3 credits
Spring 2026 Lecture Upper Division
The course will cover topics necessary for the modern "3D surveyor": it will give an overview of coordinate frames used in geodesy, surveying and mapping. What are the relationships between the various (3D) coordinate frames? How are the results of 1D/2D/3D surveys being mapped to a 2D, not necessarily flat, surface? Mapping models (projecting equations) and their characteristics will be discussed, based on the fundamentals of differential geometry and curvilinear coordinates. (Differential) Geometry and Multivariate Calculus: Cartesian, Spherical and Ellipsoidal coordinates and transformations between them. Radius of curvature. Jacobian and Metric Matrices. Geometric Geodesy: Earth-fixed frames. Geocentric, topocentric and local frames. Radius of curvature in the meridian and the prime vertical. [Differential coordinate transformations. Commutative diagram.] Reference sphere. Shortest distance over the sphere/ellipsoid. Reference ellipsoid. Reductions to the ellipsoid. Map projections: Basics of mapping. Conformal mapping. Mercator, Lambert, Stereographic. State Plane Coordinate Systems. Intro to Physical Geodesy: Shape of the Earth. Earth rotation. Inertial frames. Precession, Nutation, Polar Motion, Length of Day. Time Systems. Gravity and Gravitation. Potential Energy. Equipotential surfaces. Geoid. Height differences and the flow of water. Orthometric heights. Geodetic Reference Datums/Frames/Systems: NAD27, NGVD29, IGSN71, WGS72, GRS80, NAD83, WGS84, NAVD88, IERS Standards 1992, HARNs, GEOID90, GEOID93, GEOID96, GEOID99, GEOID2003, GEOID2009.
Learning Outcomes1Solve most 1D/2D/3D survey problems based on rigorous 1D-, 2D-, 3D-modelling.
2Perform coordinate transformations.
3Assess mapping characteristics based on principles of differential geometry.
4Develop mapping dedicated to any engineering project.
5Generate novel engineering solutions to newly presented survey problems.
6Evaluate 1D-, 2D-, 3D-models, the coordinate frames used for these and their interrelationships.
7Model the physical reality underlying most geometry-based models, in earth-fixed as well in inertial space.
Restrictions
made by Purdue students.