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Perspective-taking takes place when an individual views a situation from another's point-of-view. [1] [13] Perspective-taking has been defined along two dimensions: perceptual and conceptual. [14] Perceptual perspective-taking is the ability to understand how another person experiences things through their senses (i.e. visually or auditorily). [14]
If each of the perspective figures consists of all the points on a line (a range) then transformation of the points of one range to the other is called a central perspectivity. A dual transformation, taking all the lines through a point (a pencil) to another pencil by means of an axis of perspectivity is called an axial perspectivity. [2]
Robert Selman developed his developmental theory of role-taking ability based on four sources. [4] The first is the work of M. H. Feffer (1959, 1971), [5] [6] and Feffer and Gourevitch (1960), [7] which related role-taking ability to Piaget's theory of social decentering, and developed a projective test to assess children's ability to decenter as they mature. [4]
The results showed that children as young as three-years-old were able to perform well, and they showed evidence of perspective-taking, [10] the ability to understand a situation from an alternate point of view. Hence, evaluation of Piaget's Three Mountain Problem has shown that using objects more familiar to the child and making the task less ...
Artists may choose to "correct" perspective distortions, for example by drawing all spheres as perfect circles, or by drawing figures as if centered on the direction of view. In practice, unless the viewer observes the image from an extreme angle, like standing far to the side of a painting, the perspective normally looks more or less correct.
To move from one slice to another requires a base change; from a technical point of view base change becomes a major issue for the whole approach (see for example Beck–Chevalley conditions). A base change 'along' a given morphism g: T → S. is typically given by the fiber product, producing an object over T from one over S.
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