Positive Orientation
Positive Orientation - Related Videos
01:30
Oriented Surfaces
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2026
A surface is called orientable if a consistent choice of unit normal vector can be made at every point on the surface. A thin soap film stretched across a wire loop provides a familiar example. The film separates the air on one side from the air on the other, so one side can be selected as positive and the opposite side as negative. Once this choice is made, a unit normal vector can be assigned smoothly across the entire surface.At each point on the soap film, a unit normal vector points...
01:13
Location and Orientation of the Heart
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2024
The human heart, despite its modest size and weight, is an organ of remarkable strength and endurance. Roughly the size of a fist, the heart weighs between 250 and 350 grams and is nestled within the mediastinum, the medial cavity of the thorax. It extends obliquely for about 12 to 14 cm, resting on the superior surface of the diaphragm. The heart is positioned anterior to the vertebral column and posterior to the sternum, with two-thirds of its mass lying to the left of the midsternal line.
02:32
Position-effect Variegation
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2020
In 1928, a German botanist Emil Heitz observed the moss nuclei with a DNA binding dye. He observed that while some chromatin regions decondense and spread out in the interphase nucleus, others do not. He termed them euchromatin and heterochromatin, respectively. He proposed that the heterochromatin regions reflect a functionally inactive state of the genome. It was later confirmed that heterochromatin is transcriptionally repressed, and euchromatin is transcriptionally active chromatin.
13:44
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Cited by 13 •
2013
We demonstrate methods for the detection of architectural distortion in prior mammograms. Oriented structures are analyzed using Gabor filters and phase portraits to detect sites of radiating tissue patterns. Each site is characterized and classified using measures to represent spiculating patterns. The methods should assist in the detection of breast cancer.
12:09
Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations
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Cited by 14 •
2013
A methodology to estimate ventricular fiber orientations from in vivo images of patient heart geometries for personalized modeling is described. Validation of the methodology performed using normal and failing canine hearts demonstrate that that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.
FAQs
For an ordered basis, the determinant provides the decisive test: a positive determinant relative to a reference basis preserves the reference orientation, whereas a negative determinant reverses it. This algebraic criterion lets geometry and coordinate calculations distinguish two otherwise comparable configurations by their ordering, making orientation an algebraic as well as geometric property.
In the plane, counterclockwise traversal serves as the usual positive choice, so clockwise traversal represents the opposite orientation. The distinction is not merely visual: changing the traversal direction changes the sign assigned to orientation-sensitive quantities, including line integrals and boundary terms. Stating the convention prevents equivalent geometric paths from receiving inconsistent signs in later calculations.
For a parametrized curve or surface, the selected tangent vectors establish an ordering, while the associated normal direction records which side is positive. Altering that choice reverses the orientation even when the underlying geometric set remains unchanged. This distinction is essential when a surface or curve appears in an integral, because the sign depends on the chosen directional data.
First identify the orientation assigned to the region or surface, then choose the boundary traversal compatible with that choice. For planar boundaries, the positive convention is typically counterclockwise; for surfaces, the traversal must agree with the selected normal direction. Applying this consistently is what makes Green’s and Stokes’ theorems produce the intended sign.
The Jacobian records how a coordinate transformation changes oriented volume or area locally. A positive Jacobian indicates that the transformation preserves the chosen orientation, while a negative Jacobian indicates reversal. Checking its sign therefore helps interpret whether new coordinates maintain the original ordering and prevents sign errors when geometric quantities are transferred between coordinate descriptions.
Orientation must be specified whenever a line or surface integral depends on direction, rather than only on the underlying set. Reversing the selected direction changes the sign of the resulting integral, so the same curve or surface can yield opposite values under opposite orientations. Recording the traversal, tangent ordering, or normal direction makes the reported result reproducible.