In this assignment, you will write code to visualize two-dimensional scalar fields through the use of contours. Contours will be constructed using the Marching Squares algorithm discussed in class. Your main task will be to implement this algorithm.

Please click here to create your repository


This assignment is designed to teach you the basics of scalar field visualization through combinations of geometric features (isocontours) and color mapping. Specific objectives include:

  • Implementing the marching squares algorithm for extracting isocontours in a piecewise manner.
  • Utilizing a case-table structure to maintain repeated computational structure and develop the algorithm in a compact way
  • Further practice in using SVG paths and d3’s features for constructing them
  • Experimenting with visual encoding of scalar fields utilizing both isocontour outlines and filled isocontours.


We will again attempt to visualize a weather simulation of Hurricane Isabel that we used in A06. This dataset is stored in the file data.js, but instead of using the array data, we will mostly focus on two arrays, temperatureCells and pressureCells. Each array contains objects that look like:

    NW: value-at-nw-corner,
    NE: value-at-ne-corner,
    SW: value-at-sw-corner,
    SE: value-at-se-corner,
    Row: i,
    Col: j

So, unlike A06, the main selections we are doing will be cell-focused rather than vertex-focused. Thus, each element you draw will be based on the collection of four values stored in the four corners (northwest (NW), northeast (NE), southwest (SW), and southeast (SE) of the cell, rather than just drawing each data value as one square. Thus, instead of having a grid of \(50\times50\) squares, this assignment will process the data as a grid of \(49\times49\) cells.

Before writing the full marching squares code in Parts 1 and 2, we recommend that you try to understand at a high level what the template code is doing. A good way to start is to write code that adds a fixed, small shape inside of each square (i.e. an svg rect or circle) regardless of what marching squares case the cell corresponds to. Particularly, note how the functions includesOutlineContour() and includesFilledContour() are used as d3 selection filters in their respective plot creation functions createOutlinePlot() and createFilledPlot(). The functions you code in this assignment will be called by these components.

Part 1: Implementing Contour Outlines

First, you will implement the computation of outline contours using marching squares. To do this, you will complete the skeleton code function generateOutlineContour() in a11.js. This function should return an SVG path specifier (the d attribute) for the contour located at a given cell d. When successfully implemented, you should see images that look like:

plot1-temp plot1-pres
Temperature Contours Pressure Contours

Note that, like in A06 we have spaced out each cell to be exactly \(10\times10\) pixels. So, within generateOutlineContour(), you should return a path specified using units between \([0,10]\) for both the \(x\)- and \(y\)-coordinates. We have provided transformations so that the position \((0,0)\) in the local coordinate space for each cell corresponds to the SW value, and the position \((10,10)\) corresponds to the NE value.

Thus, the way the skeleton code is set up, the path for each separate square can be specified in a “local” coordinate system (use your web browser’s debugger to inspect the DOM after executing the skeleton code and pay attention to the transform attribute in each of the g elements). In other words, you should not have to write code to decide on what position along the SVG each square should be drawn.

You may choose to generate the SVG path specifier however you please. The string that you return must be in SVG path syntax, so you can write functions for this on your own. Alternatively, you could also use d3.line() to compute this string, similar to in past assignments. Note that for certain cases, you may need to return multiple, disconnected lines, so if you use d3 you may need to use the .defined() function to create breaks in the line.

Part 2: Implementing Filled Contours

Second, you will implement the computation of filled contours, again using marching squares to compute the boundary of contours. To do this, you will complete the skeleton code function generateFilledContour() as well as the function includesFilledContour() in a11.js. When successfully implemented, you should see images that look like:

plot2-temp plot2-pres
Temperature Filled Contours Pressure Filled Contours

You will have to take care to notice the order in which filled contours are draw. In this case, we will draw multiple, overlapping contours and rely on the order in which they are drawn to see them visually. In the function createFilledPlot() you’ll see that currentContour is set in each iteration of the loop. Consequently, the function createFilledPlot() draws the contours will highest value first and then layers the lower values on top of them. A filled contour should just indicate all regions that have the function value currentContour or lower.

Thus, you need draw something in a different set of cells than in Part 1,selected with a condition you’ll specify in includesFilledContour(). And, the case table that you produce in generateFilledContour() must provide the full outline for the polygon that spans the cell, rather than just the polyline that lives on its border.

All visual characteristics, such as the color map used to set the fill color, have been provided for you and you should not need to modify these.


You should use git to submit all source code files. The expectation is that your code will be graded by cloning your repo and then executing it within a modern browser (Chrome, Firefox, etc.)

Please provide a file that provides a text description of how to run your program and any parameters that you used. Also document any idiosyncrasies, behaviors, or bugs of note that you want us to be aware of.

To summarize, my expectation is that your repo will contain:

  1. A file
  2. A index.html file
  3. An a11.js file
  4. All other Javascript files necessary to run the code (including data.js and d3.js plus any others you require)
  5. Any .css files containing style information



Reason Value
Bugs or syntax errors -10 each bug at grader's discretion to fix

Point Breakdown of Features

Requirement Value
Consistent modular coding style 5
External documentation ( following the template provided in the base repository 5
Header documentation, Internal documentation (Block for functions and Inline descriptive comments). Wherever applicable / for all files 10
Expected output / behavior for your chart based on the assignment specification, including

Correctly implementing the case table for Part 120
Correctly interpolating positions for each case table for Part 115
Correctly selecting which cells to draw in Part 2 with includesFilledContour10
Correctly implementing the case table for Part 220
Correctly interpolating positions for each case table for Part 215

Total 100/100

Cumulative Relationship to Final Grade

Worth 6% of your final grade

Extra Credit

Implementing features above and beyond the specification may result in additional extra credit, please document these in your Particularly, you may want to consider additional user interface features that allow you to select a different number of contours or otherwise inspect or annotate the visualization more closely.