Perspective As Ideology
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Orthographic and Perspective Projection—Part 1 Drawing As
I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S From 3D to 2D: Orthographic and Perspective Projection—Part 1 •History • Geometrical Constructions 3D Viewing I • Types of Projection • Projection in Computer Graphics Andries van Dam September 15, 2005 3D Viewing I Andries van Dam September 15, 2005 3D Viewing I 1/38 I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Drawing as Projection Early Examples of Projection • Plan view (orthographic projection) from Mesopotamia, 2150 BC: earliest known technical • Painting based on mythical tale as told by Pliny the drawing in existence Elder: Corinthian man traces shadow of departing lover Carlbom Fig. 1-1 • Greek vases from late 6th century BC show perspective(!) detail from The Invention of Drawing, 1830: Karl Friedrich • Roman architect Vitruvius published specifications of plan / elevation drawings, perspective. Illustrations Schinkle (Mitchell p.1) for these writings have been lost Andries van Dam September 15, 2005 3D Viewing I 2/38 Andries van Dam September 15, 2005 3D Viewing I 3/38 1 I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Most Striking Features of Linear Early Perspective Perspective • Ways of invoking three dimensional space: shading • || lines converge (in 1, 2, or 3 axes) to vanishing point suggests rounded, volumetric forms; converging lines suggest spatial depth -
CS 4204 Computer Graphics 3D Views and Projection
CS 4204 Computer Graphics 3D views and projection Adapted from notes by Yong Cao 1 Overview of 3D rendering Modeling: * Topic we’ve already discussed • *Define object in local coordinates • *Place object in world coordinates (modeling transformation) Viewing: • Define camera parameters • Find object location in camera coordinates (viewing transformation) Projection: project object to the viewplane Clipping: clip object to the view volume *Viewport transformation *Rasterization: rasterize object Simple teapot demo 3D rendering pipeline Vertices as input Series of operations/transformations to obtain 2D vertices in screen coordinates These can then be rasterized 3D rendering pipeline We’ve already discussed: • Viewport transformation • 3D modeling transformations We’ll talk about remaining topics in reverse order: • 3D clipping (simple extension of 2D clipping) • 3D projection • 3D viewing Clipping: 3D Cohen-Sutherland Use 6-bit outcodes When needed, clip line segment against planes Viewing and Projection Camera Analogy: 1. Set up your tripod and point the camera at the scene (viewing transformation). 2. Arrange the scene to be photographed into the desired composition (modeling transformation). 3. Choose a camera lens or adjust the zoom (projection transformation). 4. Determine how large you want the final photograph to be - for example, you might want it enlarged (viewport transformation). Projection transformations Introduction to Projection Transformations Mapping: f : Rn Rm Projection: n > m Planar Projection: Projection on a plane. -
Bridges Conference Paper
Bridges 2020 Conference Proceedings Dürer Machines Running Back and Forth António Bandeira Araújo Universidade Aberta, Lisbon, Portugal; [email protected] Abstract In this workshop we will use Dürer machines, both physical (made of thread) and virtual (made of lines) to create anamorphic illusions of objects made up of simple boxes, these being the building blocks for more complex illusions. We will consider monocular oblique anamorphosis and then anaglyphic anamorphoses, to be seen with red-blue 3D glasses. Introduction In this workshop we will draw optical illusions – anamorphoses – using simple techniques of orthographic projection derived from descriptive geometry. The main part of this workshop will be adequate for anyone over 15 years of age with an interest in visual illusions, but it is especially useful for teachers of perspective and descriptive geometry. In past editions of Bridges and elsewhere at length [1, 6] I have argued that anamorphosis is a more fundamental concept than perspective, and is in fact the basic concept from which all conical perspectives – both linear and curvilinear – are derived, yet in those past Bridges workshops I have used anamorphosis only implicitly, in the creation of fisheye [4] and equirectangular [3] perspectives . This time we will instead focus on a sequence of constructions of the more traditional anamorphoses: the so-called oblique anamorphoses, that is, plane anamorphoses where the object of interest is drawn at a grazing angle to the projection plane. This sequence of constructions has been taught at Univ. Aberta in Portugal since 2013 in several courses to diverse publics; it is currently part of a course for Ph.D. -
Anamorphosis: Optical Games with Perspective’S Playful Parent
Anamorphosis: Optical games with Perspective's Playful Parent Ant´onioAra´ujo∗ Abstract We explore conical anamorphosis in several variations and discuss its various constructions, both physical and diagrammatic. While exploring its playful aspect as a form of optical illusion, we argue against the prevalent perception of anamorphosis as a mere amusing derivative of perspective and defend the exact opposite view|that perspective is the derived concept, consisting of plane anamorphosis under arbitrary limitations and ad-hoc alterations. We show how to define vanishing points in the context of anamorphosis in a way that is valid for all anamorphs of the same set. We make brief observations regarding curvilinear perspectives, binocular anamorphoses, and color anamorphoses. Keywords: conical anamorphosis, optical illusion, perspective, curvilinear perspective, cyclorama, panorama, D¨urermachine, color anamorphosis. Introduction It is a common fallacy to assume that something playful is surely shallow. Conversely, a lack of playfulness is often taken for depth. Consider the split between the common views on anamorphosis and perspective: perspective gets all the serious gigs; it's taught at school, works at the architect's firm. What does anamorphosis do? It plays parlour tricks! What a joker! It even has a rather awkward dictionary definition: Anamorphosis: A distorted projection or drawing which appears normal when viewed from a particular point or with a suitable mirror or lens. (Oxford English Dictionary) ∗This work was supported by FCT - Funda¸c~aopara a Ci^enciae a Tecnologia, projects UID/MAT/04561/2013, UID/Multi/04019/2013. Proceedings of Recreational Mathematics Colloquium v - G4G (Europe), pp. 71{86 72 Anamorphosis: Optical games. -
Perpective Presentation2.Pdf
Projections transform points in n-space to m-space, where m<n. Projection is 'formed' on the view plane (planar geometric projection) rays (projectors) projected from the center of projection pass through each point of the models and intersect projection plane. In 3-D, we map points from 3-space to the projection plane (PP) (image plane) along projectors (viewing rays) emanating from the center of projection (COP): TYPES OF PROJECTION There are two basic types of projections: Perspective – center of projection is located at a finite point in three space Parallel – center of projection is located at infinity, all the projectors are parallel Plane geometric projection Parallel Perspective Orthographic Axonometric Oblique Cavalier Cabinet Trimetric Dimetric Single-point Two-point Three-point Isometric PARALLEL PROJECTION • center of projection infinitely far from view plane • projectors will be parallel to each other • need to define the direction of projection (vector) • 3 sub-types Orthographic - direction of projection is normal to view plane Axonometric – constructed by manipulating object using rotations and translations Oblique - direction of projection not normal to view plane • better for drafting / CAD applications ORTHOGRAPHIC PROJECTIONS Orthographic projections are drawings where the projectors, the observer or station point remain parallel to each other and perpendicular to the plane of projection. Orthographic projections are further subdivided into axonom etric projections and multi-view projections. Effective in technical representation of objects AXONOMETRIC The observer is at infinity & the projectors are parallel to each other and perpendicular to the plane of projection. A key feature of axonometric projections is that the object is inclined toward the plane of projection showing all three surfaces in one view. -
From 3D to 2D: Orthographic and Perspective Projection—Part 1
I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S From 3D to 2D: Orthographic and Perspective Projection—Part 1 • History • Geometrical Constructions • Types of Projection • Projection in Computer Graphics Andries van Dam September 13, 2001 3D Viewing I 1/34 I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Drawing as Projection • A painting based on a mythical tale as told by Pliny the Elder: a Corinthian man traces the shadow of his departing lover detail from The Invention of Drawing, 1830: Karl Friedrich Schinkle (Mitchell p.1) Andries van Dam September 13, 2001 3D Viewing I 2/34 I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Early Examples of Projection • Plan view (orthographic projection) from Mesopotamia, 2150 BC is earliest known technical drawing in existence Carlbom Fig. 1-1 • Greek vases from late 6th century BC show perspective(!) • Vitruvius, a Roman architect, published specifications of plan and elevation drawings, and perspective. Illustrations for these writings have been lost Andries van Dam September 13, 2001 3D Viewing I 3/34 I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Most Striking Features of Linear Perspective • || lines converge (in 1, 2, or 3 axes) to a vanishing point • Objects farther away are more foreshortened (i.e., smaller) than closer ones • Example: perspective cube edges same size, with farther ones smaller parallel edges converging Andries van Dam September 13, 2001 3D Viewing I 4/34 I N T R O D U C T I O N T O C O M P U T E R G R A P H I C S Early Perspective -
Anamorphic Perspective & Illusory Architecture
Anamorphic Perspective & Illusory Architecture 31.07.2003 11:24 Uhr Anamorphic Perspective & Illusory Architecture ! Dr. Tomás García Salgado, BSArch, MSArch, PhD, UNAMprize, SNIm. Faculty of Architecture, National Autonomus University of México. mailto:[email protected] ! Abstract namorphic perspective can be sometimes quite paradoxical. This is the case with the famous false vault by Andrea Pozzo at Saint Ignatius in Rome. Pozzo himself did not consider this painting as an anamorphic projection, but it is indeed. Pozzo deduced the correct perspective drawing for the large canvas (intelaiautura), but what the observer sees is quite different. This article is divided into three A úterest. The parts that can be read separately depending upon the reader’s in first part gives us an historical review through some treatises related to the subject and some famous masterpieces. The second part deals with the principles that govern anamorphic perspective, considering the basic cases of projection. One of these cases is preúsented in detail in this part. Finally, the third part is devoted to the analysis of the vaults of Sant’Ignazio and Collegio Romano by means of the author’s method, termed Modular Perúspective. For a better understanding of the origin of Saint Ignatius’s vault, we include a brief historical background in order to grasp the idea that Pozzo’s painting is fundamentally an architectural solution instead of a purely pictorial exercise. 1. Historical Background It is quite common to encounter the theme of anamorphic perspective in the standard literature for all types of applications, from portraits to murals and scenography, to architecture itself. -
2.1 Perspective Transformation Wi Th One Vanishing Point The
PHOTOINTERPRETATION AND SMALL SCALE STEREOPLOTTING WITH DIGITALLY RECTIFIED PHOTOGRAPHS WITH GEOMETRICAL CONSTRAINTS1 Gabriele FANGI, Gianluca GAGLIARDINI, Eva Savina MALINVERNI University of Ancona, via Brecce Bianche, 60131 Ancona, Italy Phone: ++39.071.2204742, E-mail: [email protected] [email protected] KEY WORDS: Architectural photogrammetry, self-calibration, rectification, stereoscopy, vanishing points ABSTRACT It is well know that it is possible to use the vanishing point geometry to assess the orientation parameters of the photographic image. Here we propose a numerical or graphical procedure to estimate such parameters, assuming that in the imaged object are present planar surfaces, straight-line edges, and right angles. In addition, by means of the same estimated parameters, it is possible to project the same image onto a selected plane say to rectify the image. The advantages are that non-metric images, taken from archives or books also, provided a good geometry and quality, are suitable for the task. From one side the role of the classical line photogrammetry is taken more and more over by laser scanning, and on the other side, this simplified procedure enables the researcher to use photogrammetric techniques for stereoscopy and interpretation, thematic mapping, research. The convergent non- stereoscopic images rectified with digital photogrammetric techniques, are then made suitable for stereoscopy. In fact the rectification corrects for tilt displacement and not for relief displacement, but it is just relief displacement that enables stereoscopy. Some examples of stereoplotting and photo-interpretation with digitally rectified photographs are shown. 1 INTRODUCTION The possibility to use non-metric images is normally linked to the availability of the control information in the imaged object, usually control points to be input in a bundle adjustment procedure or DLT. -
Classical Viewing Classical Viewing Planar Geometric Projections
Classical Viewing Classical Viewing Objectives • Viewing requires three basic elements - One or more objects • Introduce the classical views - A viewer with a projection surface - Projectors that go from the object(s) to the projection • Compare and contrast image formation surface by computer with how images have been • Classical views are based on the relationship among formed by architects, artists, and these elements engineers - The viewer picks up the object and orients it how she would like to see it • Learn the benefits and drawbacks of • Each object is assumed to constructed from flat each type of view principal faces - Buildings, polyhedra, manufactured objects Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005 1 Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005 2 Planar Geometric Projections Classical Projections • Standard projections project onto a plane • Projectors are lines that either - converge at a center of projection (COP) - are parallel • Such projections preserve lines - but not necessarily angles • Nonplanar projections are needed for applications such as map construction Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005 3 Angel: Interactive Computer Graphics 4E © Addison-Wesley 2005 4 1 Taxonomy of Planar Perspective vs Parallel Geometric Projections • Computer graphics treats all projections planar geometric projections the same and implements them with a single pipeline • Classical viewing developed different parallel perspective techniques for drawing each type of projection -
VIEWPOINTS Mathematical Perspective and Fractal Geometry in Art
VIEWPOINTS Mathematical Perspective and Fractal Geometry in Art Marc Frantz Indiana University Annalisa Crannell Franklin & Marshall College Draft, May 19, 2007 Contents Preface v 1 Introduction to Perspective and Space Coordinates 1 Artist Vignette: Sherry Stone Clifton 9 2 Perspective by the Numbers 15 Artist Vignette: Peter Galante 26 3 Vanishing Points and Viewpoints 33 Artist Vignette: Jim Rose 43 4 Rectangles in One-Point Perspective 51 What’s My Line: A Perspective Game 62 5 Two-Point Perspective 67 Artist Vignette: Robert Bosch 85 6 Three-Point Perspective and Beyond 93 Artist Vignette: Dick Termes 116 7 Anamorphic Art 123 Artist Vignette: Teri Wagner 128 8 Fractal Geometry 135 Artist Vignette: Kerry Mitchell 150 iii Preface Origin of the Text Viewpoints is an undergraduate text in mathematics and art suit- able for math-for-liberal-arts courses, mathematics courses for fine art majors, and introductory art classes. Instructors in such courses at more than 25 institutions have already used an earlier online ver- sion of the text, called Lessons in Mathematics and Art. The material in these texts evolved from courses in mathematics and art which we developed in collaboration and taught at our respective institutions. In addition, this material has been tested at, and influenced by, a series of week-long Viewpoints faculty development workshops (see php.indiana.edu/˜mathart/viewpoints). The initial course development and the first Viewpoints workshops were supported by the Indiana University Mathematics Through- out the Curriculum project, the Indiana University Strategic Direc- tions Initiative, Franklin & Marshall College, and the National Sci- ence Foundation (NSF-DUE 9555408). -
Perspective Drawing and Projective Geometry
Perspective Drawing and Projective Geometry Capstone WeiPing Li The Renaissance was a cultural movement that profoundly affected European intellectual life in the early modern period (15th century). Beginning in Italy, and spreading to the rest of Europe by the 16th century, its influence was felt in literature, philosophy, art, music, politics, science, religion, and other aspects of intellectual inquiry. Renaissance scholars employed the humanist method in study, and searched for realism and human emotion in art. Humanists asserted "the genius of man ... the unique and extraordinary ability of the human mind." One of the distinguishing features of Renaissance art was its development of highly realistic linear perspective. Giotto di Bondone (1267–1337) is credited with first treating a painting as a window into space, but it was not until the demonstrations of architect Filippo Brunelleschi (1377–1446) and the subsequent writings of Leon Battista Alberti (1404–1472) that perspective was formalized as an artistic technique. The development of perspective was part of a wider trend towards realism in the arts and reflecting the general world view of people connected to it. Painting not using Perspective Method: Initial word panel of Psalm Perspective method not used Perspective method not used Perspective method not used Perspective method not used Perspective method used: Masaccio, Trinity Perspective method used Perspective method used: Leonardo Da Vinci: Adoration (unfinished) Perspective method used Donatello: St. George and the Dragon Perspective method used Donatello: The Feast of Herod Perspective method used Donatello: The Feast of Herod Artists such as Masaccio strove to portray the human form realistically, developing techniques to render perspective and light more naturally. -
Perspective Projection Worksheets-Solutions
The plan of a water feature is shown. The height of the paving slabs are 10mm thick. Make a perspective drawing of the water feature when the position of the spectator and picture plane are as shown. The horizon line and vanishing point are also shown. Draw the perspective view of the model. Vanishing point Horizon line 10 Ground line Edge view of picture plane Spectator DESIGN & COMMUNICATION GRAPHICS PERSPECTIVE PROJECTION 1 Name:____________________________ Date:___________________ (3D View not to scale) VP1 Horizon line VP2 35 20 Ground Line Fig. 1 A Plan of Picture Plane Vanishing Parallel 2 Vanishing Parallel 1 The plan of a right rectangular prism of Spectator height 20mm which rests on the ground plane is shown in Fig.1. Also shown is the position of the spectator. The picture plane passes through corner A and the horizon line is 35mm above the ground line. Draw a perspective view of the prism. Perspective Projection 2 The plan of a Rubex Cube is shown. Also shown is the position of the spectator and picture plane. The horizon line is 85mm above the ground line. Draw the perspective view. VP1 VP2 HORIZON LINE 85 60 20 20 Height line GROUND LINE VP1 VP2 PICTURE PLANE DESIGN & COMMUNICATION GRAPHICS S.P. PERSPECTIVE PROJECTION 3 Name:____________________________ Date:___________________ (3D View not to scale) VP1 Horizon line 35 VP2 20 Ground Line Fig. 1 Plan of Picture Plane Vanishing Parallel 1 Vanishing Parallel 2 The plan of a right rectangular prism of height 20mm which rests on the ground Spectator plane is shown in Fig.1.