15458  COURSE PROFILE
Course Level: Undergraduate
Frequency Offered: Generally offered once per year (Spring or Fall)  confirm course offerings for upcoming semesters by accessing the university Schedule of Classes.
Course Relevance (who should take this course?): This course is for students interested in working with 3D data. Examples include: physical/numerical simulation, computer vision, computer graphics, robotics, architecture/art/design, medical or anatomical data analysis.
Key Topics: 
Background Knowledge: 
Learning Resources: 
 geometry algorithms
 curves and surfaces
 curvature
 connections and parallel transport
 exterior algebra
 exterior calculus
 Stokes’ theorem
 simplicial homolog
 de Rham cohomology
 HelmholtzHodge decomposition
 conformal mapping
 finite element methods
 numerical linear algebra.
Applications include: approximation of curvature, curve and surface smoothing, surface parameterization, vector field design, and computation of geodesic distance 
Basic knowledge of linear algebra, vector calculus, and programming.


Course Goals/Objectives: 
Assessment Structure: 

 Our main goal is to show how fundamental geometric concepts (like curvature) can be understood from complementary computational and mathematical points of view.
 This dual perspective enriches understanding on both sides, and leads to the development of practical algorithms for working with realworld geometric data. Along the way we will revisit important ideas from calculus and linear algebra, putting a strong emphasis on intuitive, visual understanding that complements the more traditional formal, algebraic treatment.
 The course provides essential mathematical background as well as a large array of realworld examples and applications. It also provides a short survey of recent developments in digital geometry processing and discrete differential geometry.

 http://brickisland.net/DDGSpring2016/gradingpolicy/
 Assignments – 60%
 (10%) A1: Topological Invariants (+code setup)
 (10%) A2: Discrete Curvature
 (10%) A3: Surface Fairing
 (10%) A4: Direction Field Design
 (10%) A5: Surface Parameterization
 (10%) A6: Geodesic Distance
 Final Project – 24%
 (8%) – presentation
 (8%) – writeup
 (8%) – implementation
 Discussion – 16%
 (8%) – inclass/web participation
 (8%) – reading summaries/questions

 Prerequisites Required: (15112 and 15122) and (21141) and (21259)
 Minimum Grades in Prereqs: C
 Corequisites: None
 Prerequisite for:
 Antirequisites: None
 CrossListed: 15858
 Substitutes: None
 Related Courses: None
 Reservations: Some reservations are for Students in MSC; Some reservations are for Students in CS

Most Recent Syllabus: http://brickisland.net/DDGSpring2016/coursesyllabus/ 
Special Permission Required: No (if yes, please see Notes) 
Units: 12 
Course Website: http://geometry.cs.cmu.edu/ddg 
Department Website: https://www.csd.cs.cmu.edu 
College Website: http://www.cs.cmu.edu/ 
Sample class notes: http://www.cs.cmu.edu/~kmcrane/Projects/DGPDEC/paper.pdf 
Sample Assignment: http://brickisland.net/DDGSpring2016/assignments/ 
Sample Lecture Recording: Typically no recorded lectures 
Notes: This course is crosslisted with graduate level number 15858. Graduate students MUST enroll in the graduate level version of the course. Graduate students will NOT be enrolled into the undergraduate level course and will ber emoved from the waitlist without notification.

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_{last updated 05.12.2017}