DOCSLIB.ORG

Surface Details

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Surface Details ✫ Incorp orate ne details in the scene. ✫ Mo deling with p olygons is impractical. ✫ Map an image texture/pattern on the surface Catmull, 1974; Blin & Newell, 1976. ✫ Texture map Mo dels patterns, rough surfaces, 3D e ects. ✫ Solid textures 3D textures to mo del wood grain, stains, marble, etc. ✫ Bump mapping Displace normals to create shading e ects. ✫ Environment mapping Re ections of environment on shiny surfaces. ✫ Displacement mapping Perturb the p osition of some pixels. CPS124, 296: Computer Graphics Surface Details Page 1 Texture Maps ✫ Maps an image on a surface. ✫ Each element is called texel. ✫ Textures are xed patterns, pro cedurally gen- erated, or digitized images. CPS124, 296: Computer Graphics Surface Details Page 2 Texture Maps ✫ Texture map has its own co ordinate system; st-co ordinate system. ✫ Surface has its own co ordinate system; uv -co ordinates. ✫ Pixels are referenced in the window co ordinate system Cartesian co ordinates. Texture Space Object Space Image Space (s,t) (u,v) (x,y) CPS124, 296: Computer Graphics Surface Details Page 3 Texture Maps v u y xs t s x ys z y xs t s x ys z CPS124, 296: Computer Graphics Surface Details Page 4 Texture Mapping CPS124, 296: Computer Graphics Surface Details Page 5 Texture Mapping Forward mapping: Texture scanning ✫ Map texture pattern to the ob ject space. u = f s; t = a s + b t + c; u u u v = f s; t = a s + b t + c: v v v ✫ Map ob ject space to window co ordinate sys- tem. Use mo delview/pro jection transformations. Drawback: Selected texture patch usual do es not match with pixel b oundaries. ✫ Requires fractional pixel calculations. CPS124, 296: Computer Graphics Surface Details Page 6 Inverse Mapping y xs t -1 -1 M M PV T s x ys z ✫ Map screen co ordinate system to ob ject space. ✫ Map ob ject co ordinate system to texture space. ✫ Avoids fractional pixel calculations. ✫ Allows anti-aliasing. ✫ Requires calculating inverse transformations; 1 1 M ;M . PV T 1 M can be computed from pro jection and PV mo delview matrices gluUnproject 1 Computing M is not easy. T CPS124, 296: Computer Graphics Surface Details Page 7 Parametric Representation Curves: Co ordinates are represented as functions of one parameter. t = xt;yt; t 2 [a; b] Line: ` : a + b t; a + b t, t 2 R 1 1 2 2 Surfaces: Co ordinates of each p oint is represented as a function of u and v . S u; v = xu; v ;yu; v ;zu; v . ✫ Sphere: S u; v = r cos u cos v; r cos u sin v; r sin u =2 u =2; 0 v 2. ✫Cylinder: S u; v = r cos u; r sin u; v 0 u 2; 0 v h. CPS124, 296: Computer Graphics Surface Details Page 8 Inverse Mapping: An Example y t (u,v) s x z u = ; v = y 0 =2; 0 y 1 x = sin ; z = cos ; y = v: 1 1 M : u = sin x; v = y: PV Map texture origin to left b ottom corner of the surface u = s =2; v = t: 1 Pro jected pixels are mapp ed to texture with M : T 2u 1 M : s = t = v: T 2 1 s = sin x t = z: CPS124, 296: Computer Graphics Surface Details Page 9 Object to Texture Mapping 1 How do es one de ne a reasonable M ? T Bier & Sloan, 1986: Two-step pro cess: S -mapping: Mapping from a 2D texture space to a simple 3D surface, e.g., cylinder. 0 T u; v ! T x ;y ;z : i i i O-mapping: Mapping from the 3D texture pat- tern onto the ob ject surface. 0 T x ;y ;z ! Ox ;y ;z : i i i w w w CPS124, 296: Computer Graphics Surface Details Page 10 Two-Step Inverse Mapping Inverse mapping: Apply them in the reverse or- der! -1 S -1 O M-1 CPS124, 296: Computer Graphics Surface Details Page 11 S -Mapping Four p ossible surfaces: Plane, cylinder, sphere, box. Cylinder: ; z 1 r ; z z S : ; z ! 0 0 c d ✫c; d: Scaling factors. ✫ Texture origin is mapp ed to the p oint ;z 0 0 on the cylinder. Sphere: ; ', stereographic pro jection. θ (α,β) φ (θ,φ) 2 S : ; ' ! ; 2 2 1=2 1 + 1 + + 2 2 2 1=2 1 + 1 + + = tan ' cos , = tan ' sin . CPS124, 296: Computer Graphics Surface Details Page 12 S -Mapping t s t Back Left Bottom Right Top s Front CPS124, 296: Computer Graphics Surface Details Page 13 O -Mapping P' P' P P (ii) (i) P' P' P P (iii) C (iv) ✫ : Intermediate surface 0 ✫ P : Intersection of with a ray emanating from P . ✫ Direction of : i Re ection direction ii Normal of O at P iii CP ; C: centroid of O 0 iv : Normal of at P ✫ ii, iii are bad if is cylinder. CPS124, 296: Computer Graphics Surface Details Page 14 3D Textures Intro duced by Peachey and Perlin in 1985. ✫ De ne texture to be a 3D image. Carving out an ob ject from a 3D solid ma- terial. ✫ Ignoring scaling, M is identity. T ✫ Distortion is minimized. ✫ Three dimensional vector elds can be mapp ed coherently. ✫ Texture is generated by a pro cedure. ✫ Example: Wood grain can be mapp ed as a set of cylinders with resp ect to a presp eci ed axis. CPS124, 296: Computer Graphics Surface Details Page 15 3D Textures Basic texture 3D noise textured object 3D texture Textures object Object CPS124, 296: Computer Graphics Surface Details Page 16 Anti-aliasing & Texture Mapping Aliasing is particularly visible in p erio dic and co- herent textures. With Without Antialiasing Antialiasing CPS124, 296: Computer Graphics Surface Details Page 17 Anti-aliasing & Texture Mapping ✫ A pixel is mapp ed to a curvilinear quadrilat- eral. ✫ A single pixel may cover many texels. ✫ Compute a weighted sum of texel values cov- ered by the pixel. ✫ Summation is called ltering. Two-step pro cess: ✫ De ne and approximate the texture over which ltering is p erformed. ✫ Integrate by weighing and summing the texel values within the ltering area. CPS124, 296: Computer Graphics Surface Details Page 18 Anti-aliasing: Weight Functions Blinn & Newell, 1976: Pyramid weight function Preimage of Approximation Preimage of the pixel center Greene & Heckb ert, 1986: Elliptical weighted av- erage ✫ Approximate a pixel by circle. ✫ Circle always maps to an ellipse in the texture space. ✫ Find the texels that lie inside the ellipse. ✫ Use a lo ok-up table to determine the weighted value of each texel. CPS124, 296: Computer Graphics Surface Details Page 19 Anti-aliasing & Texture Mapping Mip-mapping: multum in parvo Williams, 1983 ✫ Store many texture images. ✫ i-th image is obtained by scaling down the pre- vious image by half along each axis. ✫ E ectively a 3D database. ✫ Given a pixel, search in the image with an ap- propriate resolution. CPS124, 296: Computer Graphics Surface Details Page 20 Texture Mapping in Op enGL Geometric Vertices Rasterization Display processing Pixel Pixels operations ✫ Relies on the pip eline architecture ✫ Texture mapping is done at the rasterization stage. glTexImage2D GL TEXTURE 2D, level, comp, w, h, b order, format, typ e, tarray GLubyte my texel[512][512]; glTexImage2D GL TEXTURE 2D, 0, 3, 512, 512, 0 GL RGB, GLuint, tarray; glEnableGL TEXTURE 2D; ✫ level: Multiple levels of texture maps; 0 for one level. ✫ comp: integer between 1 and 4; sp eci es how many of R, G, B, and A comp onents sp eci ed. ✫ format: Format of the texture map. CPS124, 296: Computer Graphics Surface Details Page 21 Texture Mapping in Op enGL glTexCoord2f s, t Assigns the two dimensional texture co ordinates to a vertex. (a) (b) glBeginGL QUAD; glTexCoord2f 0.0, 0.0; glVertex3f x1, y1, z1; glTexCoord2f 1.0, 0.0; glVertex3f x2, y2, z2; glTexCoord2f 1.0, 1.0; glVertex3f x3, y3, z3; glTexCoord2f 0.0, 1.0; glVertex3f x4, y4, z4; glEnd CPS124, 296: Computer Graphics Surface Details Page 22 CPS124, ✫ Texture ob jects 296: T exture glGenTexturesn, *names; glBindTexturetarget, name; Computer ✫ Rep eating the texture pattern Mapping glTexParameteriGL TEXTURE WRAP S,GL REPEAT Graphics glTexParameteri GL TEXTURE WRAP S,GL CLAMP Use GL TEXTURE WRAP T for t-co ordinates ✫ Assign a pixel color to the nearest texel in Surf glTexParameterf GL TEXTURE2D, penGL Op GL TEXTURE MAG FILTER, GL NEAREST a ce glTexParameterf GL TEXTURE2D, Det GL TEXTURE MIN FILTER, GL NEAREST ails ✫ GL LINEAR: Interp olates the color using a 2 2 average. P age 23 Bump Mapping Perturb normals in the illumination mo del calcu- lations. ✫ S u; v : Parameterized surface ✫ S = @Su; v =@ u, S = @Su; v =@ v . u v ✫ N u; v = S S ; n = N=jN j u v ✫bu; v : Bump function 0 0 0 S u; v = S u; v + bu; v n N u; v = S S v u @ 0 S = Su; v + bu; v n u @u = S + b n + bn u u u S + b n u u 0 S S + b n v v v 0 N S S + b S n + b n S + u v u u v v b b n n u v = S S + b S n + b n S u v u u v v CPS124, 296: Computer Graphics Surface Details Page 24 Bump Mapping S(u) b(u) S'(u) N'(u) CPS124, 296: Computer Graphics Surface Details Page 25 Bump Mapping ✫ De ne bump functions analytically. ✫ Use lo ok-up tables for bump functions. ✫ Approximate b ;b with nite di erences.
Recommended publications
  • Planar Maps: an Interaction Paradigm for Graphic Design

    Planar Maps: an Interaction Paradigm for Graphic Design

    CH1'89 PROCEEDINGS MAY 1989 PLANAR MAPS: AN INTERACTION PARADIGM FOR GRAPHIC DESIGN Patrick Baudelaire Michel Gangnet Digital Equipment Corporation Pads Research Laboratory 85, Avenue Victor Hugo 92563 Rueil-Malmaison France In a world of changing taste one thing remains as a foundation for decorative design -- the geometry of space division. Talbot F. Hamlin (1932) ABSTRACT Compared to traditional media, computer illustration soft- Figure 1: Four lines or a rectangular area ? ware offers superior editing power at the cost of reduced free- Unfortunately, with typical drawing software this dual in- dom in the picture construction process. To reduce this dis- terpretation is not possible. The picture contains no manipu- crepancy, we propose an extension to the classical paradigm lable objects other than the four original lines. It is impossi- of 2D layered drawing, the map paradigm, that is conducive ble for the software to color the rectangle since no such rect- to a more natural drawing technique. We present the key angle exists. This impossibility is even more striking when concepts on which the new paradigm is based: a) graphical the four lines are abutting as in Fig. 2. We feel that such a objects, called planar maps, that describe shapes with multi- restriction, counter to the traditional practice of the designer, ple colors and contours; b) a drawing technique, called map is a hindrance to productivity and creativity. In this paper sketching, that allows the iterative construction of arbitrarily we propose a new drawing paradigm that will permit a dual complex objects. We also discuss user interface design is- interpretation of Fig.
  • An Introduction to Topology the Classification Theorem for Surfaces by E

    An Introduction to Topology the Classification Theorem for Surfaces by E

    An Introduction to Topology An Introduction to Topology The Classification theorem for Surfaces By E. C. Zeeman Introduction. The classification theorem is a beautiful example of geometric topology. Although it was discovered in the last century*, yet it manages to convey the spirit of present day research. The proof that we give here is elementary, and its is hoped more intuitive than that found in most textbooks, but in none the less rigorous. It is designed for readers who have never done any topology before. It is the sort of mathematics that could be taught in schools both to foster geometric intuition, and to counteract the present day alarming tendency to drop geometry. It is profound, and yet preserves a sense of fun. In Appendix 1 we explain how a deeper result can be proved if one has available the more sophisticated tools of analytic topology and algebraic topology. Examples. Before starting the theorem let us look at a few examples of surfaces. In any branch of mathematics it is always a good thing to start with examples, because they are the source of our intuition. All the following pictures are of surfaces in 3-dimensions. In example 1 by the word “sphere” we mean just the surface of the sphere, and not the inside. In fact in all the examples we mean just the surface and not the solid inside. 1. Sphere. 2. Torus (or inner tube). 3. Knotted torus. 4. Sphere with knotted torus bored through it. * Zeeman wrote this article in the mid-twentieth century. 1 An Introduction to Topology 5.
  • Surface Physics I and II

    Surface Physics I and II

    Surface physics I and II Lectures: Mon 12-14 ,Wed 12-14 D116 Excercises: TBA Lecturer: Antti Kuronen, [email protected] Exercise assistant: Ane Lasa, [email protected] Course homepage: http://www.physics.helsinki.fi/courses/s/pintafysiikka/ Objectives ● To study properties of surfaces of solid materials. ● The relationship between the composition and morphology of the surface and its mechanical, chemical and electronic properties will be dealt with. ● Technologically important field of surface and thin film growth will also be covered. Surface physics I 2012: 1. Introduction 1 Surface physics I and II ● Course in two parts ● Surface physics I (SPI) (530202) ● Period III, 5 ECTS points ● Basics of surface physics ● Surface physics II (SPII) (530169) ● Period IV, 5 ECTS points ● 'Special' topics in surface science ● Surface and thin film growth ● Nanosystems ● Computational methods in surface science ● You can take only SPI or both SPI and SPII Surface physics I 2012: 1. Introduction 2 How to pass ● Both courses: ● Final exam 50% ● Exercises 50% ● Exercises ● Return by ● email to [email protected] or ● on paper to course box on the 2nd floor of Physicum ● Return by (TBA) Surface physics I 2012: 1. Introduction 3 Table of contents ● Surface physics I ● Introduction: What is a surface? Why is it important? Basic concepts. ● Surface structure: Thermodynamics of surfaces. Atomic and electronic structure. ● Experimental methods for surface characterization: Composition, morphology, electronic properties. ● Surface physics II ● Theoretical and computational methods in surface science: Analytical models, Monte Carlo and molecular dynamics sumilations. ● Surface growth: Adsorption, desorption, surface diffusion. ● Thin film growth: Homoepitaxy, heteroepitaxy, nanostructures.
  • Texture / Image-Based Rendering Texture Maps

    Texture / Image-Based Rendering Texture Maps

    Texture / Image-Based Rendering Texture maps Surface color and transparency Environment and irradiance maps Reflectance maps Shadow maps Displacement and bump maps Level of detail hierarchy CS348B Lecture 12 Pat Hanrahan, Spring 2005 Texture Maps How is texture mapped to the surface? Dimensionality: 1D, 2D, 3D Texture coordinates (s,t) Surface parameters (u,v) Direction vectors: reflection R, normal N, halfway H Projection: cylinder Developable surface: polyhedral net Reparameterize a surface: old-fashion model decal What does texture control? Surface color and opacity Illumination functions: environment maps, shadow maps Reflection functions: reflectance maps Geometry: bump and displacement maps CS348B Lecture 12 Pat Hanrahan, Spring 2005 Page 1 Classic History Catmull/Williams 1974 - basic idea Blinn and Newell 1976 - basic idea, reflection maps Blinn 1978 - bump mapping Williams 1978, Reeves et al. 1987 - shadow maps Smith 1980, Heckbert 1983 - texture mapped polygons Williams 1983 - mipmaps Miller and Hoffman 1984 - illumination and reflectance Perlin 1985, Peachey 1985 - solid textures Greene 1986 - environment maps/world projections Akeley 1993 - Reality Engine Light Field BTF CS348B Lecture 12 Pat Hanrahan, Spring 2005 Texture Mapping ++ == 3D Mesh 2D Texture 2D Image CS348B Lecture 12 Pat Hanrahan, Spring 2005 Page 2 Surface Color and Transparency Tom Porter’s Bowling Pin Source: RenderMan Companion, Pls. 12 & 13 CS348B Lecture 12 Pat Hanrahan, Spring 2005 Reflection Maps Blinn and Newell, 1976 CS348B Lecture 12 Pat Hanrahan, Spring 2005 Page 3 Gazing Ball Miller and Hoffman, 1984 Photograph of mirror ball Maps all directions to a to circle Resolution function of orientation Reflection indexed by normal CS348B Lecture 12 Pat Hanrahan, Spring 2005 Environment Maps Interface, Chou and Williams (ca.
  • Digital Mapping & Spatial Analysis

    Digital Mapping & Spatial Analysis

    Digital Mapping & Spatial Analysis Zach Silvia Graduate Community of Learning Rachel Starry April 17, 2018 Andrew Tharler Workshop Agenda 1. Visualizing Spatial Data (Andrew) 2. Storytelling with Maps (Rachel) 3. Archaeological Application of GIS (Zach) CARTO ● Map, Interact, Analyze ● Example 1: Bryn Mawr dining options ● Example 2: Carpenter Carrel Project ● Example 3: Terracotta Altars from Morgantina Leaflet: A JavaScript Library http://leafletjs.com Storytelling with maps #1: OdysseyJS (CartoDB) Platform Germany’s way through the World Cup 2014 Tutorial Storytelling with maps #2: Story Maps (ArcGIS) Platform Indiana Limestone (example 1) Ancient Wonders (example 2) Mapping Spatial Data with ArcGIS - Mapping in GIS Basics - Archaeological Applications - Topographic Applications Mapping Spatial Data with ArcGIS What is GIS - Geographic Information System? A geographic information system (GIS) is a framework for gathering, managing, and analyzing data. Rooted in the science of geography, GIS integrates many types of data. It analyzes spatial location and organizes layers of information into visualizations using maps and 3D scenes. With this unique capability, GIS reveals deeper insights into spatial data, such as patterns, relationships, and situations - helping users make smarter decisions. - ESRI GIS dictionary. - ArcGIS by ESRI - industry standard, expensive, intuitive functionality, PC - Q-GIS - open source, industry standard, less than intuitive, Mac and PC - GRASS - developed by the US military, open source - AutoDESK - counterpart to AutoCAD for topography Types of Spatial Data in ArcGIS: Basics Every feature on the planet has its own unique latitude and longitude coordinates: Houses, trees, streets, archaeological finds, you! How do we collect this information? - Remote Sensing: Aerial photography, satellite imaging, LIDAR - On-site Observation: total station data, ground penetrating radar, GPS Types of Spatial Data in ArcGIS: Basics Raster vs.
  • Geotime As an Adjunct Analysis Tool for Social Media Threat Analysis and Investigations for the Boston Police Department Offeror: Uncharted Software Inc

    Geotime As an Adjunct Analysis Tool for Social Media Threat Analysis and Investigations for the Boston Police Department Offeror: Uncharted Software Inc

    GeoTime as an Adjunct Analysis Tool for Social Media Threat Analysis and Investigations for the Boston Police Department Offeror: Uncharted Software Inc. 2 Berkeley St, Suite 600 Toronto ON M5A 4J5 Canada Business Type: Canadian Small Business Jurisdiction: Federally incorporated in Canada Date of Incorporation: October 8, 2001 Federal Tax Identification Number: 98-0691013 ATTN: Jenny Prosser, Contract Manager, [email protected] Subject: Acquiring Technology and Services of Social Media Threats for the Boston Police Department Uncharted Software Inc. (formerly Oculus Info Inc.) respectfully submits the following response to the Technology and Services of Social Media Threats RFP. Uncharted accepts all conditions and requirements contained in the RFP. Uncharted designs, develops and deploys innovative visual analytics systems and products for analysis and decision-making in complex information environments. Please direct any questions about this response to our point of contact for this response, Adeel Khamisa at 416-203-3003 x250 or [email protected]. Sincerely, Adeel Khamisa Law Enforcement Industry Manager, GeoTime® Uncharted Software Inc. [email protected] 416-203-3003 x250 416-708-6677 Company Proprietary Notice: This proposal includes data that shall not be disclosed outside the Government and shall not be duplicated, used, or disclosed – in whole or in part – for any purpose other than to evaluate this proposal. If, however, a contract is awarded to this offeror as a result of – or in connection with – the submission of this data, the Government shall have the right to duplicate, use, or disclose the data to the extent provided in the resulting contract. GeoTime as an Adjunct Analysis Tool for Social Media Threat Analysis and Investigations 1.
  • Surface Water

    Surface Water

    Chapter 5 SURFACE WATER Surface water originates mostly from rainfall and is a mixture of surface run-off and ground water. It includes larges rivers, ponds and lakes, and the small upland streams which may originate from springs and collect the run-off from the watersheds. The quantity of run-off depends upon a large number of factors, the most important of which are the amount and intensity of rainfall, the climate and vegetation and, also, the geological, geographi- cal, and topographical features of the area under consideration. It varies widely, from about 20 % in arid and sandy areas where the rainfall is scarce to more than 50% in rocky regions in which the annual rainfall is heavy. Of the remaining portion of the rainfall. some of the water percolates into the ground (see "Ground water", page 57), and the rest is lost by evaporation, transpiration and absorption. The quality of surface water is governed by its content of living organisms and by the amounts of mineral and organic matter which it may have picked up in the course of its formation. As rain falls through the atmo- sphere, it collects dust and absorbs oxygen and carbon dioxide from the air. While flowing over the ground, surface water collects silt and particles of organic matter, some of which will ultimately go into solution. It also picks up more carbon dioxide from the vegetation and micro-organisms and bacteria from the topsoil and from decaying matter. On inhabited watersheds, pollution may include faecal material and pathogenic organisms, as well as other human and industrial wastes which have not been properly disposed of.
  • Arcgis® + Geotime®: GIS Technology to Support the Analysis Of

    Arcgis® + Geotime®: GIS Technology to Support the Analysis Of

    ® ® In many application areas, this is not enough: Geo- spatial and temporal correlations between the data ArcGIS + GeoTime : GIS technology should be studied, so that, on the basis of this insight, the available data - more and more numerous - can to support the analysis of telephone be translated into knowledge and therefore in appropriate decisions . In the area of ​​security, to name an example, all this results in the predictive traffic data analysis of the spatial-temporal occurrence of crimes. Lastly, a technologically advanced GIS platform must Giorgio Forti, Miriam Marta, Fabrizio Pauri ® ensure data sharing and enable the world of mobile devices (system of engagement). ® There are several ways to share data / information, all supported by ArcGIS, such as: sharing within a single Historical mobile phone traffic billboards analysis is organization, according to the profiles assigned becoming increasingly important in investigative Figure 2: Sample data representation of two (identity); the sharing of multiple organizations that activities of public security organizations around the cellphone users in GeoTime may / should share confidential data (a very common world, and leading technology companies have been situation in both Public Security and Emergency trying to respond to the strong demand for the most Other predefined analysis features are already Management); public communication, open to all (for suitable tools for supporting such activities. available (automatic cluster search, who attends sites example, to report investigative success, or to of investigation interest, mobility compatibility with communicate to citizens unsafe areas for the Originally developed as a project funded in the United participation in events, etc.), allowing considerable frequency of criminal offenses).
  • 3D Modeling: Surfaces

    3D Modeling: Surfaces

    CS 430/536 Computer Graphics I Overview • 3D model representations 3D Modeling: • Mesh formats Surfaces • Bicubic surfaces • Bezier surfaces Week 8, Lecture 16 • Normals to surfaces David Breen, William Regli and Maxim Peysakhov • Direct surface rendering Geometric and Intelligent Computing Laboratory Department of Computer Science Drexel University 1 2 http://gicl.cs.drexel.edu 1994 Foley/VanDam/Finer/Huges/Phillips ICG 3D Modeling Representing 3D Objects • 3D Representations • Exact • Approximate – Wireframe models – Surface Models – Wireframe – Facet / Mesh – Solid Models – Parametric • Just surfaces – Meshes and Polygon soups – Voxel/Volume models Surface – Voxel – Decomposition-based – Solid Model • Volume info • Octrees, voxels • CSG • Modeling in 3D – Constructive Solid Geometry (CSG), • BRep Breps and feature-based • Implicit Solid Modeling 3 4 Negatives when Representing 3D Objects Representing 3D Objects • Exact • Approximate • Exact • Approximate – Complex data structures – Lossy – Precise model of – A discretization of – Expensive algorithms – Data structure sizes can object topology the 3D object – Wide variety of formats, get HUGE, if you want each with subtle nuances good fidelity – Mathematically – Use simple – Hard to acquire data – Easy to break (i.e. cracks represent all primitives to – Translation required for can appear) rendering – Not good for certain geometry model topology applications • Lots of interpolation and and geometry guess work 5 6 1 Positives when Exact Representations Representing 3D Objects • Exact
  • Techniques for Spatial Analysis and Visualization of Benthic Mapping Data: Final Report

    Techniques for Spatial Analysis and Visualization of Benthic Mapping Data: Final Report

    Techniques for spatial analysis and visualization of benthic mapping data: final report Item Type monograph Authors Andrews, Brian Publisher NOAA/National Ocean Service/Coastal Services Center Download date 29/09/2021 07:34:54 Link to Item http://hdl.handle.net/1834/20024 TECHNIQUES FOR SPATIAL ANALYSIS AND VISUALIZATION OF BENTHIC MAPPING DATA FINAL REPORT April 2003 SAIC Report No. 623 Prepared for: NOAA Coastal Services Center 2234 South Hobson Avenue Charleston SC 29405-2413 Prepared by: Brian Andrews Science Applications International Corporation 221 Third Street Newport, RI 02840 TABLE OF CONTENTS Page 1.0 INTRODUCTION..........................................................................................1 1.1 Benthic Mapping Applications..........................................................................1 1.2 Remote Sensing Platforms for Benthic Habitat Mapping ..........................................2 2.0 SPATIAL DATA MODELS AND GIS CONCEPTS ................................................3 2.1 Vector Data Model .......................................................................................3 2.2 Raster Data Model........................................................................................3 3.0 CONSIDERATIONS FOR EFFECTIVE BENTHIC HABITAT ANALYSIS AND VISUALIZATION .........................................................................................4 3.1 Spatial Scale ...............................................................................................4 3.2 Habitat Scale...............................................................................................4
  • Surface Topology

    Surface Topology

    2 Surface topology 2.1 Classification of surfaces In this second introductory chapter, we change direction completely. We dis- cuss the topological classification of surfaces, and outline one approach to a proof. Our treatment here is almost entirely informal; we do not even define precisely what we mean by a ‘surface’. (Definitions will be found in the following chapter.) However, with the aid of some more sophisticated technical language, it not too hard to turn our informal account into a precise proof. The reasons for including this material here are, first, that it gives a counterweight to the previous chapter: the two together illustrate two themes—complex analysis and topology—which run through the study of Riemann surfaces. And, second, that we are able to introduce some more advanced ideas that will be taken up later in the book. The statement of the classification of closed surfaces is probably well known to many readers. We write down two families of surfaces g, h for integers g ≥ 0, h ≥ 1. 2 2 The surface 0 is the 2-sphere S . The surface 1 is the 2-torus T .For g ≥ 2, we define the surface g by taking the ‘connected sum’ of g copies of the torus. In general, if X and Y are (connected) surfaces, the connected sum XY is a surface constructed as follows (Figure 2.1). We choose small discs DX in X and DY in Y and cut them out to get a pair of ‘surfaces-with- boundaries’, coresponding to the circle boundaries of DX and DY.
  • What Is Geovisualization? to the Growing Field of Geovisualization

    What Is Geovisualization? to the Growing Field of Geovisualization

    This issue of GeoMatters is devoted What is Geovisualization? to the growing field of geovisualization. Brian McGregor uses geovisualiztion to by Joni Storie produce animated maps showing settle- ment patterns of Hutterite colonies. Dr. Marc Vachon’s students use it to produce From a cartography perspective, dynamic presentation options to com- videos about urban visualization (City geovisualization represents a change in municate knowledge. For example, at- Hall and Assiniboine Park), while Dr. how knowledge is formed and repre- lases require extra planning compared Chris Storie shows geovisualiztion for sented. Traditional cartography is usu- to individual maps, structurally they retail mapping in Winnipeg. Also in this issue Honours students describe their ally seen a visualization (a.k.a. map) could include hundreds of maps, and thesis projects for the upcoming collo- that is presented after the conclusion all the maps relate to each other. Dr. quium next March, Adrienne Ducharme is reached to emphasize or compliment Danny Blair and Dr. Ian Mauro, in the tells us about her graduate research at the research conclusions. Geovisual- Department of Geography, provide an ELA, we have a report about Cultivate ization changes this format by incor- excellent example of this integration UWinnipeg and our alumni profile fea- porating spatial data into the analysis with the Prairie Climate Atlas (http:// tures Michelle Méthot (Smith). (O’Sullivan and Unwin, 2010). Spatial www.climateatlas.ca/). The combina- Please feel free to pass this newsletter data, statistics and analysis are used to tion of maps with multimedia provides to anyone with an interest in geography. answer questions which contribute to for better understanding as well as en- Individuals can also see GeoMatters at the Geography website, or keep up with the conclusion that is reached within riched and informative experiences of us on Facebook (Department of Geog- the research.