The 'Precessions' tooling for polishing and figuring flat, spherical and aspheric surfaces

Optics Express
|May 23, 2009
PubMed

Related Concept Videos

Wood Surfacing01:14

Wood Surfacing

Wood surfacing is a critical finishing process designed to smoothen the wood surface, enhance its dimensional accuracy, and make handling safer. This process compensates for potential shrinkage during the seasoning phase by marginally increasing the wood dimensions before surfacing. It also helps correct some distortions that may occur as the wood dries.
The equipment used in the surfacing process is a plane equipped with rotating blades. This tool efficiently smoothens the wood surface and can...
Field Procedure for Staking Out Curves01:26

Field Procedure for Staking Out Curves

Staking out curves is an essential process in construction to ensure the accurate alignment of structures along a curved path. This task involves positioning stakes at calculated locations corresponding to the curve's design, effectively translating plans into physical markers in the field. The process begins by determining the geometric parameters of the curve, including the radius, central angle, and tangent distances. These parameters are critical for identifying key points such as the Point...
Tangent Planes to a Parametric Surface01:22

Tangent Planes to a Parametric Surface

A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...
Tangent Planes to Surfaces01:19

Tangent Planes to Surfaces

In multivariable calculus, the concept of a tangent plane plays a central role in approximating curved surfaces. When dealing with a surface defined by a function of two variables, such as z = f(x, y), the tangent plane at a given point provides the best linear approximation to the surface near that point. This local linearization allows complex, nonlinear geometries to be treated using simpler, planar models.The construction of the tangent plane involves taking vertical slices of the surface...
Production of Formed Elements01:34

Production of Formed Elements

Hemangioblasts are multipotent stem cells originating from the mesoderm. They give rise to hematopoietic stem cells (HSCs), which undergo hematopoiesis to produce all the formed elements of blood. This process is regulated by a complex network of hematopoietic growth factors, including transcription factors, growth factors, and cytokines. These factors stimulate the HSCs to divide and differentiate, though some HSCs remain undifferentiated to maintain a self-renewing pool.
Most HSCs commit to...
Parametric Surfaces01:30

Parametric Surfaces

A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...