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GEOM 5624 ̶ SPECIAL TOPICS IN GEOMATICS
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: Director Approval
Advanced seminar dealing with topics in Geomatic Sciences, to be selected according to staff and student interests. The course will be designed to address professional current events, advanced skills, special knowledge, and/or particular topics of interest.

Program Description

Land Surveying is the science of determining the position of points on the surface of the Earth through the application of mathematics and the use of specialized instruments. The term “ Earth surface” refers to everything on Earth that can be explored: the bottom of the seas, bays, lakes and rivers; the interior of caves and mines; mountains and deserts; and even the frozen and desolated polar regions. Surveying includes the measurement of angles and distances, the establishment of horizontal and vertical control points, plan confection, cadastral measurements, highway tracing and building locations, submarine topography and oceanic depths, plus the location of legal boundaries.

Degree Offered

The Department of Civil & Environmental Engineering and Land Surveying offers undergraduate courses leading to the degree of Bachelor of Science in Land Surveying and Mapping (B.S.L.S.).

Mission

Provide the theoretical and technical knowledge through an educational experience that enriches the lives of program students so that they are prepared to enhance the surveying profession and protect the health and welfare of the public while expanding the base of knowledge through research and scholarship.

Objectives

1. Contribute to society with professionals that execute their work following the principles of moral conduct and ethics.

2. Generate graduates with the necessary knowledge and techniques to pursue education at a graduate level.

3. Generate graduates that can be employed and successfully work in a broad range of sub disciplines within the field.

4. Demonstrate an understanding of the need for lifelong learning via successful completion of continuous education.

Outcomes

The graduates of the Land Surveying and Mapping program will have:

1. An ability to identify, formulate, and solve broadly defined technical or scientific problems by applying knowledge of mathematics and science and/or technical topics to areas relevant to the discipline.

2. An ability to formulate or design a system, process, procedure or program to meet desired needs.

3. An ability to develop and conduct experiments or test hypotheses, analyze and interpret data and use scientific judgment to draw conclusions.

4. An ability to communicate effectively with a range of audiences.

5. An ability to understand ethical and professional responsibilities and the impact of technical and/or scientific solutions in global, economic, environmental, and societal contexts.

6. An ability to function effectively on teams that establish goals, plan tasks, meet deadlines, and analyze risk and uncertainty.

Enrollment

ACADEMIC YEAR	ENROLLMENT
2013-2014	75
2014-2015	71
2015-2016	51
2016-2017	37
2017-2018	24
2018-2019	18
2019-2020	20

Graduation Data

ACADEMIC YEAR	DEGREES AWARDED
2012-2013	19
2013-2014	13
2014-2015	12
2015-2016	13
2016-2017	15
2017-2018	12
2018-2019	3

Curriculum

Curriculum Sequence

Minimum Graduation Requirements

Graduation Requirements

The Department of Civil & Environmental Engineering and Land Surveying offers undergraduate courses leading to the degree of Bachelor of Science in Land Surveying and Mapping (BSLS). In order to get this degree, the student must complete the following minimum requirements:

Minimum Graduation Requirements

4 Credit-hours in Mathematics

9 Credit-hours in Basic Sciences

18 Credit-hours in Socio-Humanistic Studies and Languages

9 Credit-hours in Engineering Science and Management

33 Credit-hours in Surveying

38 Credit-hours in Geomatic Sciences

6 Credit-hours in Department Electives

3 Credit-hours in Free Elective

120 Total Credit-hours

Developmental Studies

All students who apply for admission and those selected who are admitted to Land Surveying and Mapping Program must show evidence that they have acquired the necessary skills and abilities to progress through this major. Those failing to do so (as reflected by the results of their College Entrance Examination Board tests, PUPR’s placement test results, previous university experience, other tests, or criteria) will be required to take developmental courses. These courses are designed to help students to overcome deficiencies in languages, mathematics, and or science. These developmental courses are in addition to the 120 credits of the Land Surveying and Mapping Program. The courses are awarded their corresponding credits according to the contact hours. The courses are the following:

Developmental Studies Component

Course	Title	Credit-Hours
MATH 0102	Preparatory Mathematics	3
MATH 0106	Elementary Algebra	3
MATH 0110	Intermediate Algebra	3
MATH 1330	Precalculus I	3
MATH 1340	Precalculus II	3
SCIE 0110	Introduction to Physics	3
ATUL 0100	Adjustment to University Life	3
ENGL 0100	Preparatory English	3
ENGL 0110	English Grammar	3
SPAN 0100	Preparatory Spanish	3
SPAN 0110	Spanish Grammar	3

Course Description

Land Surveying Courses

SURV 2095 ̶ PRINCIPLES OF SURVEYING FOR ENGINEERS LAB ENGINEERS
One credit-hour. Three hours per week and field laboratory. Prerequisites: ENGI 1140, ENGI 2210
Through conferences and field practices, the student will learn the basic surveying concepts applicable for route design and construction of route.

SURV 2202 ̶ SURVEYING ANALYSIS
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: MATH 1340
Analytical geometry review and elements of linear algebra as applied to the analysis of land surveying problems; and introduction to plane surveying calculations

SURV 2300 ̶ LEGAL ASPECTS IN SURVEYING I
Three credit-hours. Two two-hour lecture period per week. Prerequisite: GEOM 2102
Aspects of Local and Federal legal system related to the professional Surveyor practice. Ethical principles in the surveying profession. Legal aspects of the federal Retract Systems. Federal surveying practices.

SURV 2302 ̶ FUNDAMENTALS OF SURVEYING
Four credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 2202 and MATH 1350. Corequisite: SURV 2303
The theory and practice of land surveying. Measurement of difference in elevations using leveling network. Measurement of distances using tapes and other methods; also measurement of angles. Application to boundary identification.

SURV 2303 ̶ FUNDAMENTALS OF SURVEYING LABORATORY
Zero credit-hours. One four-hour laboratory period per week. Prerequisites: SURV 2202 and MATH 1350. Corequisite: SURV 2302
Laboratory practice of land surveying related to course SURV 2302. The practices will concentrate on the uses of Land Surveying Instruments. Measurement of difference in elevations using differential and trigonometric leveling. Measurement of distances using tapes and other methods; also measurement of angles. Application to Traverse and Polygonal closure.

SURV 2304 ̶ LEGAL ASPECT IN SURVEYING II
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: SURV 2300
Aspects of Local legal system related to the professional Surveyor practice. Ethical principles in the surveying profession. Surveying permit regulations applicable.

SURV 2802 ̶ VISUALIZATION OF SPATIAL INFORMATION
Three credit- hours. Two two-hour lecture periods per week. Prerequisites: GEOM 2800, MATH 1340
Basic knowledge of spatial information management and visualization using computer software (CAD).

SURV 3204 ̶ ANALYSIS AND ADJUSTMENT OF SURVEY MEASUREMENT
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 3306 (MIN C), SURV 3307
The concept of measurement, precision and accuracy, random, systematic and blunder errors are introduced in this course. Probability, reliability and statistical testing applied to analysis of survey data. Error propagation and alignment, and some examples of least-squares adjustment method are presented in this course.

SURV 3306 ̶ ADVANCED SURVEYING
Four credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 2302, SURV 2303, Concurrent: SURV 3307
Use of conventional signs to make sketches and field notes. Selection and use of equipment for topographic survey. Carrying out the topographic survey in the field. Computation of the results of the survey, plot of the points (manually and computer-assisted). Interpolation of contour lines. Area and volume computation.

SURV 3307 ̶ ADVANCED SURVEYING LABORATORY
Zero credit-hours. One four-hour laboratory period per week Prerequisites: SURV 2302, SURV 2303, Concurrent: SURV 3306
Laboratory and field practice related to Advanced Surveying course topics.

SURV 3308 ̶ SURVEYING PRACTICE
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 3402 and SURV 3403
Discussion and development of land surveying project. The course will require field work, boundary and topography survey, design of evidence gathering, resurvey, retracement and analysis techniques for complex Land Survey System, riparian, mineral, land-grant and fraudulent surveys; case studies.

SURV 3402 ̶ ROUTE SURVEYING
Four credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 3306, SURV 3307 Concurrent SURV 3403
Geometric properties and design elements of horizontal and vertical alignment needed for the design and layout of routes.

SURV 3403 ̶ ROUTE SURVEYING LABORATORY
Zero credit-hours. One four-hour laboratory period per week. Prerequisites: SURV 3306, SURV 3307; Concurrent SURV 3402
Laboratory practice of the main concepts related to course SURV 3402: Route Survey. The practices will concentrate in the application of geometric properties and design elements of horizontal and vertical alignment needed for the design and layout of routes.

SURV 3804 ̶ COMPUTER APPLICATION FOR LAND SURVEYORS
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 2302, SURV 2303, SURV 2802
Computer applications used for the land surveying professional practice. Computer drafting.

SURV 4404 ̶ CONSTRUCTION SURVEYING
Three credit-hours. Two two-hour lecture periods per week and field laboratory. Prerequisites: SURV 3402, SURV 3204
Principles of construction surveying as used in various types of construction projects.

Geomatic Sciences Courses

GEOM 2102 ̶ INTRODUCTION TO GEOMATICS
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: None
Geomatics comprises the science, technology, and art involved in the measurement, representation, analysis, management, retrieval and display of spatial data concerning both the Earth’s physical features and the built environment. It includes cadastral surveying, mapping sciences, land management, geographic information systems, geodesy, photogrammetry, remote sensing, hydrographic surveying and surveying ocean mapping. It has applications in all disciplines which depend on spatial data, including environmental studies, planning, engineering, navigation, geology and geophysics, oceanography, land development, land ownership, land administration and land use management. It is thus fundamental to all the geosciences disciplines which use spatially related data. This course offers the student an introduction to the fundamentals of these topics, a review of historic events and future of the profession.

GEOM 2800 ̶ INFORMATION SYSTEMS FOR LAND SURVEYORS
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: None
In this course the students will develop skills in the use of computers, component, operative systems, printers, plotters, scanners, graphics, digital images, software, presentation and written data used in the presentation. They will also be introduced to information systems concepts and the appropriate techniques for effective administration and the use of them. The course will place special attention to the design, development and management of databases either for office management or Geographic Information Systems.

GEOM 3502 ̶ FUNDAMENTALS OF GEODESY
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 2302 and SURV 2303
Introduce the concepts of geodesy, geoids, earth gravity field. Relate Geodesy to other geosciences. Introduce the integrated Global Geodetic Observing System (IGGOS) and the concept of geodetic network.

GEOM 3604 ̶ CARTOGRAPHIC DESIGN
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: GEOM 2102
Introduction to concepts and theories of cartographic design. Special attention to cartographic modeling and visualization through the use of thematic cartography concepts.

GEOM 3606 ̶ DIGITAL CARTOGRAPHY
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: GEOM 3604
Introduction to digital cartography concepts. The course covers techniques, error handling and software used for the creation of vector and raster data.

GEOM 3608 ̶ GEOGRAPHIC INFORMATION SYSTEMS
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: GEOM 3606 (Minimum C), SURV 2302 and SURV 2303
Discussion of topics related to design, development and application of Geographic Information Systems. Emphasis on problem-solving using appropriate modeling tools.

GEOM 3702 ̶ ELEMENTS OF PHOTOGRAMMETRY
Four credit hours. Two two-hour lecture periods per week and field laboratory. Prerequisites: SURV 3306 and SURV 3307. Corequisite: GEOM 3703
Principles of Photogrammetry using aerial and terrestrial photography. History of photogrammetry, aerial cameras and camera calibration, geometry of the aerial photograph, stereoscopy and stereoscopes, parallax, and the theory and techniques of orientation. Stages of planning, flight design, and the terrestrial controls in Photogrammetry surveys.

GEOM 3703 ̶ ELEMENTS OF PHOTOGRAMMETRY LABORATORY
Zero credit-hours. One four-hour laboratory period per week. Prerequisites: SURV 3306 and SURV 3307. Corequisite: GEOM 3702
Laboratory practice for the GEOM 3702: Elements of Photogrammetry course.

GEOM 4104 ̶ DENDROLOGY
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: SURV 2302 and SURV 2303
Introduction to trees, their identifying characteristic, habitats, distribution, and systematic classification.

GEOM 4108 ̶ SENIOR PROJECT I
One credit-hour. One two-hour lecture periods per week. Prerequisites: SURV 3308, GEOM 4610, and Department Head Authorization.
Senior Project research proposal. Thru their respective research, students should be able to apply the skills and knowledge acquired in their previous years of study to a land surveying related research. Individual presentations will be made to the professors during the quarter. At the end of the quarter, final presentations will be made to a panel of professor. Approval of the research proposal should wrap-up this course.

GEOM 4109 ̶ SENIOR PROJECT II
Four credit-hours. Two two-hour lecture periods per week. Prerequisites: GEOM 4108 and Department Head Authorization.
Implementation of the student’s research proposed in Senior Project I course. Thru the research students should be able to apply the skills and knowledge acquired in their previous years of study. At the end of the quarter, a public defense of the research will be made to a panel of professor. Technical report should wrap-up this course.

GEOM 4112 ̶ SENIOR PROJECT II Extension
Zero credit-hours. Prerequisites: Department Head Authorization.
Course that provides the student the opportunity to continue the development of his/her Senior Project II.

GEOM 4504 ̶ SURVEYING SPACE TECHNIQUES
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: GEOM 3502
The very basic principles of satellite geodesy and the concept of satellite positioning techniques will be introduced. Satellite Laser Ranging, altimetry, and Very Long Baseline, Interferometry will be discussed briefly.

GEOM 4510 ̶ GLOBAL POSITIONING SYSTEM
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: GEOM 3502
Fundamentals of coordinate systems used in satellite geodesy, importance of the earth’s gravity field and perturbation forces acting on the satellites will be introduced. Elements of planning and carrying out GPS-survey will be discussed.

GEOM 4610 ̶ LAND DEVELOPMENT
Three credit-hours. Two two-hour lecture periods per week and field laboratory. Prerequisite: GEOM 3608
This course covers a discussion on the principles and regulations governing the use and development of land. Historic review of land use patterns in Puerto Rico. Revision of zoning and subdivision regulations used in Puerto Rico.

GEOM 4612 ̶ THE MUNICIPAL REFORM LEGAL SYSTEM
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: GEOM 4610
Land Use planning and development process at the municipal level changed with adoption of Law 81 of August of 1991, better known as Ley de Municipios Autónomos (Municipal Reform Law). This course emphasizes on topics of this law, especially the ones related to land use planning process.

GEOM 4702 ̶ INTRODUCTION TO REMOTE SENSING & IMAGE INTERPRETATION
Three credit-hours. Two two-hour lecture periods per week. Prerequisites: GEOM 3702 and GEOM 3703
This course introduces the students to the principles of image interpretation. The interpretation is based on aerial photographs and satellite imagery. At the end of the course students should be able to correctly use remote sensing imagery. Also, they will be able to analyze and understand the basic concepts in the field.

GEOM 5600 ̶ GEOSPATIAL INFORMATION SCIENCE FUNDAMENTALS
Four credit-hours. One four-hour lecture per week. Prerequisite: None
This course provides an introduction to the principles and concepts necessary to work in a digital cartographic environment, especially in the context of geographic information systems (GIS). The course also introduces the student to the basic concepts of performing spatial analyses using a geographic information system (GIS). The first part of the course gives an overview of basic cartography and mapping concepts and theories, which are fundamental to understanding and using a GIS. The second part of the course focuses on concepts and theories of GIS, including some of it the analysis capabilities. Other technologies such as remote sensing and global navigation satellite systems will be discussed.

GEOM 5614 ̶ CADASTRAL & LAND INFORMATION SYSTEMS
Three credit hours. Two two-hour lecture periods per week. Prerequisite: GEOM 3608
Principles of cadastral systems, their history and contemporary development globally and in Puerto Rico. Emphasis on Land Information Systems and multipurpose cadastre.

GEOM 5616 ̶ GIS FOR SITE DESIGN
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: None
This is an introductory to intermediate-level GIS course that focuses on the application of geographic information systems in the practice of urban and regional planning, with a focus on site design. Topics covered will include data models and structures, coordinate systems and projections, thematic mapping, spatial analysis, acquisition and integration of spatial data from various sources, and GIS application development.

GEOM 5624 ̶ SPECIAL TOPICS IN GEOMATICS
Three credit-hours. Two two-hour lecture periods per week. Prerequisite: Director Approval
Advanced seminar dealing with topics in Geomatic Sciences, to be selected according to staff and student interests. The course will be designed to address professional current events, advanced skills, special knowledge, and/or particular topics of interest.

Laboratories

The Land Surveying and Mapping Program develops skills on three main laboratories: GIS and Cartography Lab, Remote Sensing and Photogrammetry Lab, and Engineering Simulations and Land Surveying Lab. Since the surveying profession is practiced mainly in the field, practical experience with the use of our equipment is acquired in the field.

yade.geom module¶

Create arbitrarily-aligned box composed of facets, with given center, extents and orientation. If any of the box dimensions is zero, corresponding facets will not be created. The facets are oriented outwards from the box.

center (Vector3) – center of the box
extents (Vector3) – half lengths of the box sides
orientation (Quaternion) – orientation of the box
wallMask (bitmask) – determines which walls will be created, in the order -x (1), +x (2), -y (4), +y (8), -z (16), +z (32). The numbers are ANDed; the default 63 means to create all walls
**kw – (unused keyword arguments) passed to utils.facet

list of facets forming the box

Create arbitrarily-aligned bunker, composed of facets, with given center, radii, heights and orientation. Return List of facets forming the bunker;

dBunker ______________ | | | | | | hBunker | | | | | | |____________| \ / \ / \ / hOutput \ / \____/ | | |____| hPipe dOutput

center (Vector3) – center of the created bunker
dBunker (float) – bunker diameter, top
dOutput (float) – bunker output diameter
hBunker (float) – bunker height
hOutput (float) – bunker output height
hPipe (float) – bunker pipe height
orientation (Quaternion) – orientation of the bunker; the reference orientation has axis along the \(+x\) axis.
segmentsNumber (int) – number of edges on the bunker surface (>=5)
wallMask (bitmask) – determines which walls will be created, in the order up (1), down (2), side (4). The numbers are ANDed; the default 7 means to create all walls
angleRange ((θmin,Θmax)) – allows one to create only part of bunker by specifying range of angles; if None , (0,2*pi) is assumed.
closeGap (bool) – close range skipped in angleRange with triangular facets at cylinder bases.
**kw – (unused keyword arguments) passed to utils.facet;

Create arbitrarily-aligned cone composed of facets, with given center, radius, height and orientation. Return List of facets forming the cone;

center (Vector3) – center of the created cylinder
radiusTop (float) – cone top radius
radiusBottom (float) – cone bottom radius
radiusTopInner (float) – inner radius of cones top, -1 by default
radiusBottomInner (float) – inner radius of cones bottom, -1 by default
height (float) – cone height
orientation (Quaternion) – orientation of the cone; the reference orientation has axis along the \(+x\) axis.
segmentsNumber (int) – number of edges on the cone surface (>=5)
wallMask (bitmask) – determines which walls will be created, in the order up (1), down (2), side (4). The numbers are ANDed; the default 7 means to create all walls
angleRange ((θmin,Θmax)) – allows one to create only part of cone by specifying range of angles; if None , (0,2*pi) is assumed.
closeGap (bool) – close range skipped in angleRange with triangular facets at cylinder bases.
**kw – (unused keyword arguments) passed to utils.facet;

Create arbitrarily-aligned cylinder composed of facets, with given center, radius, height and orientation. Return List of facets forming the cylinder;

center (Vector3) – center of the created cylinder
radius (float) – cylinder radius
height (float) – cylinder height
radiusTopInner (float) – inner radius of cylinders top, -1 by default
radiusBottomInner (float) – inner radius of cylinders bottom, -1 by default
orientation (Quaternion) – orientation of the cylinder; the reference orientation has axis along the \(+x\) axis.
segmentsNumber (int) – number of edges on the cylinder surface (>=5)
wallMask (bitmask) – determines which walls will be created, in the order up (1), down (2), side (4). The numbers are ANDed; the default 7 means to create all walls
angleRange ((θmin,Θmax)) – allows one to create only part of bunker by specifying range of angles; if None , (0,2*pi) is assumed.
closeGap (bool) – close range skipped in angleRange with triangular facets at cylinder bases.
**kw – (unused keyword arguments) passed to utils.facet;

Please, do not use this function directly! Use geom.facetCylinder and geom.facetCone instead. This is the base function for generating cylinders and cones from facets.

Create arbitrarily-aligned helix composed of facets, with given center, radius (outer and inner), pitch and orientation. Return List of facets forming the helix;

center (Vector3) – center of the created cylinder
radiusOuter (float) – outer radius
radiusInner (float) – inner height (can be 0)
orientation (Quaternion) – orientation of the helix; the reference orientation has axis along the \(+x\) axis.
segmentsNumber (int) – number of edges on the helix surface (>=3)
angleRange ((θmin,Θmax)) – range of angles; if None , (0,2*pi) is assumed.
**kw – (unused keyword arguments) passed to utils.facet;

Create arbitrarily-aligned Parallelepiped composed of facets, with given center, extents, height and orientation. If any of the parallelepiped dimensions is zero, corresponding facets will not be created. The facets are oriented outwards from the parallelepiped.

center (Vector3) – center of the parallelepiped
extents (Vector3) – half lengths of the parallelepiped sides
height (Real) – height of the parallelepiped (along axis z)
orientation (Quaternion) – orientation of the parallelepiped
wallMask (bitmask) – determines which walls will be created, in the order -x (1), +x (2), -y (4), +y (8), -z (16), +z (32). The numbers are ANDed; the default 63 means to create all walls
**kw – (unused keyword arguments) passed to utils.facet

list of facets forming the parallelepiped

Create arbitrarily-aligned polygon composed of facets, with given center, radius (outer and inner) and orientation. Return List of facets forming the polygon;

center (Vector3) – center of the created cylinder
radiusOuter (float) – outer radius
radiusInner (float) – inner height (can be 0)
orientation (Quaternion) – orientation of the polygon; the reference orientation has axis along the \(+x\) axis.
segmentsNumber (int) – number of edges on the polygon surface (>=3)
angleRange ((θmin,Θmax)) – allows one to create only part of polygon by specifying range of angles; if None , (0,2*pi) is assumed.
**kw – (unused keyword arguments) passed to utils.facet;

Please, do not use this function directly! Use geom.facetPloygon and geom.facetHelix instead. This is the base function for generating polygons and helixes from facets.

yade.geom. facetSphere ( center, radius, thetaResolution=8, phiResolution=8, returnElementMap=False, **kw ) [source] ¶

Create arbitrarily-aligned sphere composed of facets, with given center, radius and orientation. Return List of facets forming the sphere. Parameters inspired by ParaView sphere glyph

center (Vector3) – center of the created sphere
radius (float) – sphere radius
thetaResolution (int) – number of facets around “equator”
phiResolution (int) – number of facets between “poles” + 1
returnElementMap (bool) – returns also tuple of nodes ((x1,y1,z1),(x2,y2,z2),…) and elements ((id01,id02,id03),(id11,id12,id13),…) if true, only facets otherwise
**kw – (unused keyword arguments) passed to utils.facet;