New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Advanced Topics in Computer Graphics

by: Dr. Elyssa Ratke

Advanced Topics in Computer Graphics CMPS 290

Marketplace > University of California - Santa Cruz > ComputerScienence > CMPS 290 > Advanced Topics in Computer Graphics
Dr. Elyssa Ratke
GPA 4.0


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in ComputerScienence

This 16 page Class Notes was uploaded by Dr. Elyssa Ratke on Monday September 7, 2015. The Class Notes belongs to CMPS 290 at University of California - Santa Cruz taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/182267/cmps-290-university-of-california-santa-cruz in ComputerScienence at University of California - Santa Cruz.


Reviews for Advanced Topics in Computer Graphics


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/07/15
Review of Type inference Un ryped rer39ms Ax e In rr39oduce Type variables x 0c Typing r39ules generate cons rr39ain rs 39oc3y ocy3 BinT Solve cons rr39ain rs 39oczin l39 in r BzinT yzin r Conclude Axin r in r e 15 Jan 2004 290G Lecture 4 1 16 Representation Analysis and Polymorphic Types Lec rur39e 4 15 Jan 2004 290G Lecture 4 2 16 Representation Analysis Which values in a program must have the same representation Not all values of a type need be represented identically Shows abstraction boundaries Which values must have the same representation Those that are used quottogetherquot 15 Jan 2004 290G Lecture 4 3 16 The Idea Old Type language T06T gtTin139 New Type language Ever39y Type is a pair old rype x variable T06 I T gt T8in1398 15 Jan 2004 290G Lecture 4 4 16 Old Type Inference Rules Akelnl Akezme AX0X Axaxker lerea Akchx Awlxech n Akelezg Akelnl Akelnl Akezne Akezne AI QJT3 7172am lein r 7273 AHHm Ake1e2im Akifelez nz 15 Jan 2004 290G Lecture 4 5 16 New Type Inference Rules A I e1r1 A I e2 2 72 Ax 05XUBX AX aX8X I e 239 71 72 gt 053 A I X20X8X A I 1Xeax x gt my A I el e2 053 AI e1271 AI e1r1 AI ezm2 AI e2272 AI es22393 2391 2392 infug Z391im398 2392 2393 AI iin r8 AI e1e2in r8 AI ifelezgm2 15 Jan 2004 290G Lecture 4 6 16 Example A lambda Ter39m x xx yk 2x wif x y 2 1 w Equivalence classes x xx yk 2x wif x y z 1 w 15 Jan 2004 290G Lecture 4 7 16 Lackwif Repr39esen ra rion analysis for39 C Very simple efficien r and probably useful Some ugly pieces Eg handling of cas rs 15 Jan 2004 290G Lecture 4 8 16 Applications Reengineeringquot Make some values more abs rrac r Find bugs Every equivalence class wi rh a maloc should have a free Jus r explain wha r pieces of The program inferacf 15 Jan 2004 290G Lecture 4 9 16 Polymorphism 15 Jan 2004 290G Lecture 4 10 16 Polymorphism Wha r is Type of Xxx Is i r in r in r 0c 0c bool bool 01 B 0L all of The above 15 Jan 2004 290G Lecture 4 11 16 Context Sensitivity Polymorphic Types Add a new class of types called fype schemes UVOLC7T Example A polymorphic identity function Van gt 05 Note All quontifiers are at top level 15 Jan 2004 290G Lecture 4 12 16 The Key Idea AI e r a no r free in A AI e Vow This is called general2mm 15 Jan 2004 290G Lecture 4 13 16 Insfam iafion Polymorphic assump rions can be used as usual Bu r we s rill need To Turn a polymorphic rype info a monomor39phic Type for39 The o rher39 rype rules To work AI e Vom AI e 039T39a 15 Jan 2004 290G Lecture 4 14 16 Where is Type Inference Strong Handles da ra s rr39uc rur39es smoo rhly Works in infini re domains Se r of Types is unlimi red No forwards backwards dis rincTion Type polymorphism for con rex r sensi rivi ry 15 Jan 2004 290G Lecture 4 15 16 CMPS 2900 Topics Spring 708 1 Convex Sets 0 A ine sets 0 Convex sets 0 Convex combinations and convex hull o cones and conic combinations 0 hyperplanes and half spaces o Norms and Norm balls 0 polyhedra o Convexity preserving operations intersection image of convex set under af ne transformation 0 Perspective function 0 dual cones generalized conic inequalities minimumminimal elements 0 Separating hyperplane theorem 0 Supporting hyperplane theorem 2 Convex functions 0 De nitions of convexity concavity strict convexity o convex if every restriction to a line is convex 0 First order condition 0 Second order condition 0 Epigraphs and sub level sets Jensen s inequality 0 Closure under non negative weighted sums composition with a ine functions point wise max and sup composition with scalar function minimization over convex set 0 conjugate function 0 quasi convexity 3 Optimization problems 0 Problems in standard form 0 Domain feasible optimal and locally optimal points


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Kyle Maynard Purdue

"When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the I made $280 on my first study guide!"

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.