Surfaces | Geometry processing
In mathematics, an implicit surface is a surface in Euclidean space defined by an equation An implicit surface is the set of zeros of a function of three variables. Implicit means that the equation is not solved for x or y or z. The graph of a function is usually described by an equation and is called an explicit representation. The third essential description of a surface is the parametric one: , where the x-, y- and z-coordinates of surface points are represented by three functions depending on common parameters . Generally the change of representations is simple only when the explicit representation is given: (implicit), (parametric). Examples: 1. * The plane 2. * The sphere 3. * The torus 4. * A surface of genus 2: (see diagram). 5. * The surface of revolution (see diagram wineglass). For a plane, a sphere, and a torus there exist simple parametric representations. This is not true for the fourth example. The implicit function theorem describes conditions under which an equation can be solved (at least implicitly) for x, y or z. But in general the solution may not be made explicit. This theorem is the key to the computation of essential geometric features of a surface: tangent planes, surface normals, curvatures (see below). But they have an essential drawback: their visualization is difficult. If is polynomial in x, y and z, the surface is called algebraic. Example 5 is non-algebraic. Despite difficulty of visualization, implicit surfaces provide relatively simple techniques to generate theoretically (e.g. Steiner surface) and practically (see below) interesting surfaces. (Wikipedia).
Worldwide Calculus: Implicit Differentiation- Multivariable Calculus
Lecture on 'Implicit Differentiation- Multivariable Calculus' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
Topics in Curve and Surface Implicitization, David Cox (Amherst College) [2007]
Slides for this talk: https://drive.google.com/file/d/1quB7Lg_dXTPow_qLLDeW2Zv6m9G4X4AN/view?usp=sharing (credits to zubrzetsky) Topics in Curve and Surface Implicitization Saturday, June 2, 2007 - 10:30am - 11:20am EE/CS 3-180 David Cox (Amherst College) This lecture will discuss sever
From playlist Mathematics
Section (3 5) Implicit Derivatives
Applied Calculus – Section (3.5) – Implicit Derivatives This lecture discusses compares explicit and implicit functions. We work out an example that can be differentiated both explicitly and implicitly and show equivalent results. Examples are worked out which invoke other derivative rules
From playlist Applied Calculus
Calculus 1 Lecture 2.7: Implicit Differentiation
Calculus 1 Lecture 2.7: Implicit Differentiation
From playlist Calculus 1 (Full Length Videos)
The Astonishing Implicit Function Theorem
Video about the Implicit Function Theorem (multivariable calculus topic). Despite being a topic from multivariable calculus, the content here is designed to be accessible to any people who have taken at least one course of single variable calculus. #math #multivariablecalculus #SoME2 #3b1b
From playlist Summer of Math Exposition 2 videos
What is implicit differentiation?
► My Derivatives course: https://www.kristakingmath.com/derivatives-course Most often in calculus, you deal with explicitly defined functions, which are functions that are solved for y in terms of x. In that case, finding the derivative is usually really simple, because you just call the
From playlist Popular Questions
Maria Angelica Cueto - "Implicitization of surfaces via geometric tropicalization"
Implicitization of surfaces via geometric tropicalization - Research lecture at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Lecture 09: Introduction to Geometry (CMU 15-462/662)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/
From playlist Computer Graphics (CMU 15-462/662)
Describing Surfaces Explicitly, Implicitly & Parametrically // Vector Calculus
How can we describe two-dimensional surfaces, even if they are embedded in 3D space? Similar to the three ways to describe curves in 2D, we can do this explicitly, implicitly, or parametrically. In the case of parametrically we get TWO parameters and choose them to try and naturally repres
Level curves and level surfaces -- Calculus III
This lecture is on Calculus III. It follows Part III of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus III
Lecture 12: Geometric Queries (CMU 15-462/662)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/
From playlist Computer Graphics (CMU 15-462/662)
Graph Implicit Equations (Quadric Surfaces) Using 3D Calc Plotter
New url for the 3D plotter: https://c3d.libretexts.org/CalcPlot3D/index.html This video explains how to graph implicit equations using the 3D Calc Plotter JavaScript App.
From playlist 3D Calc Plotter
Tropical Geometry - Lecture 12 - Geometric Tropicalization | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Worldwide Calculus: Level Sets & Gradient Values
Lecture on 'Level Sets & Gradient Values' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Multivariable Derivatives
Implicit Differentiation Introduction 4K
I find the derivative of an ellipse using implicit differentiation and explicit differentiation. We then find points along the curve where the tangent line has a slope of zero and a slope which is undefined. Check out http://www.ProfRobBob.com, there you will find my lessons organized
From playlist Calculus (New)
Lec 11 | MIT 18.086 Mathematical Methods for Engineers II
Level Set Method View the complete course at: http://ocw.mit.edu/18-086S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06
MATH331: Riemann Surfaces - part 1
We define what a Riemann Surface is. We show that PP^1 is a Riemann surface an then interpret our crazy looking conditions from a previous video about "holomorphicity at infinity" as coming from the definition of a Riemann Surface.
From playlist The Riemann Sphere