Geometric Constraints of Visual Space

Perspective space has been introduced as a computational model of visual space. The model is based on geometric features of visual space. The model has proven to describe a range of phenomena related to the visual perception of distance and size. Until now, the model lacks a mathematical description...

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Autor principal:	Casper J. Erkelens
Formato:	article
Lenguaje:	EN
Publicado:	SAGE Publishing 2021
Materias:	Psychology BF1-990
Acceso en línea:	https://doaj.org/article/b1215aaa84e54d24bf8619e7aa426fe2
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id	oai:doaj.org-article:b1215aaa84e54d24bf8619e7aa426fe2
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spelling	oai:doaj.org-article:b1215aaa84e54d24bf8619e7aa426fe22021-12-01T23:33:40ZGeometric Constraints of Visual Space2041-669510.1177/20416695211055212https://doaj.org/article/b1215aaa84e54d24bf8619e7aa426fe22021-11-01T00:00:00Zhttps://doi.org/10.1177/20416695211055212https://doaj.org/toc/2041-6695Perspective space has been introduced as a computational model of visual space. The model is based on geometric features of visual space. The model has proven to describe a range of phenomena related to the visual perception of distance and size. Until now, the model lacks a mathematical description that holds for complete 3D space. Starting from a previously derived equation for perceived distance in the viewing direction, the suitability of various functions is analyzed. Functions must fulfill the requirement that straight lines, oriented in whatever direction in physical space, transfer to straight lines in visual space. A second requirement is that parallel lines oriented in depth in physical space, converge to a finite vanishing point in visual space. A rational function for perceived distance, compatible with the perspective-space model of visual space, satisfies the requirements. The function is unique. Analysis of alternative functions shows there is little tolerance for deviations. Conservation of the straightness of lines constrains visual space to having a single geometry. Visual space is described by an analytical function having one free parameter, that is, the distance of the vanishing point.Casper J. ErkelensSAGE PublishingarticlePsychologyBF1-990ENi-Perception, Vol 12 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Psychology BF1-990
spellingShingle	Psychology BF1-990 Casper J. Erkelens Geometric Constraints of Visual Space
description	Perspective space has been introduced as a computational model of visual space. The model is based on geometric features of visual space. The model has proven to describe a range of phenomena related to the visual perception of distance and size. Until now, the model lacks a mathematical description that holds for complete 3D space. Starting from a previously derived equation for perceived distance in the viewing direction, the suitability of various functions is analyzed. Functions must fulfill the requirement that straight lines, oriented in whatever direction in physical space, transfer to straight lines in visual space. A second requirement is that parallel lines oriented in depth in physical space, converge to a finite vanishing point in visual space. A rational function for perceived distance, compatible with the perspective-space model of visual space, satisfies the requirements. The function is unique. Analysis of alternative functions shows there is little tolerance for deviations. Conservation of the straightness of lines constrains visual space to having a single geometry. Visual space is described by an analytical function having one free parameter, that is, the distance of the vanishing point.
format	article
author	Casper J. Erkelens
author_facet	Casper J. Erkelens
author_sort	Casper J. Erkelens
title	Geometric Constraints of Visual Space
title_short	Geometric Constraints of Visual Space
title_full	Geometric Constraints of Visual Space
title_fullStr	Geometric Constraints of Visual Space
title_full_unstemmed	Geometric Constraints of Visual Space
title_sort	geometric constraints of visual space
publisher	SAGE Publishing
publishDate	2021
url	https://doaj.org/article/b1215aaa84e54d24bf8619e7aa426fe2
work_keys_str_mv	AT casperjerkelens geometricconstraintsofvisualspace
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Geometric Constraints of Visual Space

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