First of all, I love mathematics (algebra, geometry, and calculus) because I love to solve numerical problems in my head. Since attending San Jose State University, I have been studying computer science and doing scientific computation. One of the most interesting types of scientific computation is symbolic computation, or computer algebra, Symbolic computation is a subcategory of scientific computation that develops the manipulation and solution of expressions in symbolic form. I remember taking a linear algebra class (Math 129a) two years ago. In that class, I used this handy-dandy application called GNU Octave to do MATLAB math exercises. MATLAB, “a high-level language and interactive environment for numerical computation”, performs symbolic computation from the command line on the computer. Using MATLAB lets everyone define symbolic math expressions and operate them for mathematical purposes. According to MathWorks, there is a list of mathematical areas that use MATLAB and its performances:
“1) Calculus: Performs differentiation and definite/indefinite integration, calculates limits, and computes summation/product series.
2) Linear Algebra: Performs matrix analysis on symbolic matrices, executes matrix operations and transformations with functions, and gets symbolic expressions for the eigenvalues and eigenvectors.
3) Formula Manipulation and Simplification: Simplifies long expressions into shorter forms, transforms expressions to particular forms, and replaces parts of expressions with specified symbolic or numeric values.”
I think symbolic computation is fun because you get to study the algorithms with the implementation and applications to computer science and engineering. For example, here is how it is done:
In[1]: 5x - 2x + 3 Out[1]: 3 + 3x
References
1) “Symbolic Computations in MATLAB.” The MathWorks, Inc. 1994-2013. Web. 5 Dec. 2013. <http://www.mathworks.com/products/symbolic/description4.html>
2) “MATLAB - The Language of Technical Computing.” The MathWorks, Inc. 1994-2013. Web. 5 Dec. 2013. <http://www.mathworks.com/products/matlab/>
3) “Matrices.” Vanderbilt University School of Engineering. 2013. Web. 5 Dec. 2013. <http://engineering.vanderbilt.edu/ge/es140/Otherlinks/MatlabTutorial/Matrices.php>
Computer graphics is basically a different category of graphics which represents the image data from a computer. When I think of computer graphics, I immediately think of computer animation, which is the art of creating moving images on a computer screen. Computer animation is well-known for various images on films, computer games, television programs, commercials, and so on. One of the most interesting applications in the field of computer graphics, CGI (Computer Generated Imagery), has been used to draw 3D computer graphics to scenes and special effects in movies. Many animation studios, such as Walt Disney Animation Studios and Pixar, use CGI to make their films more lively and animated. As you read along, you can see how CGI is put together in animated films.
The Lion King has presented few of the computer-animated sequences by CGI. For example, the “wildebeest stampede” was a three-dimensional sequence, with hundreds of wildebeest to run and hop simultaneously down the gorge. First, the animators draw a hand-drawn model of the wildebeest and give it to the CGI team to make it look evolved as a computer-generated one. Next, they take the model and multiplied it into hundreds of wildebeest in order to make an extensive stampede. According to CGI artistic supervisor Scott F. Johnston, he built a “follow-the-leader” simulation, a visual simulation “where animators can control the behavior of the wildebeests as leaders and followers.” Johnston explains the simulation’s process that “followers have to follow their leader, but avoid one another because they do not want the wildebeest to bump into each other.” Then, they build a pre-dimensional background grid that matches the perspective and the look of the background that is similar to the screen. On that grid, they placed one of the simulations where each of the bugs gets replaced by the running, hopping wildebeests. Finally, the team add the entire sequence in final color. Before that, they wanted to give each wildebeest randomized colors for testing, so the directors could say that the scene is likable, but they want to point out a few flaws like take the pink eyes out of the yellow face or make one of the them run faster. Once the testing is done, they add different shades of pale colors (gray, black, and brown) to make various wildebeest look realistic.
With CGI, everyone can enjoy watching animated movies and experiencing the real life images drawn on the screen. Disney’s latest animated movie is Frozen. Over the holidays, check out this movie and pay close attention to the beautiful art work (CGI).
References
1) “The Ballroom.” Disney Wiki. Web. 2 Dec. 2013. <http://disney.wikia.com/wiki/The_Ballroom>
2) Fine, Kelly. “This Week in History: Toy Story and CGI.” Spiceworks. Spiceworks Inc., 2006 - 2013. 22 Nov. 2013. Web. 2 Dec. 2013. <http://community.spiceworks.com/topic/412181-this-week-in-history-toy-story-and-cgi>
3) jamaldisney. "Lion King Computer Animation CGI and traditional hand drawn." Youtube. Web. 5 Dec. 2013. <http://www.youtube.com/watch?v=HLmAT6t5kL0>
5) Tracy, Joe. “An Inside Look at the Original Beauty and the Beast.” Digital Media FX Magazine. Digital Media FX, 2001. Web. 2 Dec. 2013. <http://www.digitalmediafx.com/Beauty/Features/originalbeauty.html>
