Plotting Implicit Functions

Slides:



Advertisements
Similar presentations
EXAMPLE 1 Find the axis of symmetry and the vertex Consider the function y = – 2x x – 7. a. Find the axis of symmetry of the graph of the function.
Advertisements

CW Matrix Division We have seen that for 2x2 (“two by two”) matrices A and B then AB  BA To divide matrices we need to define what we mean by division!
9.3 Graphing Quadratic Functions
Lesson 5.2 AIM: Review of Vertex and Axis of Symmetry.
Chinese Remainder Theorem. How many people What is x? Divided into 4s: remainder 3 x ≡ 3 (mod 4) Divided into 5s: remainder 4 x ≡ 4 (mod 5) Chinese Remainder.
Color and Color Models Angel 2.5 Angel: Interactive Computer Graphics5E © Addison-Wesley
1 Graphics CSCI 343, Fall 2015 Lecture 34 Curves and Surfaces III.
Sample Problems for Class Review
1 Introduction to Computer Graphics with WebGL Ed Angel Professor Emeritus of Computer Science Founding Director, Arts, Research, Technology and Science.
1 E. Angel and D. Shreiner: Interactive Computer Graphics 6E © Addison-Wesley 2012 Marching Squares Ed Angel Professor Emeritus of Computer Science University.
Chapter 1 Functions Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 3 Derivatives Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Graphing Quadratic Functions
Do Now Find the value of y when x = -1, 0, and 2. y = x2 + 3x – 2
Sampling and Aliasing Ed Angel
9.3 Graphing Quadratic Functions
Quadratic Functions and Their Graphs
Chapter 3 Differentiation
Sampling and Aliasing Ed Angel Professor Emeritus of Computer Science
Angel: Interactive Computer Graphics5E © Addison-Wesley 2009
Chapter 2 Limits Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
University of New Mexico
Graphing Absolute Value Equations in two variables
Introduction to Computer Graphics with WebGL
Image Formation Ed Angel Professor Emeritus of Computer Science,
Isaac Gang University of Mary Hardin-Baylor
Introduction to Computer Graphics with WebGL
Chapter 17 Linked Lists.
Chapter 19 Binary Search Trees.
Rendering Curves and Surfaces
Designing Parametric Cubic Curves
11.7 Motion in Space Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 4 Inheritance.
Chapter 14 Graphs and Paths.
Vectors, Normals, & Shading
Introduction to Computer Graphics with WebGL
Building Models Ed Angel Professor Emeritus of Computer Science
Chapter 3 Integration Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Physics-based simulation for visual computing applications
Rasterization and Antialiasing
Projections and Hidden Surface Removal
Chapter 10 Datapath Subsystems.
11.8 Length of Curves Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 20 Hash Tables.
Copyright © 2011 Pearson Education, Inc
Introduction to Computer Graphics with WebGL
Rasterization and Antialiasing
GRAPHING PARABOLAS To graph a parabola you need : a) the vertex
Angel: Interactive Computer Graphics4E © Addison-Wesley 2005
Introduction to Computer Graphics with WebGL
Image Formation Ed Angel
Chapter 1 Functions Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
The Facts to Be Explained
© T Madas.
Introduction: Some Representative Problems
Copyright © 2008 Pearson Education, Inc
Relate Multiplication and Division
Graphing Quadratic Equations
Labeling Contour Lines
Circuit Characterization and Performance Estimation
Implementation III Ed Angel Professor Emeritus of Computer Science
Chapter 2 Part 1 Data and Expressions.
Chapter 6 Dynamic Programming.
Marching Squares Ed Angel
Angel: Interactive Computer Graphics5E © Addison-Wesley 2009
Chapter 2 Reference Types.
Angel: Interactive Computer Graphics5E © Addison-Wesley 2009
Multiplying and Dividing Decimals
Copyright © 2011 Pearson Education, Inc
Cell Culture Engineering XI
Presentation transcript:

Plotting Implicit Functions Angel 2.11 Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Angel: Interactive Computer Graphics5E © Addison-Wesley 2009 Cell of Data Points Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Angel: Interactive Computer Graphics5E © Addison-Wesley 2009 Values at Each Point Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Angel: Interactive Computer Graphics5E © Addison-Wesley 2009 Choose Simplest Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Angel: Interactive Computer Graphics5E © Addison-Wesley 2009 Interpolation Don’t have to divide evenly x = xi + x(a-c)/(a-b) Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Vertex Label Cases (not unique) Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Angel: Interactive Computer Graphics5E © Addison-Wesley 2009 Unique Vertex Labels Due to symmetry Rotations Inverses Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Recursive Subdivisions Possibly Needed Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Angel: Interactive Computer Graphics5E © Addison-Wesley 2009 Ambiguity Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Angel: Interactive Computer Graphics5E © Addison-Wesley 2009 Subdivision to Solve Might need to repeat Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Interpolation “Smoothes” Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Contour Visualization Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com Inc. All rights reserved.