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.

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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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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## Step 2: Case Study 1

As an example of the dimensional estimation for 3D modeling from the plannar image(s), a simple cubic object (a 1.5mL eppendorf tube holder) is chosen as the subject of interest while its photographs (or photos) are chosen as the plannar images.

## Step 3: Collection of Metric Data and Measurements

Measurements are done on each of these photos (when neccessary) to obtain all dimensional parametric data required (length, width, height and others). In order to apply the calculations for the volume ratios of this object, at least two dimensions are required to be measured.

Regarding the technique/tool of measurement, a ruler is used in this case as an example. For more precise measurements, a digital way is preferred, e.g. by/in software like Adobe Photoshop.

Regarding the technique/tool of measurement, a ruler is used in this case as an example. For more precise measurements, a digital way is preferred, e.g. by/in software like Adobe Photoshop.

## Step 4: Considerations of Different View Angles/perspectives

The previous measurements are a bit unrealistic as they are under or assumed the condition of perfect perspective (i.e. viewing right at the center without any skew angles that may result in a false length/measurement).

Thus, it is neccessary to take into account additional factors that may influence the calculations. The most prominent factors would be the distance between the camera and the object, the rotation of the object and the field of view (FOV) of the camera.

After a virtual experiment conducted in 3DS MAX using simple meshes, data are collected and tabulated as table 2 while the significance of the factor is estimated by one way ANOVA statistical analysis (95% confidence). It has been shown that there are no significant differences in the angle θ when the condition is varied by FOV only while both the camera distances and object rotations alone created significant differences.

As a result, the optimized calculations will involve:

1) the camera distances to the object; and

2) the rotation angles of the object relative to the camera view point

Thus, it is neccessary to take into account additional factors that may influence the calculations. The most prominent factors would be the distance between the camera and the object, the rotation of the object and the field of view (FOV) of the camera.

After a virtual experiment conducted in 3DS MAX using simple meshes, data are collected and tabulated as table 2 while the significance of the factor is estimated by one way ANOVA statistical analysis (95% confidence). It has been shown that there are no significant differences in the angle θ when the condition is varied by FOV only while both the camera distances and object rotations alone created significant differences.

As a result, the optimized calculations will involve:

1) the camera distances to the object; and

2) the rotation angles of the object relative to the camera view point

## Step 5: The Optimized Algorithm

(under construction)

## Step 6: Data Analysis

The collected data are now tabulated as table 1 and calculations are done according to the ratios (scale factors).

## Step 7: (Optional) Implementation of the Data

As all dimensional parametric values are now known, a 3D modeling could be started using such values.

## Step 8: Summary

This presentation provides you a novel technique of indirect dimensional measurement of the subject of interest via photos and a simple 3D modeling and texturing tutorial. After this presentation, you shall be able to:

1) gather dimensional parametric data of the subject of interest from different photos (in different perspectives) by using ratios/scale factors.

2) estimate the dimension of the subject of interest via photos.

3) create a simple 3D model with basic materials and textures.

1) University of Hong Kong

2) The Hong Kong Polytechnic University

1) Brightstorm | Volume Ratios (http://www.brightstorm.com/math/geometry/similarity/similarity-and-volume-ratios/)

2) Scott Davidson | Sec 12.7: Similar Solids (http://www.youtube.com/embed/vtTDLHKnxOo?rel=0)

1) gather dimensional parametric data of the subject of interest from different photos (in different perspectives) by using ratios/scale factors.

2) estimate the dimension of the subject of interest via photos.

3) create a simple 3D model with basic materials and textures.

**P.S: this presentation is not completed yet but publish for testing purpose only.****Acknowledgements**1) University of Hong Kong

2) The Hong Kong Polytechnic University

**References**1) Brightstorm | Volume Ratios (http://www.brightstorm.com/math/geometry/similarity/similarity-and-volume-ratios/)

2) Scott Davidson | Sec 12.7: Similar Solids (http://www.youtube.com/embed/vtTDLHKnxOo?rel=0)