Functions Jason Smith, Josiah Manson, and Scott Schaefer Texas - PowerPoint PPT Presentation

Sep 19, 2023 •278 likes •930 views

Contouring Discrete Indicator Functions Jason Smith, Josiah Manson, and Scott Schaefer Texas A&M University Indicator Functions Discrete Indicator Functions (DIF) Extracted Surface Motivation [Green 2007] Motivation [Warner Bros

Contouring Discrete Indicator Functions Jason Smith, Josiah Manson, and Scott Schaefer Texas A&M University
Indicator Functions
Discrete Indicator Functions (DIF)
Extracted Surface
Motivation [Green 2007]
Motivation [Warner Bros Pictures 2007]
Motivation
Motivation [Manson et al. 2008]
Marching Cubes [Wyvill et al. 1986] [Lorensen and Cline 1987]
Marching Cubes Perfect Sphere MC
Related Work [Mor et al. 1996] [Wu and Sullivan 2003] [Reitinger et al. 2005]
Related Work [Gibson and Frisken 1998] [Chica et al. 2007]
Gaussian Blur Poseidon
Gaussian Blur MC
Gaussian Blur Blur size 3
Gaussian Blur Blur size 7
Gaussian Blur Ours MC Blur
Gaussian Blur Ours MC
Contributions • Simple and easy to implement modification to the MC algorithm – Replaces the linear interpolant in MC • Computationally inexpensive • Greatly reduces surface contouring artifacts
Contouring
DIF
Dual Grid
Dual Grid
2D MC change t 0 1
2D MC change a 1 a 2
Side - Side a 1 a 2
Bottom - Top a 1 a 2
Bottom - Side a 1 a 2
Side- Top a 1 a 2
Parameter Space 1 a 2 .5 0 .5 a 1
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Parameter Space 1 a 2 .5 0 .5 a 1
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Difference from Linear Interp.
Linear functions
Linear functions
Linear functions
Expanding to 3D
Expanding to 3D
Expanding to 3D
Expanding to 3D
Expanding to 3D
Expanding to 3D MC
Expanding to 3D Ours
Expanding to 3D MC Ours
Perfect Sphere
MC
Ours
MC Ours
Sphere Normal Error 70 60 50 Degrees 40 MC Max MC Avg 30 Our Max Our Avg 20 10 0 0 5 10 15 20 25 30 Radius in Cells
MC
Ours
MC
Ours
Limitations?
Conclusion • Replaced Linear Interpolation of Marching Cubes. • Oscillation artifacts removed from surface contours while preserving details. • Inexpensive method not requiring any pre processing of function values, or post processing of output mesh.

Recommend

More on Functions Thomas Schwarz, SJ Marquette University Functions of Functions Functions

More on Functions Thomas Schwarz, SJ Marquette University Functions of Functions Functions are full-fledged objects in Python This means you can pass functions as parameters Example: Calculate the average of the values of a function at

332 views • 12 slides

The algebra of functions Given two functions, say f ( x ) = x 2 and g ( x ) = x + 1 , we can, in

The algebra of functions Given two functions, say f ( x ) = x 2 and g ( x ) = x + 1 , we can, in obvious ways, add, subtract, multiply and divide these functions. For example, the function f + g is defined simply by Elementary Functions ( f + g )(

404 views • 5 slides

Properties of (functions may return functions) Functions may be passed as parameter

Functions as first class citizens Function may be a value of an expression Properties of (functions may return functions) Functions may be passed as parameter functional Functions may be stored in data structures languages

306 views • 11 slides

Functions Declarations vs Definitions Inline Functions Class Member functions

2/21/2017 Functions in C++ Functions Declarations vs Definitions Inline Functions Class Member functions Overloaded Functions For : COP 3330. Pointers to functions Object oriented Programming (Using C++) Recursive

184 views • 6 slides

Functions How to make the person run? (See: runForest.cpp) Functions You can also use functions

Functions How to make the person run? (See: runForest.cpp) Functions You can also use functions that return bool types in an if statement or loop This is commonly used if you have complex logic as it is normally easier to write a function

260 views • 10 slides

Orthogonal Rational Functions, Associated Rational Functions and Functions of the Second Kind

Introduction ORFs and ARFs Relations Favard theorem Orthogonal Rational Functions, Associated Rational Functions and Functions of the Second Kind Karl Deckers Department of Computer Science, Katholieke Universiteit Leuven, Heverlee,

691 views • 66 slides

Functions 1 / 13 Functions A function is a reusable block of code. Functions have names

Functions 1 / 13 Functions A function is a reusable block of code. Functions have names (usually), contain a sequence of statements, and return values, either explicitly or implicitly. Weve already used several built-in functions.

152 views • 13 slides

Linear functions A. Functions in general A. Functions in general 1. definition B. Linear

1 2 Linear functions A. Functions in general A. Functions in general 1. definition B. Linear functions C. Linear (in)equalities Handbook: E. Haeussler, R. Paul, R. Wood (2011). Introductory Mathematical Analysis for business, economics and

442 views • 20 slides

Functions http://xkcd.com/221/ Fundamentals of Computer Science Outline Functions

Functions http://xkcd.com/221/ Fundamentals of Computer Science Outline Functions Library Functions Helper functions Perform calculations Output data Consolidate similar code to one location Functions Flow of

1.01k views • 23 slides

Elementary Functions Part 1, Functions Lecture 1.4a, Symmetries of Functions: Even and Odd

Elementary Functions Part 1, Functions Lecture 1.4a, Symmetries of Functions: Even and Odd Functions Dr. Ken W. Smith Sam Houston State University 2013 Smith (SHSU) Elementary Functions 2013 1 / 25 Even and odd functions In this lesson we

865 views • 71 slides

Python: Functions Functions Mathematical functions f(x) = x 2 f(x,y) = x 2 + y 2 In programming

Python: Functions Functions Mathematical functions f(x) = x 2 f(x,y) = x 2 + y 2 In programming functions also help creating better structure with decomposition Functions

2.12k views • 23 slides

Iterators and Generators Sequences: tuple, list return functions Dictionaries

4/20/20 Computational Structures in Data Computational Concepts Toolbox Science Data type: values, literals, Higher Order Functions operations, Functions as Values Expressions, Call Functions with functions as argument

55 views • 4 slides

Higher order functions Functions that take other functions as parameters Easily supported

Higher order functions Functions that take other functions as parameters Easily supported in languages that are dynamically typed and where functions treated as a type of data More complex in statically typed languages where functions

239 views • 4 slides

We have used many Python functions INF1100 Lectures, Chapter 3: Mathematical functions: from

5mm. We have used many Python functions INF1100 Lectures, Chapter 3: Mathematical functions: from math import * Functions and Branching y = sin(x)*log(x) Other functions: n = len(somelist) Hans Petter Langtangen ints = range(5, n, 2)

333 views • 4 slides

Function Transformations In this course we learn to identify a variety of functions: linear

Function Transformations In this course we learn to identify a variety of functions: linear functions, Elementary Functions quadratic and cubic functions, general polynomial Part 1, Functions Lecture 1.3a, Transformations of Functions: Shifts

774 views • 9 slides

Periodic Functions and Orthogonal Systems Periodic Functions Even and Odd Functions

Periodic Functions and Orthogonal Systems Periodic Functions Even and Odd Functions Properties of Even and Odd Functions Properties of Periodic Functions Piecewise-Defined Functions Representations of Even and Odd Extensions

501 views • 11 slides

Functions Built-in functions Youve used several functions already >>>

Functions Built-in functions Youve used several functions already >>> len("ATGGTCA") 7 >>> abs(-6) 6 >>> float("3.1415") 3.1415000000000002 >>> What are functions? A function is a

450 views • 43 slides

Functions CS1 Python 1 / 27 Functions A function is a reusable block of code. Functions

Functions CS1 Python 1 / 27 Functions A function is a reusable block of code. Functions have names (usually), contain a sequence of statements, and return values, either explicitly or implicitly. Weve already used several

461 views • 27 slides

CS 61A Discussion 2 Environments and Higher Order Functions Albert Xu Slides:

CS 61A Discussion 2 Environments and Higher Order Functions Albert Xu Slides: albertxu.xyz/teaching/cs61a/ Announcements functions can return other functions functions can return other functions take in functions as arguments functions can

561 views • 19 slides

CS 105: FUNCTIONS Max Fowler (Computer Science)

CS 105: FUNCTIONS Max Fowler (Computer Science) https://pages.github-dev.cs.illinois.edu/cs-105/web/ June 21, 2020 Video Series Four Topics Functions in Python Functions, Codeblocks Functions in Python Parameters, Arguments

833 views • 24 slides

Even and odd functions In this lesson we look at even and odd functions. A symmetry of a function

Even and odd functions In this lesson we look at even and odd functions. A symmetry of a function is a transformation that leaves the graph unchanged. Consider the functions f ( x ) = x 2 and g ( x ) = | x | whose graphs are drawn Elementary

534 views • 7 slides

Elementary Functions Part 1, Functions Lecture 1.1c, Finding the domains of functions Dr. Ken W.

Elementary Functions Part 1, Functions Lecture 1.1c, Finding the domains of functions Dr. Ken W. Smith Sam Houston State University 2013 Smith (SHSU) Elementary Functions 2013 22 / 27 Domains of functions The domain of a function is

405 views • 37 slides

Elementary Functions Part 1, Functions Lecture 1.1b, Functions defined by equations Dr. Ken W.

Elementary Functions Part 1, Functions Lecture 1.1b, Functions defined by equations Dr. Ken W. Smith Sam Houston State University 2013 Smith (SHSU) Elementary Functions 2013 13 / 27 Functions defined by equations Many functions we explore

786 views • 63 slides

Functions Programmer-Defined Functions Local Variables in Functions Overloading

Functions Programmer-Defined Functions Local Variables in Functions Overloading Function Names void Functions, Call-By-Reference Parameters in Functions Programmer-Defined Functions function declaration function call

1.21k views • 70 slides