Three-dimensional Surface
Three-dimensional Surface - Related Videos
09:24
Visualizing Surface T-Cell Receptor Dynamics Four-Dimensionally Using Lattice Light-Sheet Microscopy
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Cited by 6 •
2020
The goal of this protocol is to show how to use Lattice Light-Sheet Microscopy to four-dimensionally visualize surface receptor dynamics in live cells. Here T cell receptors on CD4+ primary T cells are shown.
03:40
Dimensional Analysis
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2020
Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units. Conversion Factors and Dimensional Analysis The unit...
09:37
Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
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Cited by 2 •
2016
A methodology for obtaining visual and quantitative root structure information from X-ray computed tomography data acquired in-soil is presented.
14:49
Self-reporting Scaffolds for 3-Dimensional Cell Culture
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Cited by 7 •
2013
Biocompatible pH responsive sol-gel nanosensors can be incorporated into poly(lactic-co-glycolic acid) (PLGA) electrospun scaffolds. The produced self-reporting scaffolds can be used for in situ monitoring of microenvironmental conditions whilst culturing cells upon the scaffold. This is beneficial as the 3D cellular construct can be monitored in real-time without disturbing the experiment.
01:16
Surface Tension and Surface Energy
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2023
When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason behind this effect is surface tension. Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
FAQs
Parametric equations describe spatial coordinates through two parameters, making them useful for tracing points across a surface and studying its geometry. Implicit equations instead specify a relation that all surface points must satisfy, which can make intersections and membership easier to identify. Choosing between them depends on whether coordinate-based description or equation-based conditions better fit the analysis.
Curvature describes how a surface departs from being flat as its shape changes through space. Multivariable calculus and differential geometry provide the mathematical framework for analyzing this behavior. Comparing curvature across different regions helps distinguish planes from more strongly curved forms, such as spheres or cylinders, and supports geometric interpretation of modeled shapes.
Boundaries identify where a surface region begins or ends, while intersections describe the points or curves shared with other geometric objects. Both features affect how a surface is interpreted and measured. Examining them is important when analyzing bounded regions, comparing connected shapes, or determining how a modeled surface relates to surrounding geometry.
Surface area can be determined by applying multivariable-calculus methods to a mathematical representation of the shape. A parametric description can organize the surface through two parameters, while an implicit relation identifies the relevant points. This analysis extends ordinary geometric measurement to curved objects and supports comparisons among planes, cylinders, spheres, and other forms.
A typical workflow begins by selecting a parametric or implicit representation, then identifying the region, boundaries, or intersections relevant to the problem. Next, multivariable calculus or differential geometry can be used to examine quantities such as area and curvature. The resulting description provides a structured basis for interpreting the surface or comparing it with other geometric objects.
They provide mathematical models for displaying physical shapes and graphical data in three dimensions. A surface representation allows visual systems to describe form, curvature, and spatial relationships rather than treating an object as an unstructured collection of points. This makes surfaces useful for communicating geometric information in computer graphics and scientific visualization.
A surface can represent a boundary or spatial form within a physical model, including fluid interfaces and fields. Its equations give researchers a way to analyze geometric properties such as curvature, area, and intersections using mathematical tools. This connection links differential geometry and multivariable calculus with scientific descriptions of changing shapes and spatial structure.