Description
Introduction
For this assignment, you’ll be working with data from NASA and the USGS to visualize on a
globe the locations where earthquakes happened between 1905 and 2007. Visualizations
incorporating geospatial data are used and analyzed in many different contexts, including
navigating a city (as seen in GPS devices), commercial development, and setting
governmental policy. This area also receives a significant amount of research attention. For
example, Prof. Vipin Kumar and others at the University of Minnesota are working on
visualizing and understanding global warming datasets as part of an NSF project (you can
find more information at http://climatechange.cs.umn.edu/).
Your assignment should look like the image below when you’ve finished it.
The earthquake dataset you’ll be using includes 13,540 different earthquakes. The Earth
texture dataset from NASA is available in resolutions down to 500m/pixel (although getting
this to display on your graphics card is well beyond the scope of this assignment).
In this assignment, you will learn to:
• Visualize real-world geographical data on a 3D textured globe
• Apply textures to 3D objects
• Algorithmically create a deforming 3D mesh and display it using vertex buffers
• Define normal vectors and texture coordinates for a sphere
• Convert from spherical coordinates (latitude and longitude) to 3D Cartesian
coordinates.
Earth and Earthquake Data
We have included multiple scaled-down versions of this Earth texture with the code
distributed on the website, since you need a fairly powerful computer to render even the
lowest-quality image from the NASA page. In order of decreasing quality, the following
images are provided:
• earth.jpg: Full-resolution (8 km/px, 5400×2700) image from NASA page
• earth-2k.bmp: 2048×1024 scaled-down version of image
• earth-1k.bmp: 1024×512 version of image
• earth-512.bmp: 512×256 version of image
• earth-256s.bmp: 256×256 version of image
Almost any graphics card should be able to use the 256s version of the Earth texture. If your
computer isn’t able to use this texture, you will need to use the computers available in the
various CSE Labs. The Earth textures are stored in a equirectangular projection, which simply
means that the x coordinate corresponds directly to longitude and y directly to latitude.
The earthquake dataset contains information about the earthquake’s magnitude (a measure
of how severe the earthquake is) and its longitude and latitude. You’ll be required to display
this information on the globe in a meaningful manner. More information on the earthquakes
is available in the data file, and if you are interested, you can try to figure out ways to
integrate additional data variables into your visualization.
Requirements and Grading Rubric
You will be required to write the code that displays the Earth on screen and animates it
between flat rectangular map and a three-dimensional globe. You will also need to write the
code to display the earthquakes on the Earth. The starter code defines a single light source
that coincides with the camera, so that surfaces seen head-on (i.e. whose normal points
towards the viewer) will be bright while those that are slanted will be darker. Pressing Space
will pause the current visualization time, while the left and right arrow keys will make it slow
down and speed up respectively. Once you have the mesh being drawn, pressing M will
visualize its triangles.
Work in the “C” range will:
Use vertex buffers and element buffers to draw a rectangle subdivided into multiple triangles,
representing a flat map of the Earth. You can use the M key to view the mesh structure.
• The rectangle should lie in the xy plane,
with x going from −π to π and y going from
−π/2 to π/2. It must be divided into slices
divisions horizontally and stacks divisions
vertically. Therefore, the mesh will have
(slices+1)×(stacks+1) vertices and
2×slices×stacks triangles. On the right is an
example with 6 slices and 3 stacks.
• Fill in the necessary parts of the
Earth::getPosition() and Earth::getNormal() functions and use them to
populate the vertex and normal arrays. You should assume that the input latitude lies
between −90° to 90°, and longitude lies between −180° to 180°.
• Populate the element buffer with the appropriate vertex indices. It may help to work
out the indices by hand for a small example, say slices = 4, stacks = 2, and generalize
from there.
Work in the “B” range will:
Apply a texture of the Earth to the rectangle so that it looks like the original image.
• Remember to call unsetTexture() at the end of the Earth drawing function, so
that the texture does not get applied to things drawn afterward.
Display on the Earth all the earthquakes that have happened within the past one year of the
current visualization time.
• Use earth.getPosition() to obtain the earthquake positions such that they
match those of the sphere textures (i.e., an earthquake occurring in California must be
displayed in the same location as the California of the Earth texture). One way to tell if
your mapping is correct is if you see a lot of earthquakes along the “Ring of Fire” in the
Pacific Ocean off the coast of Asia.
• You may use the Draw:: functions to draw the earthquake markers or come up with
your own custom geometry. Earthquake sizes and colors should be based on the
earthquake data in some meaningful way. Explain and justify the mapping you choose
in your README.
Work in the “A” range will:
Change the vertex positions and normals to draw the Earth as a sphere instead of a rectangle.
• In the QuakeVis constructor, set isSpherical=1. Fill in the necessary parts of
Earth::getPosition() and Earth::getNormal().
• You will need to convert latitude and longitude into the three-dimensional Cartesian
coordinates of the corresponding point on the sphere, using the formulas
x = cos(lat) sin(lon),
y = sin(lat),
z = cos(lat) cos(lon).
Be careful that the input latitude and longitude are in degrees, not radians.
• The texture is permitted to look slightly “cut off” only at the
top and bottom stack of the Earth mesh. The image to the
right shows what this looks like when slices = 6 and stacks = 3.
(See below for why this happens.) Increasing the number of
stacks and slices will make this problem harder to see.
• The earthquakes must appear on the sphere in the correct
geographical locations (though they may not lie exactly on
the mesh if it has too few slices and stacks).
Smoothly transform the mesh between a rectangle and a sphere based on user input. The
program should start with the Earth displayed as a rectangle. When the user presses the S
key, it should continuously deform to a sphere. If S is pressed again, it should deform back to
a rectangle, and so on.
• To start with, you may call earth.setSpherical() whenever the S key is pressed
to update the state of the mesh.
• Immediately toggling the state creates an abrupt transition. Instead, it is better to
smoothly transition between the rectangular and spherical shapes, by gradually
changing the spherical parameter from 0 to 1 or vice versa over multiple frames. One
way to do this is to add a variable to QuakeVis to keep track of the target value of
spherical. Only change the target value on user input, and adjust the state of the mesh
towards the target at each frame.
• Fill in the remainder of Earth::getPosition() and Earth::getNormal() to
smoothly interpolate between the rectangular and spherical values. (Technically, the
correct normal of the interpolated shape is not simply the interpolation of the
normals, but we may pretend it is for this assignment.)
If you reduce the value of slices and stacks and then watch the mesh structure as it
interpolates between a rectangle and a sphere, you should be able to see why the texture
appears to be cut off near the poles.
Useful Math
Here are a few mathematical operations that are very common in graphics and may be useful
for this assignment:
• Linear interpolation: One way to blend smoothly between two values x and y (which
could be reals, or vectors, or matrices, etc.) is to define a function whose output varies
continuously from x to y as a scalar parameter a goes from 0 to 1. This function is
traditionally abbreviated “lerp”:
lerp(x, y, a) = x + a(y − x).
Thus, for example, lerp(x, y, 0) = x, lerp(x, y, 1) = y, and lerp(x, y, ½) = (x + y)/2.
• Clamping: A concise way to constrain a value to lie in a specified interval [a, b] is to
define a “clamp” function clamp(x, a, b) which returns a if x ≤ a, returns b if x ≥ b, and
returns x otherwise.
• Rescaling: Suppose you have a value x in the range [xmin, xmax], and you want to find
the corresponding value in [ymin, ymax]. Observe that x − xmin lies in [0, xmax − xmin],
and (x − xmin)/(xmax − xmin) lies in [0, 1], so the desired value is
y = ymin + (ymax − ymin)(x − xmin)/(xmax − xmin).
Above and Beyond
All the assignments in the course will include great opportunities for students to go beyond
the requirements of the assignment and do cool extra work. We don’t offer any extra credit
for this work — if you’re going beyond the assignment, then chances are you are already
kicking butt in the class. However, we do offer a chance to show off… While grading the
assignments the TAs will identify the best 4 or 5 examples of people doing cool stuff with
computer graphics. After each assignment, the selected students will get a chance to
demonstrate their programs to the class!
There are great opportunities for extra work in this assignment. For example, the source
website for the Earth texture (see Data Credits below) has images for each month of the year.
You could animate between the textures based upon the current time of year. We have also
included some height images that contains the elevation and bathymetry data for the
Earth, with sea level being 50% gray, and black and white indicating 8 km below and above
sea level respectively. You could use this image to visualize the shape of the Earth’s surface
by loading it with SDL_LoadBMP() and using its pixel data to displace mesh vertices along
their normals. Be creative!
Support Code
The webpage where you downloaded this assignment description also has a download link
for support code to help you get started. The support code for this assignment is a simple
program using the SDL-based engine, similar to the ones we have used before. You should
also download separately the zip file containing the texture and earthquake data files.
The support code defines a program structure and everything you need to read and parse the
earthquake data file. To make locating data files simpler, we have provided a header file
called config.hpp that contains absolute paths to your data files. You should edit this
file with the full path to your data files (e.g. “C:\Users\Turing\a3\data” or
“/home/turing/a3/data”). We will modify this file appropriately when grading your
assignment.
Handing It In
When you submit your assignment, you should include a README file. This file should
contain, at a minimum, your name and descriptions of design decisions you made while
working on this project. If you attempted any “above and beyond” work, you should note that
in this file and explain what you attempted.
When you have all your materials together, zip up the source files and the README, and
upload the zip file to the assignment hand-in link on our Moodle site. You don’t need to
include the data files, which are pretty large and which we have a copy of anyway. Any late
work should be handed in the same way, and points will be docked as described in our
syllabus.
Data Credits
The earthquake data comes from http://earthquake.usgs.gov/data/centennial/. As per
http://www.usgs.gov/laws/info_policies.html, this data is in the public domain.
Credit: U.S. Geological Survey,
Department of the Interior/USGS
The Earth texture comes from http://visibleearth.nasa.gov/view_cat.php?categoryID=1484.
As per http://visibleearth.nasa.gov/useterms.php, this data is freely available for re-use.
Credit: NASA Earth Observatory