CS1010S, Semester I, 2018/2019—Mission 2 – Side Quest 1
National University of Singapore
School of Computing
CS1010S: Programming Methodology
Semester I, 2018/2019
Mission 2 – Side Quest
Book of Advanced Spells
Release date: 29 August 2018
Due: 05 September 2018, 23:59
Required Files
• sidequest02.1-template.py
• runes.py
• graphics.py
• PyGif.py
Background
You chanced upon a shiny old book resting in one of the dark corners. Out of curiosity,
you picked up the book and begin flipping through it. Most of the contents were basic
spells that you have already learnt. However, you notice fine scribblings at the bottom
of one page. Taking a closer look, you realise that it is a cool improvised spell. “Hmm..
some mage of old must have found her spellcasting class too easy,” you think as you
begin reciting the incantation.
Note: Before you start on this side quest, you may want to read the background reading
(see Appendix).
This side quest consists of two tasks.
CS1010S, Semester I, 2018/2019—Mission 2 – Side Quest 2
Task 1: Tree (5 marks)
Implement the function tree that takes a number of slices n and a rune as arguments,
and generates a stack of runes scaled and overlayed on top of each other.
For example, the following command show(tree(4, circle_bb)) should produce the fol-
lowing depth map:
The generated tree must satisfy a few properties: the circle_bb at the top of the tree is
scaled to 1/4 of its original size (the tree has 4 layers); the next lower layer is scaled by
2/4, and so on. Note that the bottom-most layer retains its original size. The different
levels of the tree must also be spaced evenly apart.
Task 2: Conjuring Helix (10 marks)
(a) show(helix(make_cross(rcross_bb),9)) (b) Illustrative diagram
Figure 1: (a) Helix with 9 runes, (b) Illustrative diagram
Write a function helix that takes in a rune and number n as arguments and creates runic
patterns to form a helix, where n ≥ 5. From the top-view, a helix is viewed as a pattern
surrounded with a series of n runes spaced out evenly around forming a circle. From
the side view, each rune is also spaced out evenly forming a 3D helix.1. The individual
runes are scaled down to 2/n of its original size and radius of the circle is 1/2 – 1/n.
In particular, Figure 1 above can be created with:
show(helix(make_cross(rcross_bb),9))
1https://en.wikipedia.org/wiki/Helix
CS1010S, Semester I, 2018/2019—Mission 2 – Side Quest 3
(a) show(helix(make_cross(rcross_bb),12)) (b) show(helix(circle_bb,9))
Figure 2: More examples. (a) is the same as previous example but with n = 12, (b) is the same as
previous example but with the rune: circle_bb
Tip: You will need to use the sine and cosine functions by importing the Python
math module (import math) for this task. For example, to compute sin(45°), you
can use: math.sin(math.pi/4) in your code.
CS1010S, Semester I, 2018/2019—Mission 2 – Side Quest 4
Appendix: Translation and Scaling
We have defined scale and scale_independent. The former scales the rune according to
the ratio argument, the latter allows greater flexibility as you are able to pass two ratio
arguments, one for the horizontal scaling while another is for vertical scaling.
(a) show(scale(1/2, heart_bb)) (b) show(scale_independent(3/4,
1/3, heart_bb))
Figure 3: Examples of scale and scale_independent. In (a), heart_bb is scaled by 1/2 both horizon-
tally and vertically. In (b), it is scaled by 3/4 horizontally and 1/3 vertically.
The last transformation tool we have is translate. The function translates the given rune
by the given translation vector (x, y) where x and y are ratios of a 600 x 600 viewport
centred in the middle of the viewport (the actual size of the viewport is actually 800 x
600 so you will find that when a rune is translated by 1 in the x-axis, it will still be visible
whereas it will not when it is translated by 1 in the y-axis.) Note that positive x means
translating to the right, while positive y means translating down.
Figure 4: Example of a translated heart_bb. This is the result of show(translate(0.1, 0.15,
heart_bb))
Try creating an anaglyph with the following command and view them with the 3D
anaglyph glasses that was issued:
anaglyph(overlay(scale(0.8, heart_bb), circle_bb))
CS1010S, Semester I, 2018/2019—Mission 2 – Side Quest 5
Appendix: How to position runes on the viewport
This appendix will serve as a quick guide on how to position runes. Note that by default,
all the runes are centered in the middle. Therefore, all translation operation should be
relative to the center of the viewport.
Positioning using x and y values
Figure 5: Size reduced 90% and moved towards top-right.
Code for moving a rune towards the top-right corner:
show(translate(0.25, -0.25, scale(0.1, circle_bb)))
Note: Translate is done with respect to a max unit of 1. i.e. A 0.5 translation will
move a rune halfway across the viewport and 0.25 translation will move it one-quarter
across the viewport.
Positioning using angles
Figure 6: Size reduced 90% and moved towards 30° direction.
To find length x on the x-axis, you can observe in the diagram that cos(30°) = x/L.
Similarly, to find length y on the y-axis, you get sin(30°) = y/L.
Therefore we can derive the equation:
x = L * cos(30°), y = L * sin(30°).
In the above example, we have L = 0.4, x = 0.346 and y = 0.200. Therefore, we can
obtain the above example with the code:
show(translate(-0.346, -0.2, scale(0.1, circle_bb)))
Tip: In the viewport, the y-axis is inverted.
Required Files
Background
Task 1: Tree (5 marks)
Task 2: Conjuring Helix (10 marks)
Appendix: Translation and Scaling
Appendix: How to position runes on the viewport