Chapter 4: Maps, Data Entry, Editing, and Output

What is the purpose of a coordinate transformation in GIS?

To bring spatial data into a common earth-based coordinate system so all layers align

Why is coordinate transformation also called registration or georeferencing?

Because it registers layers to a map coordinate system using known reference points

What operations can a coordinate transformation perform besides converting coordinates?

Translation, rotation, and scale change within a coordinate system

Define translation in spatial data transformation.

Movement of all points the same distance in the same direction without rotation or resizing

What is a control point?

A point with known accurate coordinates used to align spatial data

List three criteria for selecting good control points.

1. High coordinate accuracy

2. Even spatial distribution

3. Easy to identify and stable location

Name four possible sources of control point coordinates.

Surveys, GPS, high-quality maps, digital data layers

What transformation uses linear equations to calculate map coordinates?

Affine transformation

How many control points are needed for affine transformation?

At least 3 mathematically, but 4+ are needed for good statistical fit

What statistical method is used to assess transformation quality?

Root Mean Square Error (RMSE)

Compare affine vs. conformal transformations.

Affine allows unequal scale changes; conformal requires equal scale in x and y directions

What is raster resampling?

Changing raster cell values when converting coordinate systems or cell sizes

Name three raster resampling methods.

1. Nearest neighbor

2. bilinear interpolation

3. cubic convolution

What is digitizing in GIS?

Capturing map data by tracing features into vector format

Give three reasons why digitizing is needed.

To create new maps, correct wrong features, or add missing features

What is the difference between heads down and heads up digitizing?

Heads down uses a tablet and puck; heads up uses a computer screen with images

How many control points are usually needed for digitizing?

At least 4, often called “tics”

What are typical accuracy ranges for manual digitizing?

Between 0.075 mm and 0.25 mm

Compare point mode, line mode, and stream digitizing (in ArcGIS?)

• Point mode records points

• Line mode records lines with vertices

• Stream mode automatically collects many vertices

What are common problems with manual digitizing?

Labor intensive, operator fatigue, errors, slow speed, registration issues

Define nodes and vertices in digitizing.

Nodes are line endpoints; vertices are intermediate points that define shape

What are undershoots and overshoots?

Errors where lines fail to connect (undershoot) or extend past the connection point (overshoot)

Explain dangle length, snap tolerance, and weed tolerance.

• Dangle length removes small dangling lines

• Snap tolerance connects close nodes

• Weed tolerance reduces excess vertices

What is spline interpolation used for?

To smooth digitized lines

How are attributes added during or after digitizing?

At time of digitizing with codes or later through database linking

What is scanning?

Converting paper maps into raster images using light sensors

What are drawbacks of scanning maps?

Includes all marks/stains, large files, must retrace features into vector

What is skeletonizing?

A line-thinning process applied to scanned rasters before vectorization

What is map generalization?

Simplifying or approximating real-world features when represented on a map

What factors influence map design and layout?

Target audience, purpose, viewing setting, available resources

List five essential map elements.

1. Title

2. scale

3. legend

4. north arrow

5. source/metadata

Why might a north arrow not always point straight up?

Because map orientation may differ from north

Give two risks of poor symbolization.

Overuse of shapes/colors causes confusion; unclear symbols hinder map reading

What are the four main principles of map design?

Legibility, visual contrast, visual balance, figure-ground relationship

How does visual balance differ from geometric balance?

Visual balance arranges elements around the visual center (slightly above geometric center)

What is figure-ground relationship in maps?

The visual distinction where some elements stand out as figure and others recede as background

Define metadata with examples.

Data about data, including source, date, coordinate system, and attributes

Affine Transformation Equations

$E = a_1x + b_1y + T_E$, $N = a_2x + b_2y + T_N$

What does the affine transformation do?

It converts digitizer/scanner coordinates $(x,y)$ into map projection coordinates $(E,N)$ by applying scale, rotation, and translation

What do E and N represent?

Map projection coordinates (Easting and Northing)

What do $x$ and $y$ represent?

Raw digitized coordinates from tablet or image

What do $T_E$ and $T_N$ represent?

Translation shifts that move the dataset into the correct location

What do $a_1, b_1, a_2, b_2$ represent?

Scale changes and rotation factors that adjust size and orientation

How many unknown parameters are in affine transformation?

6 total: $T_E, T_N, a_1, b_1, a_2, b_2$

How many equations does one control point provide?

2 equations (one for Easting, one for Northing)

Minimum number of control points needed

3 (for 6 equations), but 4+ are recommended for a better statistical fit

Why are more than 3 control points preferred?

Extra points allow statistical fitting and reduce errors from any single bad point

Formula for RMSE

$\text{RMSE} = \sqrt{\frac{1}{n}\sum e_i^2}$

What does RMSE measure?

The average error between the true control point coordinates and the transformed coordinates

What is $e_i$ in the RMSE formula?

Residual distance between a point’s true coordinate and its transformed coordinate

What is $n$ in the RMSE formula?

Number of control points used

Why is RMSE important in georeferencing?

It quantifies how well the transformation fits — smaller RMSE means higher accuracy