Contents
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26.1 Introduction 26.1 Introduction
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26.1.1 Geometry of perspective 26.1.1 Geometry of perspective
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26.1.1a Basic Geometry 26.1.1a Basic Geometry
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26.1.1b Projective Invariants 26.1.1b Projective Invariants
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26.1.1c Projective Transformations 26.1.1c Projective Transformations
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26.1.1d Projective Transformations of a Line 26.1.1d Projective Transformations of a Line
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26.1.1e Projective Transformations of a 2-D Object 26.1.1e Projective Transformations of a 2-D Object
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26.1.1f Projective Transformations of 3-D Objects 26.1.1f Projective Transformations of 3-D Objects
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26.1.2 Types of perspective 26.1.2 Types of perspective
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26.2 Size Perspective 26.2 Size Perspective
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26.2.1 Experiments on size as a cue to distance 26.2.1 Experiments on size as a cue to distance
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26.2.2 Familiar size as a cue to distance 26.2.2 Familiar size as a cue to distance
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26.2.3 Size discrimination and matching 26.2.3 Size discrimination and matching
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26.3 Linear Perspective 26.3 Linear Perspective
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26.3.1 Information contained in linear perspective 26.3.1 Information contained in linear perspective
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26.3.2 Judging surface inclination from linear perspective 26.3.2 Judging surface inclination from linear perspective
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26.3.2a Effects of Object Size on Linear Perspective 26.3.2a Effects of Object Size on Linear Perspective
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26.3.2b Effects of Knowledge of Object Shape 26.3.2b Effects of Knowledge of Object Shape
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26.3.2c Depth from Parallel Perspective 26.3.2c Depth from Parallel Perspective
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26.3.3 Judgments of projective invariants 26.3.3 Judgments of projective invariants
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26.3.3a General Invariants 26.3.3a General Invariants
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26.3.3b Invariance of Cross Ratios 26.3.3b Invariance of Cross Ratios
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26.3.3c Skew Symmetry 26.3.3c Skew Symmetry
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26.3.4 Distortions in viewing pictures 26.3.4 Distortions in viewing pictures
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26.3.4a Image Taper for Frontal Objects 26.3.4a Image Taper for Frontal Objects
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26.3.4b Perspective Illusion in Pictures 26.3.4b Perspective Illusion in Pictures
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26.3.4c Images from Obliquely Viewed Objects 26.3.4c Images from Obliquely Viewed Objects
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26.3.4d Absence of Parallax in Pictures 26.3.4d Absence of Parallax in Pictures
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26.3.5 Drawing in Perspective 26.3.5 Drawing in Perspective
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26.4 Position and Perceived Distance 26.4 Position and Perceived Distance
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26.4.1 Effect of height in the field of view 26.4.1 Effect of height in the field of view
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26.4.2 Optical adjacency 26.4.2 Optical adjacency
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26.4.3 The visual horizon and absolute distance 26.4.3 The visual horizon and absolute distance
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26.4.3a Basic Requirements 26.4.3a Basic Requirements
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26.4.3b Effects of Surface Discontinuities 26.4.3b Effects of Surface Discontinuities
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26.4.3c Effects of Surface Extent 26.4.3c Effects of Surface Extent
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26.4.3d Effects of Prisms 26.4.3d Effects of Prisms
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26.4.4 Height in the field and size judgments 26.4.4 Height in the field and size judgments
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26.5 Texture Perspective 26.5 Texture Perspective
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26.5.1 Types of texture gradient 26.5.1 Types of texture gradient
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26.5.1a Texture Size 26.5.1a Texture Size
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26.5.1b Texture Density 26.5.1b Texture Density
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26.5.1c Aspect Ratio 26.5.1c Aspect Ratio
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26.5.2 Texture gradients and perceived inclination 26.5.2 Texture gradients and perceived inclination
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26.5.2a Underestimation of Surface Inclination 26.5.2a Underestimation of Surface Inclination
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26.5.2b Comparison of Texture Cues 26.5.2b Comparison of Texture Cues
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26.5.2c Effects of Texture Inhomogeneity 26.5.2c Effects of Texture Inhomogeneity
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26.6 Texture Gradients on Curved Surfaces 26.6 Texture Gradients on Curved Surfaces
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26.6.1 Defining and measuring 3-D shape 26.6.1 Defining and measuring 3-D shape
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26.6.2 Texture gradients on cylindrical surfaces 26.6.2 Texture gradients on cylindrical surfaces
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26.6.3 Texture gradients on complex surfaces 26.6.3 Texture gradients on complex surfaces
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26.7 Reversible Perspective 26.7 Reversible Perspective
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26.7.1 Reversible perspective in 2-D displays 26.7.1 Reversible perspective in 2-D displays
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26.7.2 Reversible perspective of 3-D objects 26.7.2 Reversible perspective of 3-D objects
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Cite
Abstract
The chapter starts with an account of the geometry of perspective and of the various types of perspective, including size perspective, linear perspective, and simple and complex texture gradients. This is followed by a review of the evidence regarding the relative effectiveness of the different types of perspective for judging the three-dimensional structure of surfaces and objects. There is a discussion of how the perceived distance of an object is influenced by its location on a ground surface and by the height of the image of the object relative to the horizon. The chapter ends with an account of reversible perspective in two-dimensional displays and three-dimensional objects.
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