Gradually varied surface

Digital geometry

In mathematics, a gradually varied surface is a special type of digital surfaces. It is a function from a 2D digital space (see digital geometry) to an ordered set or a chain. A gradually varied function is a function from a digital space to where and are real numbers. This function possesses the following property: If x and y are two adjacent points in , assume , then , , or . The concept of the continuous function in digital space (can be called digitally continuous functions) was proposed by Azriel Rosenfeld in 1986. It is a function in which the value (an integer) at a digital point is the same or almost the same as its neighbors. In other words, if x and y are two adjacent points in a digital space, |f(x) − f(y)| ≤ 1. So we can see that the gradually varied function is defined to be more general than the digitally continuous function. The gradually varied function was defined by L. Chen in 1989. An extension theorem related to above functions was mentioned by Rosenfeld (1986) and completed by Chen (1989). This theorem states: Let and . The necessary and sufficient condition for the existence of the gradually varied extension of is : for each pair of points and in , assume and , we have , where is the (digital) distance between and . The gradually varied surface has direct relationship to graph homomorphism. (Wikipedia).

Parameterized Surfaces

This video explains how to parameterized a equation of a surface.

From playlist Surface Integrals

(New Version Available) Parameterized Surfaces

New Version: https://youtu.be/0kKBPbmzwm8 This video explains how to parameterized a equation of a surface. http://mathispower4u.wordpress.com/

From playlist Surface Integrals

Cylindrical Surfaces

This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/

From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates

Transform from parameter space to parametric surface

From playlist Surface integrals

Surface Area of Prisms and Pyramids

This video is about finding the Surface Area of Prisms and Pyramids

From playlist Surface Area and Volume

Light and Optics 5_1 Refractive Surfaces

The bending of light rays at the interface of refracting surfaces.

From playlist Physics - Light and Optics

Let s vary

From playlist Drawing a sphere

Introduction to gradually varied flows

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Gradually varied flow equations

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Classification of gradually varied flow

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Gradually varied flow profiles with change in bed slopes

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Mechanical Fourier Machine

For more content: https://www.dev-mind.blog/ The wood circles represents the terms in the series. The "size" of the circle is the magnitude of the corresponding coefficient. The initial angle is the phase of the coefficient. Each circle spins with an increasing speed (frequency). In this

From playlist Fourier

Classification of gradually varied flow

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Gradually varied flow computations RK method

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Rotating parametric surface

From playlist Surface integrals

How to make Very Flat Optical Surfaces on Glass

The video shows (hands on) how a nanometer level flat optical surface can be made. It first discusses the principle of the continuous pitch polisher, also known as the planetary polisher or optical lap master. 00:00 Intro of flat surface creation / polishing 00:37 Optical flatness specs

From playlist optics

Energy, momentum specific force

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Spatially varied flow

Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering

Parameterizing Surfaces

Multivariable calculus lecture focusing on Parameterizing Surfaces

From playlist Multivariable Derivatives

Cosmology Lecture 9

(March 11, 2013) Leonard Susskind presents the theory of cosmological inflation under which the early universe expanded exponentially before the Big Bang. This theory explains the lack of observed magnetic monopoles and the uniformity of the cosmic microwave background radiation. Origina

From playlist Lecture Collection | Cosmology

Gradually varied surface

Related pages