3D modeling is a common technique adopted in a wide range of areas (including industry, medicine, education, games and design).In particular regard to the 3D computer graphics, 3D modeling is a process of developing a mathematical representation (usually in terms of vertices and matrices) of the three-dimensional surface(s) of the subject of interest (usually refer to objects and by specialised software, e.g. AutoCAD, 3DS MAX, Maya, etc.). The precision of modeling is in part determined by the details of the dimensional information.

Although the demand for and the degree of precision in modeling may depend on the contexts/applications, dimensional precision influences the perception and conception of the viewer. Additionally, as part of the essential properties of object/space representation, dimension is one of the key parameters required in the modeling process and by the aforementioned specialised software.

As vision is vital to human activities, plannar images are commonly available in our environment as a source of information and/or as a form of record mainly for information purposes. Thus, in addition to the direct measurements for the subject of interest, dimensional data can also be acquired from the plannar images (in particular photographs) of the subject of interest via parametric measurements.

In this presentation, a technique of dimensional estimation is proposed based on the mathematical concept of geometry.

Step 1: The Volume Ratio and Scale Factors

In a 3D modeling process, one of the main features to be reproduced is the appearance/contour of the subject of interest. Regardless the overall size and rotations, the creation will perceived as congruent or similar (a lesser extent) to the subject of interest if certain feature(s) for identification is/are present. As a common feature for identification, contour of the subject of interest is usually presented as a group of vertices that link together in a specific pattern while each of these vertices has a different distance and vector to the other counterparts (vertices). Thus, when the dimentional relationships (in particular the relative distances and vectors) among these vertices are preserved, the specific dimensional pattern (contour) of the subject of interest could be reproduced again via/on other medium/media of presentation (e.g. on a paper or in a cybergenic dimension).

In a plannar image (e.g. photograph), although the overall size and rotations of the subject of interest may differ, the contour of such subject is preserved. Thus, in an ideal condition that the overall rotations (facing the viewer) of the subject of interest in reality is the same as the one in the plannar image (with no extra changes but overall size), the dimensions measured on the plannar image (e.g. photograph) for the subject of interest may be used for estimating the dimension of the subject of interest in reality by implementing the mathematical concept of volume ratio or scale factors.

(the following video is credited to the YouTube user: Scott Davidson)

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