview of geometric modeling techniques used in computer aided design (CAD). It discusses representation of curves including Hermite curves, Bezier curves, B-spline curves, and rational curves. It also covers surface modeling techniques such as surface patches, Coons patches, and Bicubic patches. For solid modeling, it describes constructive solid geometry (CSG) and boundary representation (B-rep) techniques. CSG uses boolean operations on primitives to create models while B-rep defines models based on their bounding faces, edges and vertices.
This document provides an introduction to computer-aided design (CAD). It defines CAD and computer-aided manufacturing (CAM) as using computers to aid in design and manufacturing functions. The document outlines the basic product design cycle and how CAD/CAM can be integrated at various stages, including computer-aided drafting, process planning, and computer-controlled manufacturing. It also describes the basic hardware and software components of CAD systems, including how interactive computer graphics are used to aid designers. Finally, it summarizes the general six-phase design process.
This document discusses different types of surface modelling techniques. Parametric surfaces and implicit surfaces are the two main types used in modelling systems. Parametric surfaces are defined by a set of coordinate functions, while implicit surfaces are defined by a polynomial equation. Common parametric surfaces include planes, ruled surfaces, surfaces of revolution, and B-splines. Multiple parametric surface patches can be joined to model more complex shapes. Surface modelling allows representing complex object geometries and is useful for mass properties calculation, interference detection, and finite element analysis.
The document is a syllabus for a Solid Modeling and Drafting course that discusses curves, surfaces, and geometric modeling. It covers curve representation methods including parametric and non-parametric, types of curves like analytic and synthetic, and examples of analytic curves like lines and circles. It also discusses surface representation and types of surfaces. The objectives are to introduce curves and surfaces modeling and their implementation in geometric modeling.
This document provides an overview of assembly modelling including interference checking, tolerance analysis, mass property calculations, mechanism simulation, and interference checking. It discusses assembly modelling approaches like bottom-up and top-down, assembly planning considerations, mating conditions, tolerance systems, and methods for tolerance analysis including worst-case, statistical, and Monte Carlo simulation methods. Mass properties like mass, center of gravity, and moments of inertia are also covered. Mechanism simulation advantages and disadvantages are outlined as well as the purpose of interference checking in assemblies.
The document discusses geometric transformations in computer-aided design. It begins by defining various geometric transformations including translation, rotation, scaling, shearing, and reflection. It then describes how to represent points and perform transformations using matrix algebra with homogeneous coordinates. The document provides examples of combining multiple transformations through concatenation and calculating inverse transformations via matrix inversion. It concludes with two examples problems applying transformations to geometric shapes.
This document discusses graphic standards and provides details about GKS, CORE, IGES, and their use. It explains that GKS is an international standard for 2D graphics and describes its primitives like polyline and text. It also discusses IGES for exchanging CAD models between different software packages through a neutral file format. The document includes an example of drawing a duck using GKS primitives and an IGES file case study.
Bezier surfaces are parametric surfaces used in computer graphics and CAD/CAM. They are based on Bernstein polynomials and control points. A Bezier surface is defined by a grid of control points that determine the shape of the surface. Changing control points modifies the shape globally. B-spline surfaces allow for more local control and ensure continuity between patches. Coons patches interpolate between four boundary curves to generate a smooth surface. Sculptured surfaces are used for complex, free-form shapes and consist of blended parametric surface patches.
Unit 2-ME8691 & COMPUTER AIDED DESIGN AND MANUFACTURINGMohanumar S
This document discusses different geometric modeling techniques. It describes wireframe modeling where object edges are represented by lines. Surface modeling uses techniques like patches to represent curved surfaces. Solid modeling represents objects as solids to avoid misinterpretation. Constructive solid geometry and boundary representation are two common solid modeling techniques. CSG uses primitives and Boolean operations while boundary representation uses edges, vertices and faces to define boundaries.
This document discusses algorithms for hidden surface removal in 3D computer graphics. It describes two main classifications of algorithms - object space and image space. It then provides details on various algorithms including Painter's algorithm (object space), Z-buffer algorithm (image space), and Warnock's area subdivision algorithm. The key aspects and approaches of each algorithm are summarized.
This document describes a method for 3D reconstruction from a single image using single-view metrology. Key steps include detecting vanishing points to establish directions in the scene, calculating planar homographies to map image points to world coordinates, and using metric constraints to estimate distances and reconstruct occluded objects. Examples demonstrate reconstructing buildings and objects from single images. Limitations include reliance on planar surfaces and regular object shapes.
This document summarizes different types of surfaces that are important from a CAD/CAM perspective. It discusses analytic surfaces like planes, ruled surfaces, tabulated surfaces, and surfaces of revolution which are defined by equations. It also discusses synthetic surfaces like Hermite bi-cubic surfaces, Bezier surfaces, B-spline surfaces, Coons surfaces, fillet surfaces, and offset surfaces which are defined by a set of data points and approximated with polynomials. The document provides examples and definitions of each surface type.
Unit 4-ME8691 & COMPUTER AIDED DESIGN AND MANUFACTURINGMohanumar S
This document provides information on numerical control systems and computer numerical control (CNC) systems. It defines numerical control and describes traditional NC, CNC, and DNC systems. It discusses the basic components of NC systems including software, machine control units, and machine tools. It also covers CNC machine construction, driving systems, tooling systems, applications, advantages, and disadvantages of NC and CNC machines. Finally, it discusses topics like part programming fundamentals, coordinate systems, canned cycles, and micromachining.
The document discusses assembly modeling and provides information on various topics related to assembly modeling including interference checking, tolerance analysis, mass property calculations, and mechanism simulation. It describes the bottom-up and top-down approaches to assembly, with bottom-up involving creating individual parts independently and inserting them into the assembly, while top-down involves creating an assembly layout sketch first before finalizing individual parts. It also discusses how tolerances are specified in parts and how greater tolerances increase costs.
Unit 3-ME8691 & COMPUTER AIDED DESIGN AND MANUFACTURINGMohanumar S
This document discusses various CAD standards including:
1. Graphical standards like GKS and OpenGL that define graphics primitives and device independence.
2. Data exchange standards like IGES and STEP that define neutral formats for transferring geometric and non-geometric CAD data between systems.
3. Communication standards like LAN and WAN that define how CAD data is transferred over networks between systems.
The goals of CAD standards are to enable interoperability and portability of CAD data across different software and hardware platforms. They aim to support the complete transfer of product description data.
Assembly modeling allows components to be brought together to define a more complex product representation. It facilitates collaboration between different teams to ensure the assembly works together. An assembly contains component objects that can be individual parts or subassemblies. There are two main approaches to assembly modeling - bottom-up builds the assembly from individual pre-made parts, while top-down designs parts within the assembly context. Mating conditions like concentric or parallel define relationships between components.
Introduction, Conventional and Revised with CAD/CAM Product cycle, Application of computers to the design process, comparison of capabilities of designers and computers, Reasons for implementing CAD, Benefits of CAD, CAD workstation,
The document discusses various computer-aided design (CAD) standards used for data exchange, including graphics standards like GKS and OpenGL, as well as data exchange standards like IGES, DXF, and STEP. It provides details on the purpose and requirements of each standard, explaining concepts like layers, entities, and file structure. The key standards discussed are IGES for shape data exchange, DXF for CAD file interchange, and STEP for comprehensive product data across the design and manufacturing lifecycle.
This document discusses different types of surface models used in computer graphics, including:
- Plane, ruled, surface of revolution, tabulated, bilinear, Coons patch, and bicubic surfaces. Plane and ruled surfaces are linear, while surfaces of revolution and tabulated surfaces are axisymmetric. Bilinear surfaces are generated by interpolating 4 endpoints and are useful for finite element analysis. Coons patches interpolate 4 edge curves. Bicubic surfaces use parametric curves and interpolation of control points to define smooth surfaces.
This document provides an overview of geometric modeling techniques used in computer aided design (CAD). It discusses representation of curves including Hermite curves, Bezier curves, B-spline curves, and rational curves. It also covers surface modeling techniques such as surface patches, Coons patches, and Bicubic patches. For solid modeling, it describes constructive solid geometry (CSG) and boundary representation (B-rep) techniques. CSG uses boolean operations on primitives to create models while B-rep defines models based on their bounding faces, edges and vertices.
This document provides an introduction to computer-aided design (CAD). It defines CAD and computer-aided manufacturing (CAM) as using computers to aid in design and manufacturing functions. The document outlines the basic product design cycle and how CAD/CAM can be integrated at various stages, including computer-aided drafting, process planning, and computer-controlled manufacturing. It also describes the basic hardware and software components of CAD systems, including how interactive computer graphics are used to aid designers. Finally, it summarizes the general six-phase design process.
This document discusses different types of surface modelling techniques. Parametric surfaces and implicit surfaces are the two main types used in modelling systems. Parametric surfaces are defined by a set of coordinate functions, while implicit surfaces are defined by a polynomial equation. Common parametric surfaces include planes, ruled surfaces, surfaces of revolution, and B-splines. Multiple parametric surface patches can be joined to model more complex shapes. Surface modelling allows representing complex object geometries and is useful for mass properties calculation, interference detection, and finite element analysis.
The document is a syllabus for a Solid Modeling and Drafting course that discusses curves, surfaces, and geometric modeling. It covers curve representation methods including parametric and non-parametric, types of curves like analytic and synthetic, and examples of analytic curves like lines and circles. It also discusses surface representation and types of surfaces. The objectives are to introduce curves and surfaces modeling and their implementation in geometric modeling.
This document provides an overview of assembly modelling including interference checking, tolerance analysis, mass property calculations, mechanism simulation, and interference checking. It discusses assembly modelling approaches like bottom-up and top-down, assembly planning considerations, mating conditions, tolerance systems, and methods for tolerance analysis including worst-case, statistical, and Monte Carlo simulation methods. Mass properties like mass, center of gravity, and moments of inertia are also covered. Mechanism simulation advantages and disadvantages are outlined as well as the purpose of interference checking in assemblies.
The document discusses geometric transformations in computer-aided design. It begins by defining various geometric transformations including translation, rotation, scaling, shearing, and reflection. It then describes how to represent points and perform transformations using matrix algebra with homogeneous coordinates. The document provides examples of combining multiple transformations through concatenation and calculating inverse transformations via matrix inversion. It concludes with two examples problems applying transformations to geometric shapes.
This document discusses graphic standards and provides details about GKS, CORE, IGES, and their use. It explains that GKS is an international standard for 2D graphics and describes its primitives like polyline and text. It also discusses IGES for exchanging CAD models between different software packages through a neutral file format. The document includes an example of drawing a duck using GKS primitives and an IGES file case study.
Bezier surfaces are parametric surfaces used in computer graphics and CAD/CAM. They are based on Bernstein polynomials and control points. A Bezier surface is defined by a grid of control points that determine the shape of the surface. Changing control points modifies the shape globally. B-spline surfaces allow for more local control and ensure continuity between patches. Coons patches interpolate between four boundary curves to generate a smooth surface. Sculptured surfaces are used for complex, free-form shapes and consist of blended parametric surface patches.
Unit 2-ME8691 & COMPUTER AIDED DESIGN AND MANUFACTURINGMohanumar S
This document discusses different geometric modeling techniques. It describes wireframe modeling where object edges are represented by lines. Surface modeling uses techniques like patches to represent curved surfaces. Solid modeling represents objects as solids to avoid misinterpretation. Constructive solid geometry and boundary representation are two common solid modeling techniques. CSG uses primitives and Boolean operations while boundary representation uses edges, vertices and faces to define boundaries.
This document discusses algorithms for hidden surface removal in 3D computer graphics. It describes two main classifications of algorithms - object space and image space. It then provides details on various algorithms including Painter's algorithm (object space), Z-buffer algorithm (image space), and Warnock's area subdivision algorithm. The key aspects and approaches of each algorithm are summarized.
This document describes a method for 3D reconstruction from a single image using single-view metrology. Key steps include detecting vanishing points to establish directions in the scene, calculating planar homographies to map image points to world coordinates, and using metric constraints to estimate distances and reconstruct occluded objects. Examples demonstrate reconstructing buildings and objects from single images. Limitations include reliance on planar surfaces and regular object shapes.
This document discusses various visible surface detection methods in computer graphics. It describes object-space methods like back-face detection that compare object surfaces, and image-space methods like depth buffering that determine visibility point-by-point. Specific algorithms covered include depth buffering, scan-line, depth sorting, BSP trees, ray casting, and methods for curved and wireframe surfaces. It also provides examples and discusses functions for implementing visibility detection in OpenGL.
Three-dimensional viewing involves considering the spatial position from which an object can be viewed, projecting 3D descriptions of objects onto a 2D viewing surface, and enclosing visible space within clipping boundaries. The viewing pipeline involves a series of transformations that convert 3D coordinates to 2D device coordinates for display. Parallel and perspective projections are two basic projection methods that transform 3D positions to 2D viewing coordinates in different ways.
3 d display-methods-in-computer-graphics(For DIU)Rajon rdx
3D computer graphics use three-dimensional representations of geometric data stored in a computer to render 2D images for later display or real-time viewing. This document discusses several 3D display methods in computer graphics including parallel projection, perspective projection, and depth cueing. Parallel projection projects points onto a plane along parallel lines, maintaining proportions but not producing realistic views. Perspective projection uses lines converging at a center point to give a more realistic impression of depth. Depth cueing varies the intensity of displayed objects based on distance to convey depth information.
This document discusses various 3D display methods in computer graphics. It describes parallel projection, which preserves proportions but not realistic views, and perspective projection, which produces realistic views but not proportions. Perspective projection has three types: one point, two point, and three point. Depth cueing and visible line identification help convey depth information. Surface rendering sets surface intensity based on lighting conditions and surface characteristics to generate realism.
The document discusses several methods for visible surface detection or hidden surface removal in 3D computer graphics, including object space and image space methods. Object space methods determine visibility in 3D coordinates and include depth sorting and binary space partitioning (BSP) trees, while image space methods determine visibility on a per-pixel basis and include the depth-buffer or z-buffer method and ray casting. The depth-buffer method uses two buffers, a frame buffer and depth buffer, to render surfaces from back to front on a pixel-by-pixel basis. BSP trees recursively subdivide space with splitting planes to give a rendering order that correctly draws objects from back to front.
This document discusses different 3D display and rendering methods. It describes parallel and perspective projections, which transform 3D objects onto a 2D plane. Parallel projection discards the z-coordinate and keeps parallel lines parallel, while perspective projection converges lines to give a realistic impression of depth. Common projection types include orthographic, oblique, cavalier and cabinet. Surface rendering involves collecting data on an object to create a 3D computer image, and is used in industries like healthcare and archaeology.
In Computer Graphics, Hidden surface determination also known as Visible Surface determination or hidden surface removal is the process used to determine which surfaces
of a particular object are not visible from a particular angle or particular viewpoint. In this scribe we will describe the object-space method and image space method. We
will also discuss Algorithm based on Z-buffer method, A-buffer method, and Scan-Line Method.
This document contains information about 3D display methods in computer graphics presented by a group of 5 students. It discusses parallel projection, perspective projection, depth cueing, visible line identification, and surface rendering techniques. The goal is to generate realistic 3D images and correctly display depth relationships between objects.
The document discusses the 2D viewing pipeline. It describes how a 3D world coordinate scene is constructed and then transformed through a series of steps to 2D device coordinates that can be displayed. These steps include converting to viewing coordinates using a window-to-viewport transformation, then mapping to normalized and finally device coordinates. It also covers techniques for clipping objects and lines that fall outside the viewing window including Cohen-Sutherland line clipping and Sutherland-Hodgeman polygon clipping.
The document discusses two-dimensional viewing and clipping techniques in computer graphics. It describes how a window defines the scene to view and a viewport defines where it is displayed. Different transformations map the window coordinates to normalized device coordinates. Clipping techniques like Cohen-Sutherland clipping and Liang-Barsky clipping are used to only display the parts of lines and polygons within the viewport boundaries. Text clipping can be done by bounding text as a whole, character-by-character, or by clipping individual character components.
This document discusses algorithms for visible surface determination (VSD) to determine which surfaces are visible during 3D rendering. It describes two main approaches: image precision, which operates at the display resolution, and object precision, which operates at the object level. It also discusses techniques like the depth buffer and depth sorting algorithms. The depth buffer method uses two buffers - a depth buffer and frame buffer - to track pixel depth and color values. It processes objects and surfaces, testing pixels and updating the buffers. Depth sorting paints surfaces in order of decreasing depth to resolve visibility.
Hidden surface removal algorithms aim to eliminate hidden parts of 3D objects when rendered on a 2D display. They use geometric sorting to distinguish visible from hidden parts, operating in either object or image space. Key considerations for these algorithms include the sorting method, exploiting various types of coherence in the scene, and being optimized for the target machine. Common algorithms are back face removal, Z-buffer, painter's, scan line, and subdivision.
The document discusses image segmentation techniques including thresholding. Thresholding divides an image into foreground and background regions based on pixel intensity values. Global thresholding uses a single threshold value for the entire image, while adaptive or local thresholding uses variable thresholds that change across the image. Multilevel thresholding can extract objects within a specific intensity range using multiple threshold values. The Hough transform is also presented as a way to connect disjointed edge points and detect shapes like lines in an image.
Geometric modeling involves mathematically describing an object's geometry using software. There are three main methods: wireframe modeling uses lines to represent edges; surface modeling represents objects' surfaces; and solid modeling displays models as solids to avoid misinterpretation. Solid modeling is most effective as it makes objects most realistic and eliminates ambiguity.
The document discusses hidden surface removal in computer graphics. It describes how hidden surface algorithms use geometric sorting to distinguish visible parts of objects from hidden parts, similar to alphabetical sorting of words. It outlines two main categories of algorithms: object space methods that operate on 3D object models and image space methods that determine visibility on a pixel-by-pixel basis. The document also covers considerations for hidden surface algorithms like sorting methods, exploiting different types of coherence, and adapting to different computer architectures.
This document contains questions from past exams on the topic of production planning and control. It is divided into 5 units which cover introductory concepts, work study, production planning and process planning, production scheduling, and inventory control. The questions range from definitions and short explanations to longer discussions requiring analyses. The document serves as a study guide for students, with questions at different levels of difficulty in each unit to test comprehension of key production planning and control topics.
The document discusses production planning and control. It defines key terms like production, production planning and control, and their objectives. It describes the functions of production planning and control like materials, machines, methods, routing, estimating, loading and scheduling, dispatching, expediting, and inspection. It also discusses topics like standardization, work study, production types, and production scheduling techniques.
This document provides a summary of important two-mark questions and answers related to the topics covered in a Computer Aided Design (CAD) course. It includes questions from five units:
1. Fundamentals of computer graphics including the design process, applications of CAD, geometric transformations, and homogeneous coordinates.
2. Geometric modeling covering curves, wireframe modeling, boundary representation vs constructive solid geometry.
3. Visual realism such as visualization techniques, lighting models, shading methods and color models.
4. Assembly of parts including assembly modeling, mating conditions, tolerancing, mass properties and interference checking.
5. CAD standards including the need for data exchange standards and important standards for exchange
This document provides an overview of geometric modeling techniques used in computer aided design (CAD). It discusses representation of curves including Hermite curves, Bezier curves, B-spline curves, and rational curves. It also covers surface modeling techniques such as surface patches, Coons patches, bicubic patches, Bezier surfaces, and B-spline surfaces. For solid modeling, it describes constructive solid geometry (CSG) and boundary representation (B-rep) techniques. CSG uses boolean operations on primitives to create models while B-rep models objects based on their bounding faces, edges, and vertices.
The document provides information about the ME6501 Computer Aided Design course at AL Ameen Engineering College. It includes 5 units that cover fundamentals of computer graphics, geometric modeling, visual realism, assembly of parts, and CAD standards. The objectives are to provide an overview of how computers are used in mechanical component design. Some key topics covered are product life cycles, sequential and concurrent engineering, CAD system architecture, and representations of curves and surfaces for geometric modeling. The outcomes are for students to be able to use computer and CAD software for modeling mechanical components.
This document discusses various quality control tools used for data collection and analysis including check sheets, Pareto charts, flow charts, cause and effect diagrams, histograms, scatter diagrams, and control charts. It provides examples of how each tool can be used to identify issues, determine root causes, and monitor processes for quality improvement in areas like manufacturing and customer service. The document emphasizes using graphical representations to more easily recognize patterns in data and determine appropriate actions.
The document provides information on new management tools including affinity diagrams, interrelationship digraphs, tree diagrams, matrix diagrams, prioritization matrices, process decision program charts (PDPC), and activity network diagrams. It defines each tool, explains the process for how to use it, and provides examples. The tools are designed to help structure brainstorming, analyze relationships between factors, break concepts down into finer levels of detail, evaluate options, identify risks and countermeasures, and plan task sequences.
This document provides an overview of failure mode and effects analysis (FMEA). It describes FMEA as a structured approach to identify ways a product or process can fail, estimate risks from specific causes, and prioritize actions to reduce risk. The document outlines the FMEA process, including establishing a team, identifying failure modes and their effects, analyzing severity, occurrence and detection, calculating a risk priority number, and developing recommended actions. It also distinguishes between design FMEA and process FMEA.
The document discusses benchmarking, which is defined as measuring an organization's internal processes and comparing them to best-in-class organizations to identify outstanding practices to adapt. It describes benchmarking as a way to move from an organization's current performance level to where it wants to be. Benchmarking can help obtain an external perspective, set strategic targets, promote performance improvements, establish a competitive edge, enhance customer satisfaction, reduce costs, improve employee morale, and help achieve quality awards. The document outlines the various levels, types, areas, methodology, model, factors for success and advantages of benchmarking.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
2. VISUALIZATION
Visualization can be defined as a technique for
creating images , diagrams or animations to
communicate ideas.
Projection and shading are common methods for
visualizing geometric models.
CAD uses isometric and perspective projection in
addition to orthographic projection for generating
rich visual images with complete design
information.
3. To project 3D to 2D objects we need to remove
the ambiguities of the different views, which can
be got by the elimination of hidden lines ,
surfaces , solid removal approaches.
Shading,
Lighting
Transparency
Coloring approaches provide more visual realism
4. Model clean up process
Generate orthographic views
Eliminate hidden lines
Changing necessary hidden lines as dashed line or
adding dimension and text to the different views.
5. Application of realism
Robot Simulations : Visualization of movement of their links and joints and end
effector movement etc.
CNC programs verification of tool movement along the path prescribed and
estimation of cup height and surface finish etc.
Discrete Even Simulation : Most of DES packages provide the user to create
shop floor environment on the screen to visualize layout of facilities, movement
of material handling systems, performance of machines and tools.
Scientific Computing : Visualization of results of FEM analysis like iso-stress
and iso-strain regions, deformed shapes and stress contours. Temperature and
heat flux in heat-transfer analysis. Display and animation of mode shape in
vibration analysis.
Flight Simulation : Cockpit training for pilots is first being provided with flight
simulators, which virtually simulates the surrounding that an actual flight will
pass through.
9. HIDDEN LINE REMOVAL
“For a given three dimensional scene, a given
viewing point and a given direction eliminate
from an appropriate two dimensional projection
of the edges and faces which the observer cannot
see”
Object space method
Image space method
10. Two main types of algorithms:
– Object space: Determine which part of the object are visible. Also called
as World Coordinates. Object is described in physical coordinate system.
– It compares the object and parts to each other within the scene definition
to determine which surface is visible.
– Image space: Determine per pixel which point of an object is visible.
Also called as Screen Coordinates. Visibility is decided point by point at
each pixel position on view plane.
– Zooming does not degrade the quality.
Object space Image space
11. Two main Hidden Surface Removal Algorithm
Techniques:
Object space: Hidden Surface Removal for all
objects
Image space:
Objects: 3 D Clipping
Transformed to Screen Coordinates
Hidden Surface Removal
12. HIDDEN LINE ELIMINATION PROCESS
DISPLAY OF RESULTS
ELIMINATION OF HIDDEN LINES
APPLICATION OF VISIBILITY TECHNIQUES
CHECKS FOR OVERLAPPING
DEPTH COMPARISION IS USED TO DETERMINE PART OR ALL OF POLYGON IS
HIDDEN
SORTING OF 2D IMAGE DATA
2D OBJECT DATA
TRANSFORMATIONS-CONTAINS VISIBLE AND INVISBLE EDGES.
3D OBJECT DATA
GEOMETRY AND TOPOLOGY
13. VISIBILITY TECHNIQUES
MINIMAX TEST
CONTAINMENT TEST
SURFACE TEST
COMPUTING SILHOUETTES
EDGE INTERSECTION
SEGMENT COMPARISONS
HOMOGENITY TEST
14. MINIMAX TEST
Minimax test (also called the overlap or bounding box test) checks if two
polygons overlap. The test provides a quick method to determine if two
polygons do not overlap.
It surrounds each polygon with a box by finding its extents (minimum and
maximum x and y coordinates) and then checks for the intersection for any two
boxes in both the X and Y directions.
If two boxed do not intersect, their corresponding polygons do not overlap (see
Figure 1). In such a case, no further testing of the edges of the polygons is
required.
If the minimax test fails (two boxes intersect), the two polygons may or may not
overlap, as shown in Figure 1. Each edge of one polygon is compared against
all the edges of the other polygon to detect intersections. The minimax test can
be applied first to any two edges to speed up this process
17. The containment test checks whether a given point lies inside a given polygon or
polyhedron. There are three methods to compute containment or surroundness.
For a convex polygon, one can substitute the X and Y coordinates of the point into
the line equation of each edge. If all substitutions result in the same sign, the
point is on the same side of each edge and is therefore surrounded.
For non-convex polygons, two other methods can be used. In the first method, we
draw a line from the point under testing to infinity as shown in Figure 2a. The semi-
infinite line is intersected with the polygon edges. If the intersection count is
even, the point is outside the polygon ( in Figure 2a). If it is odd, the point is
inside.
If one of the polygon edges lies on the semi-infinite line, a singular case arises which
needs special treatment to guarantee the consistency of the results.
The second method for non-convex polygons (Figure 2b) computes the sum of the
angles subtended by each of the oriented edges as seen from the test point. If the
sum is zero, the point is outside the polygon. If the sum is -360 or +360 the point is
inside. The minus sign reflects whether the vertices of the polygon are ordered in a
clockwise direction instead of counter clockwise.
18. Computing silhouettes
A set of edges that separates visible faces from invisible faces of an
object with respect to a given viewing direction is called silhouette
edges (or silhouettes).
The signs of the components of normal vectors of the object faces
can be utilized to determine the silhouette.
An edge that is part of the silhouette is characterized as the
intersection of one visible face and one invisible face.
An edge that is the intersection of two visible faces is visible, but
does not contribute to the silhouette.
The intersection of two invisible faces produces an invisible edge.
19.
20. Edge intersection
The hidden algorithm initially calculates the
edges intersections in 2D.
To find out partially visible lines.
The two edges intersect at a point where y2-y1=0.
Then segment comparisons are used to further
determine visibility
21.
22. Segment comparison
The image is computed scan line by line that is in
segments and displayed in the same order.
The scan line is divided into spans(dashed lines).
The visibility is determined within each span by
comparing the depths of the edge segments that
lie in the span.
Segments with maximum depth are visible
throughout the span.
23.
24. Homogeneity test
Points are compared for visibility.
Homogeneously visible
Neighborhood of point P can be projected objectively
onto neighborhood of the projection of a point.
Homogeneously invisible
Neighborhood of point P cannot be projected
objectively onto neighborhood of the projection of a
point.
In-homogeneously visible
Pr(N(P))=N(Pr(P))
Pr(N(P))≠N(Pr(P)) inhomogeneously invisible.
27. Back-face elimination
Object-space method
Works fine for convex polyhedra: ±50% removed
Concave or overlapping polyhedra: require
additional processing
Interior of objects can not be viewed
Partially visible front faces
28. Hidden line removal algorithm
Depth Algorithm or Z algorithm or Priority
algorithm
Area oriented algorithms
Overlay algorithm-Curved surface
Roberts algorithm
Hidden surface removal algorithm
Depth buffer algorithm or z-buffer algorithm
Area coherence algorithm or Warnock’s
algorithm
Scan-line algorithm or Watkin’s algorithm
Hidden solid removal algorithm
Ray tracing algorithm
29. Depth or priority algorithm
This algorithm is also known as the depth or z algorithm. The algorithm is
based on sorting all the faces (polygons) in the scene according to the
largest z coordinate value of each.
This step is sometimes known as assignment of priorities. If a face
intersects more than one face, other visibility tests besides the z depth are
needed to resolve any ambiguities.
Its basis is on the view according to the biggest Z co-ordinate value.
If face intersects more than one face, other visibility test beside z-depth is
required to solve any issue.
31. Depth or priority algorithm
Painter’s algorithm
As we utilize the procedure the painter’s way of
creating the background first and then the overlaying
layer and then the outermost layer with reducing depth.
When we view from z and x axis there is no
overlapping view.
32. Painter’s Algorithm
Assumption: Later projected polygons overwrite earlier
projected polygons
Graphics Pipeline
1 12 23 3
Oops! The red polygon
Should be obscured by
the blue polygon
33. Painter’s Algorithm
Main Idea
A painter creates a picture
by drawing background
scene elemens before
foreground ones
Requirements
Draw polygons in back-to-
front order
Need to sort the polygons
by depth order to get a
correct image
from Shirley
37. Area oriented algorithm
It is based on subdivision of given data set in a stepwise
fashion until all visible areas are determined and displayed.
38. Identify silhouette polygons – silhouette edges are
recognized and connection of silhouette edges to form closed
polygons by sorting all edges for equal end points
Assign quantitative hiding(QH) values to silhouette
polygon.
This is achieved by intersecting the polygons. The intersection points
define points where QH may change. Find QH value using depth test. 0
is visible and 1 is invisible.
Determine the visible silhouette segments.
If closed silhouette polygon is completely invisible it need not be
considered any further. If it is visible the segments with least QH values
are considered.
39. Intersect the visible silhouette segments with
partially visible faces.
To find out the partially visible and fully visible faces.
Display the interior of the visible or partially
visible polygons.
By using stack and simply enumerates all faces lying
inside a silhouette polygon.
The stack is started with a visible face and a loop
begins popping of face F2
40. Overlay algorithm
The curved surfaces are approximated as planar
surfaces.
The u-v grid is used to create grid surface which
consists of regions having straight edges.
The curves in each region are approximated as
line segment.
The 1st step is to use surface equation and grid
linear edges are created.
41. Hidden line removal for curved surface
To compute the exact visibility we introduce a
notion of visibility curves obtained by projection of
silhouette and boundary curves and decomposing the
surface into nonoverlapping regions.
The nonoverlapping and visible portions of the
surface are represented as trimmed surfaces and we
present a representation based on polygon
trapezoidation algorithms.
The curved surface is converted in polygon mesh and
calculated for visiblity.
42. Hidden surface removal algorithm
The elimination of parts of a solid objects that are
covered by others is called hidden surface
removal.
Depth buffer or Z-buffer Algorithm
Area coherence or Warnock’s algorithm
Scan-line algorithm or Watkin’s algorithm
43. Depth-Buffer Methods
43
Three surfaces overlapping pixel position (x,y) on the view plane.
The visible surface, S1, has the smallest depth value.
vx
vy
vz
3S
2S
1S
,x y
view plane
45. 45
Z-Buffer Algorithm
As we render each polygon, compare the depth of each
pixel to depth in z buffer
If less, place shade of pixel in color buffer and update z
buffer
47. Two buffer areas are required
• Depth buffer
Store depth values for each (x, y) position
All positions are initialized to minimum depth
Usually 0 – most distant depth from the viewplane
• Refresh buffer
Stores the intensity values for each position
All positions are initialized to the background
intensity
48. Z-BUFFER ALGORITHM:
• Its an extension of Frame Buffer
• Display is always stored on Frame Buffer
• Frame Buffer stores information of each and every
pixel on the screen
• Bits (0, 1) decide that the pixel will be ON or OFF
• Z- Buffer apart from Frame buffer stores the depth
of pixel
• After analyzing the data of the overlapping
polygons, pixel closer to the eye will be updated
• Resolution of X,Y => Array[X,Y]
49. Given set of polygon in image space
Z-Buffer Algorithm:
1. Set the frame buffer & Z-Buffer to a background
value
(Z-BUFFER=Zmin) where, Zmin is value
To display polygon decide=>color, intensity and depth
2. Scan convert each polygon
i.e, for each pixel, find depth at that point
If Z(X,Y)>Z-BUFFER(X,Y)
Update Z-BUFFER(X,Y)=Z(X,Y)
& FRAME BUFFER
This process will repeat for each pixel
50. • By this way we can remove hidden lines and display
those polygons which are closer to eye
• X*Y space required to maintain Z-Buffer=> X*Y
times will be scanned
• Expensive in terms of time and space as space is very
large
x
z
display
S
S’
x
y S
S’
51. Area coherence or warnock’s algorithm
Area Subdivision
Exploits area coherence: Small areas of an
image are likely to be covered by only one
polygon
Three easy cases for determining what’s in front
in a given region:
1. a polygon is completely in front of everything else in
that region
2. no surfaces project to the region
3. only one surface is completely inside the region,
overlaps the region, or surrounds the region
52. Identifying Tests
Four possible relationships
Surrounding surface
Completely enclose the area
Overlapping surface
Partly inside and partly outside the area
Inside surface
Outside surface
No further subdivisions are needed if one of the following conditions is
true
All surface are outside surfaces with respect to the area
Only one inside, overlapping, or surrounding surface is in the area
A surrounding surface obscures all other surfaces within the area boundaries
from depth sorting, plane equation
Surrounding
Surface
Overlapping
Surface
Inside
Surface
Outside
Surface
53. Warnock’s Area Subdivision
(Image Precision)
Start with whole image
If one of the easy cases is satisfied (previous slide), draw
what’s in front
Otherwise, subdivide the region and recurse
If region is single pixel, choose surface with smallest depth
Advantages:
No over-rendering
Anti-aliases well - just recurse deeper to get sub-pixel
information
Disadvantage:
Tests are quite complex and slow
54. Characteristics
Takes advantage of area coherence
Locating view areas that represent part of a single surface
Successively dividing the total viewing area into smaller rectangles
Until each small area is the projection of part of a single visible
surface or no surface
Require tests
Identify the area as part of a single surface
Tell us that the area is too complex to analyze easily
Similar to constructing a quadtree
55. 55
Process
Staring with the total view
Apply the identifying tests
If the tests indicate that the view is sufficiently
complex
Subdivide
Apply the tests to each of the smaller areas
Until belonging to a single surface
Until the size of a single pixel
Example
With a resolution 1024 1024
10 times before reduced to a point
56. Warnock’s Algorithm
Regions labeled with case
used to classify them:
1) One polygon in front
2) Empty
3) One polygon inside,
surrounding or
intersecting
Small regions not labeled
2 2 2
2222
2
2
3
3
3
3 33
3
3
3
3
3
333
3
3
1
1 1 1
1
57. SCAN LINE Z-BUFFER ALGORITHM:
• An image space method for identifying visible
surfaces
• Computes and compares depth values along the
various scan-lines for a scene
58. Scan-Line Method Basic Example
Scan Line 1:
(A,B) to (B,C) only inside S1, so color from S1
(E,H) to (F,G) only inside S2, so color from S2
Scan Line 2:
(A,D) to (E,H) only inside S1, so color from S1
(E,H) to (B,C) inside S1 and S2 , so compute & test depth
In this example we color from S1
(B,C) to (F,G) only inside S2, so color from S2
B
A
D
C
G
F
E
H
S1 S2
Scan Line 1
Scan Line 2
Scan Line 3
59. • Scanning takes place row by row
• To facilitate the search for surfaces crossing a given
scan-line an active list of edges is formed for each
scan-line as it is processed
• The active list stores only those edges that cross the
scan-line in order of increasing x
• Pixel positions across each scan-line are processed
from left to right
• We only need to perform depth calculations
• In Scan Line, Z-Buffer(X) whereas earlier it was X*Y
60. Use Z-Buffer for only 1 scan line / 1 row of pixel
• During scan conversion in the Active Edge
List(AEL)=> Calculate Z(X,Y)
i.e, -Pixel info between 1 & 2 active edges will only
be stored
-Next pixel will be stored as z=z1+∆z
-∆z will be constant but can change anywhere in
case of slope
• If Z(X,Y)>Z BUFFER(X) => Update
• If 2 polygons are present-along with Active Edge List,
Active Polygon List will also be included
• Active Polygon List=> List of polygons intersecting a
scan line
61. Hidden solid removal
The hidden solid removal of B-rep model are
algorithms such as z-buffer.
Convert CSG to B-rep.
Render it with standard hidden surface removal
techniques.
RAY TRACING
The complex 3D solid/solid intersection problem
is converted into a 1D ray/solid intersection
calculation
62. Ray tracing
If we shoot a ray from the viewpoint through the
pixel, the first object which hits is the one that is
visible at the pixel.
It can be used for both flat and curved surface.
Shoot the ray from the eyepiece one per pixel
Find the closest object blocking the path of the
ray.
Since it has infinite rays, the light rays are traced
backwards, a ray from the viewpoint is traced
through a pixel until it reaches a surface.
63.
64.
65. Ray casting
If resolution is x,y then there are xy pixels so xy
light rays are traced.
Each ray is tested for intersections with each
object in the picture including the non clipping
plane.
The intersection closest to the viewpoint is
determined since rays intersect many objects.
66. The main advantage is that it can create extremely
realistic rendering of pictures by incorporating
laws of optics for reflection and transmitting light
rays
The major disadvantage is the performance since
it starts the process a new and treat each eye ray
separately.