15-458 Discrete Differential Geometry


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
  • Helmholtz-Hodge 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 real-world 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 real-world examples and applications. It also provides a short survey of recent developments in digital geometry processing and discrete differential geometry.
  • http://brickisland.net/DDGSpring2016/grading-policy/
  • 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%) – in-class/web participation
    • (8%) – reading summaries/questions
  • Prerequisites Required: (15112 and 15122) and (21141) and (21259)
  • Minimum Grades in Prereqs: C-
  • Corequisites: None
  • Prerequisite for: 
  • Anti-requisites: None
  • Cross-Listed: 15-858
  • Substitutes: None
  • Related Courses: None
  • Reservations: Some reservations are for Students in MSC; Some reservations are for Students in CS
Most Recent Syllabus: 
Special Permission Required: No
(if yes, please see Notes)
Units: 12
Course Website:
Department Website:
College Website:
Sample class notes:
Sample Assignment:
Sample Lecture Recording:
Typically no recorded lectures
Notes: This course is cross-listed with graduate level number 15-858. 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