Orthogonal Projections
Orthogonal Projections - Related Videos
01:26
Orthogonal Trajectories
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2026
Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
10:32
Orthogonal Protein Purification Facilitated by a Small Bispecific Affinity Tag
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Cited by 7 •
2012
A novel and highly efficient two-step affinity chromatography protocol has been developed and is described in detail. The method is based on a small purification tag with two inherent affinities and is applicable to a wide range of target proteins with different properties.
08:43
Calibration Procedures for Orthogonal Superposition Rheology
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Cited by 4 •
2020
We present a detailed calibration protocol for a commercial orthogonal superposition rheology technique using Newtonian fluids including end-effect correction factor determination methods and recommendations for best practices to reduce experimental error.
02:18
Fischer Projections
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2023
Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines. While...
16:44
Born Normalization for Fluorescence Optical Projection Tomography for Whole Heart Imaging
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Cited by 15 •
2009
We suggest a Born normalized approach for Optical Projection Tomography (BnOPT) that accounts for the absorption properties of imaged samples to obtain accurate and quantitative fluorescence tomographic reconstructions. We use the proposed algorithm to reconstruct the fluorescence molecular probe distribution within small animal organs.
FAQs
To project a vector onto a unit direction, calculate its dot product with that direction, then multiply the resulting scalar by the same direction. The scalar reports how much of the original vector lies along the chosen axis, while the resulting vector preserves that directional contribution for later physical analysis.
The residual becomes useful because it isolates what the selected direction does not contain. After the projected component is subtracted, the remaining vector is perpendicular to the subspace used for the projection. This separation lets a calculation treat directional contribution and perpendicular remainder as distinct parts rather than mixing them.
Changing the selected direction or subspace changes the component that is extracted. A projection therefore does not produce an absolute decomposition independent of coordinates; it answers a directional question defined by the chosen subspace. In physics, selecting a meaningful axis determines which part of a vector receives direct physical interpretation.
To resolve a quantity, first identify the physically relevant direction and use a unit vector for that axis. Form the dot product with the original vector, multiply the axis vector by that scalar, and, when needed, subtract the result from the original. The two resulting parts separate aligned and perpendicular behavior in calculation.
On an inclined surface, projecting a force onto directions associated with the surface separates the contribution relevant to motion along that surface from the remainder. This makes the force easier to interpret than its unseparated vector form. The same operation supports analyses in which direction, rather than total magnitude alone, determines physical meaning.
For velocity analysis, projections onto coordinate axes identify the portions associated with each chosen direction. Rather than treating velocity as a single undifferentiated vector, the calculation reports directional components that can be examined separately. This is useful when the physical setup distinguishes axes, since each component corresponds to a specific coordinate direction.
Projection operators provide a compact way to represent the same directional selection in abstract vector spaces. In physics, this connects ordinary component calculations with analyses of states that may not be described only by spatial axes. Their value is organizational: they isolate a selected contribution so the remaining analysis can focus on the relevant part.