Computer Graphics, 2018
Assignment 1: Moving Circles
Submission Due: Oct. 14 (Sun.), 23:59, at i-campus
First, refer to the general instruction for computer graphics assignments,
provided separately. If somethings do not meet the general
requirements, you will lose corresponding points or the whole scores
for this assignment.
1. Objective
In computer graphics, the majority of drawing primitives are triangles.
The goal of this assignment is to learn how to draw and animate
such primitives (here, 2D). Precisely, you need to draw and move
2D colored circles on the screen.
2. Triangular Approximation of Circle
In general, a circle is represented by its center position and radius.
To draw the circle, we first need to convert it to a finite set of triangle
primitives. A common way of doing this is to approximate the circle
by dividing it to a number of equal-size triangles. This process is
called the “tessellation” or “subdivision.”
Figure 1 illustrates how to approximate a circle using 8 triangles,
resulting in an octagon. For your implementation, use more triangles
(e.g., 36 or 72 triangles) to obtain a smoother boundary.
Figure 1: An octagonal approximation of a circle.
Given a center position p0 = (x0, y0) and a radius r, you can
compute the coordinates of each boundary vertex as
p0 + r(cos θ, sin θ),
where θ indicates the angle at the xy-plane. In your shader program,
you will need to use 4D coordinates for gl Position; in that case,
use vec4(x0 + r cos θ, y0 + r sin θ, 0, 1), where 0 indicate the
z coordinate. For the moment, do not care about the last component
1 (this will be covered later in the course).
Also, recall that the default viewing volume is provided with [?1, 1]
for the x, y, and z axes.
3. Requirements
You may start from “cgbase” project, already distributed on the class
web.
If ESCAPE or ’q’ keys are pressed, the program is terminated.
Initialize the window size to 1280 × 720 (10 pt).
The program has more than 20 solid circles (Figure 2) (10 pt).
Your circle should be a circle (not an ellipse), even when the
window is being resized (10 pt).
The circles are initialized with random position, radius, color,
and speed (10 pt).
The circles’ initial positions require to avoid collision (20 pt).
The circles are moving in random directions (10 pt).
When a circle meet other circles or side walls, its direction and
speed are randomly changed to avoid overlaps (20 pt).
When you animate circles, it is better to compute the amounts of
movements based on the time difference between the current and
previous frames rather than simply using a frame counter. This
ensures that your application runs at the same speed for different
machines. It is also good to test your application in a different (e.g.,
your friend’s) machine in advance.
Figure 2: An example screenshot of a single animation frame.
4. Mandatory Requirements
What is listed below is mandatory. So, if anything is missing, you
lose 50 pt for each.
Instancing should be applied for a static vertex buffer. Your
vertex buffer should stay constant at run time, which means
positioning and coloring of the circles should be implemented
using uniform variables.
5. (Optional) Elastic Collision
It would be better to apply physics to the collision among the circles
rather than to rely solely on the random control over velocities; refer
to the following link for the elastic collision:
https://en.wikipedia.org/wiki/Elastic collision
When you apply a physically-based collision to your assignment,
you get an extra credit of 20 pt. Please note that in your report.
6. What to Submithttp://www.daixie0.com/contents/21/1837.html
Source, project, and executable files (90 pt)
A PDF report file: YOURID-YOURNAME-A1.pdf (10 pt)
Compress all the files into a single archive and rename it as
YOURID-YOURNAME-A1.7z.
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