Reliability of measuring the circumference, surface area, and volume of a body part or an object using a three-dimensional scanner

There was a method developed that generates the three-dimensional model of not axisymmetric produce, based on an arbitrary number of photos. The model can serve as a basis for calculating the surface area and the volume of produce. The efficiency of the reconstruction was tested on bell peppers and artificial shapes. In case of bell peppers 3-dimensional reconstruction was created from 4 images rotated in 45° angle intervals. The surface area and the volume were estimated on the basis of the reconstructed area. Furthermore, a new and simple reference method was devised to give precise results for the surface area of bell pepper. The results show that this 3D reconstruction-based surface area and volume calculation method is suitable to determine the surface area and volume of definite bell peppers with an acceptable error.

Download Full-text

An Anatomically Placed Tibial Tunnel does not Completely Surround a Simulated PCL Reconstruction Graft in the Proximal Tibia

The Journal of Knee Surgery ◽

10.1055/s-0041-1741430 ◽

2022 ◽

Author(s):

Christopher Kim ◽

Dustin Baker ◽

Brian Albers ◽

Scott G. Kaar

Keyword(s):

Surface Area ◽

Cruciate Ligament ◽

Tibial Tunnel ◽

Three Dimensional ◽

Pcl Reconstruction ◽

Posterior Cortex ◽

Modeling Software ◽

The Mean ◽

Tibial Cortex ◽

Area And Volume

Abstract Introduction It is hypothesized that anatomic tunnel placement will create tunnels with violation of the posterior cortex and subsequently an oblique aperture that is not circumferentially surrounded by bone. In this article, we aimed to characterize posterior cruciate ligament (PCL) tibial tunnel using a three-dimensional (3D) computed tomography (CT) model. Methods Ten normal knee CTs with the patella, femur, and fibula removed were used. Simulated 11 mm PCL tibial tunnels were created at 55, 50, 45, and 40 degrees. The morphology of the posterior proximal tibial exit was examined with 3D modeling software. The length of tunnel not circumferentially covered (cortex violation) was measured to where the tibial tunnel became circumferential. The surface area and volume of the cylinder both in contact with the tibial bone and that not in contact with the tibia were determined. The percentages of the stick-out length surface area and volume not in contact with bone were calculated. Results The mean stick-out length of uncovered graft at 55, 50, 45, and 40 degrees were 26.3, 20.5, 17.3, and 12.7 mm, respectively. The mean volume of exposed graft at 55, 50, 45, and 40 degrees were 840.8, 596.2, 425.6, and 302.9 mm3, respectively. The mean percent of volume of exposed graft at 55, 50, 45, and 40 degrees were 32, 29, 25, and 24%, respectively. The mean surface of exposed graft at 55, 50, 45, and 40 degrees were 372.2, 280.4, 208.8, and 153.3 mm2, respectively. The mean percent of surface area of exposed graft at 55, 50, 45, and 40 degrees were 40, 39, 34, and 34%, respectively. Conclusion Anatomic tibial tunnel creation using standard transtibial PCL reconstruction techniques consistently risks posterior tibial cortex violation and creation of an oblique aperture posteriorly. This risk is decreased with decreasing the angle of the tibial tunnel, though the posterior cortex is still compromised with angles as low as 40 degrees. With posterior cortex violation, a surgeon should be aware that a graft within the tunnel or socket posteriorly may not be fully in contact with bone. This is especially relevant with inlay and socket techniques.

Download Full-text

Minecraft Comes to Math Class

Mathematics Teaching in the Middle School ◽

10.5951/mathteacmiddscho.23.6.0334 ◽

2018 ◽

Vol 23 (6) ◽

pp. 334-341 ◽

Cited By ~ 1

Author(s):

Kimberly Moore

Keyword(s):

Surface Area ◽

Three Dimensional ◽

Eighth Grade ◽

Eighth Grade Students ◽

The Creation ◽

Math Class ◽

Area And Volume

Eighth-grade students use a character from Minecraft® to explore surface area and volume, resulting in the creation of a three-dimensional “Cylindrical Steve.”

Download Full-text

THE INVARIATOR DESIGN: AN UPDATE

Image Analysis & Stereology ◽

10.5566/ias.1324 ◽

2015 ◽

Vol 34 (3) ◽

pp. 147 ◽

Cited By ~ 2

Author(s):

Luis Manuel Cruz-Orive ◽

Ximo Gual-Arnau

Keyword(s):

Fixed Point ◽

Surface Area ◽

Test Line ◽

Dimensional Space ◽

Three Dimensional ◽

A Posteriori ◽

Euclidean Spaces ◽

Oriented Plane ◽

Three Dimensional Space ◽

Area And Volume

The invariator is a method to generate a test line within an isotropically oriented plane through a fixed point, in such a way that the test line is effectively motion invariant in three dimensional space. Generalizations exist for non Euclidean spaces. The invariator design is convenient to estimate surface area and volume simultaneously. In recent years a number of new results have appeared which call for an updated survey. We include two new estimators, namely the a posteriori weighting estimator for surface area and volume, and the peak-and-valley formula for surface area.

Download Full-text

Leafing through Irregular Shapes

Mathematics Teaching in the Middle School ◽

10.5951/mathteacmiddscho.21.1.0053 ◽

2015 ◽

Vol 21 (1) ◽

pp. 53-60

Author(s):

Alessandra King

Keyword(s):

Middle School ◽

Middle School Students ◽

Surface Area ◽

Three Dimensional ◽

Real Life ◽

Two Dimensional ◽

School Students ◽

Classroom Experience ◽

Irregular Shapes ◽

Area And Volume

By the time middle school students start a prealgebra course, they should have explored a variety of familiar two-dimensional and three-dimensional shapes and should have been exposed to the concepts of perimeter, area, and volume. They know that they can assign numerical values to some attributes of a shape, such as length and surface area. However, my classroom experience confirms the statement that although “students may have developed an initial understanding of area…, many will need additional experiences in measuring directly to deepen their understanding of the area of two-dimensional shapes” (NCTM 2000, p. 242). In addition, the students' previous practice with area is usually with polygons, circles, or a combination of both. However, many real-life objects cannot be described or approximated with simple geometric shapes or with combinations of shapes. Therefore, this activity, which asks students to estimate the area of irregular shapes using finer and finer grids, is not only novel but also a way to apply mathematics to real life.

Download Full-text

Using ulcer surface area and volume to document wound size

Journal of the American Podiatric Medical Association ◽

10.7547/87507315-85-2-91 ◽

1995 ◽

Vol 85 (2) ◽

pp. 91-95 ◽

Cited By ~ 4

Author(s):

JD Johnson

Keyword(s):

Surface Area ◽

Three Dimensional ◽

Ulcer Size ◽

Wound Size ◽

Length Width ◽

Dimensional Object ◽

Area And Volume

The evaluation of ulcer size is normally limited to measuring length, width, and depth, and comparing those figures to previously obtained values. These comparisons are grossly inaccurate, and a more representative technique can be used by treating the ulceration as a three-dimensional object. The author proposes several mathematical formulae that are easily computed on a hand-held calculator. The formulae use the measurements of length, width, and depth, and translate those dimensions into surface area and volume.

Download Full-text

Low-Degree Tibial Slope Angle Prevents Component Overhang by Enlarging the Lateral Plateau Surface Area in Total Knee Arthroplasty

The Journal of Knee Surgery ◽

10.1055/s-0040-1718598 ◽

2020 ◽

Author(s):

Mehmet Emin Simsek ◽

Mustafa Akkaya ◽

Safa Gursoy ◽

Özgür Kaya ◽

Murat Bozkurt

Keyword(s):

Total Knee Arthroplasty ◽

Surface Area ◽

Knee Arthroplasty ◽

Tibial Plateau ◽

Slope Angle ◽

Three Dimensional ◽

Tibial Slope ◽

Total Knee ◽

Lateral Plateau ◽

Gender Groups

AbstractThis study aimed to investigate whether overhang or underhang around the tibial component that occurs during the placement of tibial baseplates was affected by different slope angles of the tibial plateau and determine the changes in the lateral and medial plateau diameters while changing the slope angle in total knee arthroplasty. Three-dimensional tibia models were reconstructed using the computed tomography scans of 120 tibial dry bones. Tibial plateau slope cuts were performed with 9, 7, 5, 3, and 0 degrees of slope angles 2-mm below the subchondral bone in the deepest point of the medial plateau. Total, lateral, and medial tibial plateau areas and overhang/underhang rates were measured at each cut level. Digital implantations of the asymmetric and symmetric tibial baseplates were made on the tibial plateau with each slope angles. Following the implantations, the slope angle that prevents overhang or underhang at the bone border and the slope angle that has more surface area was identified. A significant increase was noted in the total tibial surface area, lateral plateau surface area, and lateral anteroposterior distance, whereas the slope cut angles were changed from 9 to 0 degrees in both gender groups. It was found that the amount of posteromedial underhang and posterolateral overhang increased in both the asymmetric and symmetric tibial baseplates when the slope angle was changed from 0 to 9 degrees. Although the mediolateral diameter did not change after the proximal tibia cuts at different slope angles, the surface area and anteroposterior diameter of the lateral plateau could change, leading to increased lateral plateau area. Although prosthesis designs are highly compatible with the tibial surface area, it should be noted that the component overhangs, especially beyond the posterolateral edge, it can be prevented by changing the slope cut angle in males and females.

Download Full-text