Fundamentals of Surveying Exam (FS) Mapping, Plats, and Spatial Data Representation Syllabus

State the basic rules for interpreting contour lines on a topographic map.

Contours never cross or split; closely spaced contours indicate steep slopes and widely spaced indicate gentle slopes; closed contours indicate hills (or depressions with hachures); contours form a 'V' pointing upstream when crossing streams/valleys.

How do you compute ground slope between two contour lines on a map?

$$S = \frac{\Delta H}{D}\times 100\% ,$$ where $\Delta H$ is the elevation difference (contour interval times number of intervals) and $D$ is the horizontal ground distance between them.

What is the difference between an 'index contour' and an 'intermediate contour'?

Index contours are heavier lines drawn at every fifth contour and labeled with their elevation; intermediate contours are the lighter, unlabeled lines between index contours.

What is a 'depression contour' and how is it symbolized?

A closed contour representing a basin or pit where elevation decreases inward. It is drawn with short hachure tick marks pointing toward the bottom (downhill) of the depression.

In digital terrain modeling, what is the difference between a DEM, DTM, and DSM?

A DEM (digital elevation model) is a gridded bare-earth elevation surface; a DTM (digital terrain model) is bare-earth elevation often with breaklines/features; a DSM (digital surface model) includes above-ground features such as buildings and vegetation (first-return surface).

What is a TIN in terrain representation, and how does it differ from a grid DEM?

A TIN (triangulated irregular network) models a surface as contiguous, non-overlapping triangles connecting irregularly spaced points. Unlike a uniform grid DEM, it places more vertices where terrain is complex and fewer where it is smooth, preserving breaklines efficiently.

What is a 'breakline' in a terrain model?

A linear feature (such as a ridge, channel, curb, or top/bottom of bank) that forces the surface model to honor an abrupt change in slope, preventing triangles from spanning across the discontinuity.

In CAD drafting, what is the difference between model space and paper (layout) space?

Model space is where geometry is drawn at full (1:1) real-world scale; paper/layout space is where viewports, title blocks, annotations, and the final plotted sheet are composed at a chosen plot scale.

What does a CAD 'layer' provide in survey drafting?

A layer organizes drawing entities by category (e.g., boundary, contours, utilities, text) and controls their color, linetype, lineweight, and visibility, allowing selective display and standardized plotting.

What is the U.S. National CAD Standard (NCS) primarily used to standardize?

Layer naming conventions, line types/weights, symbols, text styles, sheet organization, and drawing format so CAD files are consistent and exchangeable across disciplines and firms.

In CAD, what is the difference between an absolute and a relative coordinate entry?

Absolute coordinates are referenced to the drawing origin ($0,0$); relative coordinates are referenced to the last point entered (often written with an @ prefix, e.g., @dx,dy or @distance<angle).

What is 'field-to-finish' (description coding) in survey mapping?

A workflow where field data collectors assign feature/description codes to each point so that, upon import, CAD software automatically draws symbols, connects linework, and applies layers—producing a near-finished drawing with minimal manual editing.

In field-to-finish coding, what is the purpose of line/figure control codes such as 'begin line,' 'close,' and 'curve'?

They tell the software how to connect points into linework: starting a new line string, closing a figure back to its start, or fitting a curve through points—automating the drafting of features like edges of pavement and buildings.

What is the U.S. National Map Accuracy Standards (NMAS) horizontal accuracy requirement for maps at scales larger than $1{:}20{,}000$?

No more than $10\%$ of well-defined test points may be in error by more than $\frac{1}{30}$ inch at map scale (for scales larger than $1{:}20{,}000$); for $1{:}20{,}000$ and smaller the limit is $\frac{1}{50}$ inch.

What is the NMAS vertical accuracy standard?

No more than $10\%$ of elevations tested may be in error by more than one-half the contour interval; errors at checkpoints may be reduced by assuming a horizontal displacement within the permissible horizontal error.

What does the modern ASPRS Positional Accuracy Standard use to express accuracy instead of map-scale fractions?

It specifies accuracy directly in ground units at the $95\%$ confidence level using RMSE (e.g., RMSE$_x$, RMSE$_y$, RMSE$_z$), independent of map scale or contour interval.

How is the root-mean-square error (RMSE) of map coordinates computed?

$$\text{RMSE} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(z_i - z_{i,\text{check}}\right)^{2}},$$ the square root of the mean of squared differences between mapped and surveyed (check) values.

For a normally distributed error, how is the $95\%$ horizontal accuracy related to the horizontal RMSE (RMSE$_r$)?

$$\text{Accuracy}_r(95\%) \approx 1.7308 \times \text{RMSE}_r,$$ where $\text{RMSE}_r=\sqrt{\text{RMSE}_x^{2}+\text{RMSE}_y^{2}}$ (and vertical $95\% \approx 1.96\times\text{RMSE}_z$).

Define 'photogrammetry.'

The science and technology of obtaining reliable measurements, maps, and 3D information about physical objects and terrain through the analysis of photographic (and other imagery) data, typically aerial photographs.

What is the difference between a vertical, oblique, and true vertical aerial photograph?

A vertical photo is taken with the camera axis (nearly) pointing straight down; a true vertical has the axis exactly vertical; an oblique is intentionally tilted—high oblique includes the horizon, low oblique does not.

State the scale formula for a vertical aerial photograph over flat terrain.

$$S = \frac{f}{H} = \frac{\text{photo distance}}{\text{ground distance}},$$ where $f$ is the camera focal length and $H$ is the flying height above the ground (terrain).

For a vertical photo, how is photo scale computed when accounting for terrain elevation $h$ above datum?

$$S = \frac{f}{H - h},$$ where $H$ is flying height above datum and $h$ is the ground elevation; higher ground (larger $h$) yields a larger scale.

What is 'relief displacement' in an aerial photograph, and what causes it?

The radial shift of an image point away from (above datum) or toward (below datum) the principal point caused by the object's elevation difference. Its magnitude is $$d = \frac{r\,h}{H},$$ where $r$ is radial distance from the principal point, $h$ the object height, and $H$ the flying height above the base.

Define 'endlap' (forward overlap) and 'sidelap' in aerial photography and give typical values.

Endlap is the overlap between successive photos along a flight line (typically about $60\%$), required for stereo coverage. Sidelap is the overlap between adjacent flight lines (typically about $20\%$–$30\%$).

What is a stereoscopic model (stereomodel) and why is endlap required to form one?

A stereomodel is the 3D view formed when two overlapping photos taken from different positions are viewed stereoscopically. Endlap (about $60\%$) ensures each ground point appears on two consecutive photos, providing the parallax needed for 3D measurement.

What is 'parallax' in stereo photogrammetry and how does it relate to elevation?

Parallax is the apparent shift of a point's position between two overlapping photos due to the change in camera station. Higher (closer to camera) points have larger parallax; elevation is computed as $$h = H - \frac{B\,f}{p},$$ relating flying height $H$, air base $B$, focal length $f$, and parallax $p$.

What are Ground Control Points (GCPs) and why are they essential in photogrammetry?

GCPs are points with known, surveyed real-world coordinates that are identifiable in the imagery. They are used to scale, orient, and georeference the photogrammetric model (aerotriangulation) and to assess its accuracy.

List the three classic stages of orientation in analog/analytical photogrammetry.

Interior orientation (recovers camera geometry: focal length, fiducials, principal point), relative orientation (recreates the relative position/attitude of the two photos to form a stereomodel), and absolute orientation (scales and levels the model to ground control).

Compare a manned fixed-wing aircraft and a UAS (drone) as aerial imaging platforms.

Fixed-wing manned aircraft cover large areas efficiently at high altitude with large-format metric cameras; UAS/drones fly low and slow, capturing very high-resolution imagery over smaller sites at lower cost, ideal for frequent, small-area mapping but with shorter endurance and limited coverage.

What is GSD (Ground Sample Distance) in digital aerial imaging and how does flying height affect it?

GSD is the ground distance represented by one image pixel. $$\text{GSD} = \frac{p_{\text{pixel}}\,H}{f},$$ so lower flying height $H$ (or longer focal length $f$) gives a smaller GSD and finer resolution.

How does an active sensor like LiDAR differ fundamentally from a passive sensor like an aerial photographic camera?

An active sensor (LiDAR) emits its own energy (laser pulses) and measures the return, working day or night independent of sunlight; a passive sensor (camera) records reflected/emitted natural energy (sunlight) and depends on ambient illumination.

What does LiDAR stand for, and what is the basic principle of how it measures distance (time-of-flight)?

LiDAR = Light Detection And Ranging. It measures range from the round-trip travel time of an emitted laser pulse: $$R = \frac{c\,t}{2},$$ where $c$ is the speed of light and $t$ is the round-trip time.

What are LiDAR 'multiple returns' (first and last return) and what is each typically used for?

A single pulse can reflect off several surfaces. The first return often comes from the top of vegetation/canopy or structures (used for DSM), while the last return often reaches the bare ground (used for DTM/bare-earth modeling).

What is a LiDAR 'point cloud' and what is point density (points per square meter) used to describe?

A point cloud is the set of 3D (x, y, z) points returned from laser pulses representing scanned surfaces. Point density (pts/m$^2$) describes how finely the surface is sampled; higher density yields more detailed terrain and feature representation.

Compare airborne LiDAR, mobile (vehicle) LiDAR, and terrestrial (static) laser scanning.

Airborne LiDAR maps large areas/corridors of terrain from aircraft; mobile LiDAR mounts scanners on vehicles (with GNSS/IMU) for roadway/corridor mapping at driving speed; terrestrial/static laser scanning sets the scanner on a tripod for very high-density, high-accuracy scans of buildings, sites, and structures.

Why must airborne LiDAR and mobile LiDAR systems integrate GNSS and an IMU?

GNSS provides the sensor's absolute position and the IMU (inertial measurement unit) provides its attitude (roll, pitch, yaw). Together they georeference each laser return by giving the precise position and orientation of the moving scanner at the instant of each pulse.

What is LiDAR 'intensity' data and how is it useful in mapping?

Intensity is the strength of the returned laser energy for each point, related to the reflectivity of the surface. It produces a grayscale-like image that helps distinguish materials/features (e.g., pavement markings, water) and aids classification and feature extraction.

What is the standard file format for storing LiDAR point cloud data, and what is LAZ?

The LAS format (ASPRS LASer file format) is the industry standard for storing LiDAR point data including coordinates, intensity, return number, and classification. LAZ is its lossless compressed version.

In LiDAR processing, what is point 'classification' and name common ASPRS class codes.

Classification assigns each point a code identifying what it hit. Common ASPRS codes: $1=$ unclassified, $2=$ ground, $3$–$5=$ low/medium/high vegetation, $6=$ building, $7=$ noise/low point, $9=$ water.

What is orthorectification, and how does an orthophoto differ from a raw aerial photograph?

Orthorectification removes the geometric distortions of relief displacement and camera tilt using a DEM and camera parameters. The resulting orthophoto has a uniform scale throughout, so distances and areas can be measured directly like a map, unlike a raw perspective photograph.