# Capturing information on curves and surfaces from their projected images

## TL;DR

This paper explores how to recover detailed differential geometric information of curves and surfaces from multiple orthogonal projections, providing theoretical formulas for reconstruction.

## Contribution

It introduces new theoretical relationships and formulas for extracting geometric information of objects from multiple projected images, advancing understanding in shape analysis.

## Key findings

- Derived formulas for reconstructing curves from projections
- Established relations between surface contours and projections
- Theoretical framework for shape recovery from multiple views

## Abstract

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal projections in a number of directions. We discuss relations between (1) a space curve and the projected curves from several distinct directions, and (2) a surface and the apparent contours of projections from several distinct directions, in terms of differential geometry and singularity theory. In particular, formulae for recovering certain information on the original curves or surfaces from their projected images are given.