I Just Love Math
Dear reader,
Let me begin by giving you a few of the common questions, and statements most people have regarding the importance, and the existence of mathematics; specifically the higher fields (such as: Calculus, Geometry, Algebra, Trigonometry, etc.):
i. "Why do I have to learn this?"
ii. "When I grow up, when am I ever going to use this? (excluding the
possibilities of becoming an Engineer, or a Scientist)"
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iii. Math stands for:
M-ental
A-buse
T-o
H-umans
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Here's the sad reality of most of these questions/statements. The main reason they were concluded is purely attributed to our Lazy Human Nature; let that thought sink in. Now hear me out, such statements/questions were not made because a certain individual had a truly profound motivation, rather because a certain individual was going through stress; the kind of stress that everyone goes through when studying math. Makes sense? Good.
Honestly, I use to have the same opinions on Math; I felt it was boring (not a surprising opinion if you asked me), and mostly useless after I finish college. But with the help of Khan Academy's "Pixar in a Box" series, I was introduced to the beautiful harmonic convergence of math and art, through animation. Personally, I have been an artist for a very long time; ranging in different art forms such as sketching, solar painting, theatre, and even basic animation.
"For an animator, mathematics is a tool to create Images, Movement, Richness, and Fun."
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-Inigo Quilez
Technical director of Pixar
Allow me me, to run you through a part of the process regarding environment modelling. In this course, I learned the not so simple mathematics behind modelling a simple blade of grass.
i. To be able to model a blade of grass, you must first start with its base shape; the curve. One way to be able to express that curve in a mathematical sense, is through a parabola. A complete parabola is an infinite curve, we only want a tiny fraction of that curve; which is called, a "Parabolic Arc". The first part of the lesson is fully dedicated in familiarising the student with ideas about a parabola
ii. The following section introduces us to the "Control Polygon"; three connecting lines through which we can form our parabolic arc. We are taught that by marking, and connecting the control polygon's midpoints; we can produce a parabolic arc.
iii. As I've said in the beginning, computer animation is a harmonious convergence between the arts, and mathematics. The following section introduces us to the numbers crunched, behind our lush blade of grass. As we already know, to produce our parabolic arc: we must first mark, and connect the control polygon's midpoints. Before we can mark our midpoints, we must first calculate where they are.
-A given factor I forgot to mention, is that locating such points in our lines will be dependent on the coordinate plane of mathematics.
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The first formula introduced to us in locating our midpoint(s), is the: "Midpoint Formula" (obviously)
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Midpoint formula:
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Ax + Bx Ay + By
2 2
( , )
M =
iv. Finally, we are introduced to weighted averages; a specific point that is not necessarily the midpoint of points A, and B.
v. With weighted averages, we get a direct relationship between the lines of a control polygon, and its touching point with our parabolic arc.
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I hope that through my tiny share about why I've come to love mathematics; you too have come to some sort of appreciation. As an artist, I was deeply captivated by this course on environment modelling. I am very grateful for Pixar's and Khan academy's efforts in making such knowledge widely available for anyone. If you'd like to take a personal piece of the action, Here's a link to the series. It also has other courses like:
story-telling, animation, and many more.
Godbless!
That's all for now, more stuff are soon to come, make sure to visit this page soon xD!
-ETHAN :)
