Mr. Meinzen: AP Computer Science - Principles

Learning Objectives - students will :

1. Understand the Advanced Placement Computer Science Principles (AP CSP) Course & Assessments

2. Identify the purpose and use of the Engineering Notebook.

3. Organize Engineering Notebook and prepare for the AP CSP Course

P1: Project 1 : Part I : Introduction to the Create Task

 

Learning Objectives - students will :

1. Review P0 : Plan for the Create Task - The Programming Assessment : Before Create Task - Setup

2. Evaluate a Sample Student's Create Task using the Chief Reader's Report on apcentral.collegeboard.org

3. Complete a practice Create Task : Individual Written Response (IWR) using a program from a language that implements a known algorithm and abstractions as coded in procedures and lists

   1. Java Code & Video provided by teacher:
      1. Deck.java : focus on the:
         1. Algorithms : "swap" basic algorithm or the "Bubble Sort" advanced algorithm with abstraction
         2. Data Structure : arrays as lists
         3. Abstraction : methods & parameters as procedures
      2. PokerGame.java : focus on the calling of the Deck.java code

4. Complete an Individual Written Response (IWR) in your Engineering Notebook for Project 1. Refer to P0: Plan for the Create Task - The Programming Assessment : During Create Task - Goals

5. Add to Engineering Notebook a AP Score rubric (self-scored) for your IWR for Deck.java & PokerGame.java based on P0 : Plan for the Create Task - The Programming Assessment : After Create Task - Scoring

6. Submit Engineering Notebook for P1: Project 1 : Part I : Introduction to the Create Task

 

Note: Future options to develop and practice Create Tasks include:

1. Project 4 : Internet : HTML & JavaScript
2. Project 5 : Visualizations :Three Dimensional Programming using a Ray Tracer

P2: Project 2 : Numeric Systems & Math Theory : Binary, Octal, Decimal, & Hexadecimal

 

Summary :

Humans use numbers everyday. But what are numerals, number systems and how do we "use and communicate" via numbers?

Learning Objectives : Students will...

Convert : Numerals and Bases Conversions

Base	Decimal (base 10)	Binary (base 2)	Hexadecimal (base 16)	Octal (base 8)
Example 1 - Convert each from Condensed Form to Expanded Form	2579	1010 0001 0011	A13	5023
Example 2 - Convert from Hexdecimal (or Decimal)	135		87
Example 3 - Convert from Binary (or Decimal)	87	0101 0111
Example 4 - Convert from Hexadecimal (or Octal)			CC02	146002

Assess : writing Exam Questions

Write 4 (or 5) questions on any of the above lectures and/or practice problems that you would expect to see on an AP Exam...this must be done by noting the appropriate Essential Knowledge (EK) statement that matches your Test Question.

1. Test Questions: Multiple Choice. Must include 5 (or 4) options and one (or more) correct answers.

2. Test Questions: Short Answer with Solutions. May include fill-in-the-blank for longer questions.

3. Test Questions: Free Response. Must require student to write a solution to a problem either by

   1. giving a programming code for students to read and understand, or
   2. giving a arithmetic problem in several bases requireing students to write multiple mathematical steps accurately and with precision.

Explore : Topics I : Numeric and Number Systems

[pick one from the following list]

1. Kurt Godel's Incompleteness Theorem

2. Irrational and Transcendent (i.e. non-algebraic or non-polynomial) Numbers

3. HyperReal and HyperComplex Numbers, Superreal, Surreal Numbers, Rings, Fields, Quaternions, SuperNatural Numbers

4. Lambda-Calculus & Computable Numbers

5. Aleph Numbers - Cardinality (i.e. size) of Infinite Sets -

• The Integers and the Natural Numbers have the same Cardinality (Aleph-null)

• The Real Number System is "bigger" than the Integers (Aleph-one).

• What has Cardinality greater than the Real Numbers?

6. Rudy Rucker's Book - Infinity and the Mind

7. First Fundamental Theorem of Arithmetic

Details of short description

• at least one fact with an inline citation that references at least one reliable and identifiable source placed as a footnote (this will be used to understand and avoid plagiarism in the course),
• where/how it the topic is used or discovered,
• the problem(s) the topic addresses (create at least one example math problem and solve the example),
• Your description should be in 3rd person (no "I" or "you"), 1 page long, double-spaced, 12pt, Times New Roman.

Explore : Topics II : Numeric Operations (Arithmetic)

[pick one from the following list]

1. Procedure(s) to multiply by other than the given base.

2. Procedure(s) to divide by other than the given base.

3. Negatives in Binary (2's complement procedure).

4. Bitwise shifting operator by example (>>, <<, >>>, <<<)

5. Use the decimal point to indicate when bases switch from positive exponents to negative exponents.

6. Create a "times table" for Decimal, Binary, and for Hexidecimal digits.

7. Program a Number System Calculator in Java & Swing

8. Program a Number System Calculator in Javascript

Details of short description

• at least one fact with an inline citation that references at least one reliable and identifiable source placed as a footnote (this will be used to understand and avoid plagiarism in the course),
• where/how it the topic is used or discovered,
• the problem(s) the topic addresses (create at least one example math problem and solve the example),
• Your description should be in 3rd person (no "I" or "you"), 1 page long, double-spaced, 12pt, Times New Roman.

 

Instruction : a series of 4 Lectures will be given :

Lecture 1 : Numerals : how we write/communicate numbers.

Example A - different ways to write the same Number (note: there are many more ways than the 8 listed here):

1. 27 (Hindu-Arabic numeral system used in most modern societies)

2. twenty-seven (English-language based numeral system - verbal communications)

3. XXVII (roman numerals - old but not designed for computation)

4. 0001 1011 (binary numerals - computer representations)

5. ///// ///// ///// ///// ///// // (tally system - simple)

6. one score and seven (English ala Lincoln)

7. 00:27:00 (sexagesimal system - based on degrees:minutes:seconds) and one of the oldest numeral systems in existence. Ancient Babylonians used to compute time, geography, and angles...base-60 avoids many issues with fractions/division due to the First Fundamental Theorem of Arithmetic)

8. 1B (hexadecimal system which uses the digits 0,1..9,A,B,C,D,E,F

Example B - the numerals 0, 1, 2, and 3 in mathematical set-theoretic notation...uses only the three symbols: {,}

• 0 = {},

• 1 = {0} = {{}},

   

• 2 = {0,1} = {{},{{}}},

• 3 = {0,1,2} = {{},{{}},{{},{{}}}}

Lecture 2 : Numbers : how we use numbers to count, measure, and label objects.

1. When we use numbers to "count" objects, we are referring to the "cardinality" property.

2. When we use numbers to compare ("bigger versus smaller") against objects, we are referring to the "comparison" property.

3. When we use numbers to label objects (like the list below) we are referring to the "nominal" property.

Usually we just talk about "Number Systems" which are sets of numbers.

1. Natural Numbers (aka Counting Numbers)

   • If used to describe the "size" of an object then we call the number a Cardinal such as 5 bananas [five is the cardinality of the set of bananas].
   • If used to describe a property of an object for comparison purposes then we call the number a Measurement such as "I scored an 85% on the test." The 85% by itself does not mean anything unless we compare it to other scores. (If the measurement includes a magnitude and a unit--a word such as "meter"-- it is called a Quantity.)
   • If used only as a label rather than for any calculations, then the Number is a Nominal such as this listing or numbering of the definitions for Cardinal, Measurement, and Nominal...we could have just used a bulleted list instead of a numbered list.

2. Integers - no fractions or decimals, includes positives, negatives, and 0.

3. Rationals (i.e. Fractions) + Irrationals (i.e. non-terminating, non-repeating decimals) = Real Numbers

4. Real + Imaginary = Complex Numbers (numbers that can go round-and-round)

Lecture 3 : Numeral Base Systems : Decimal, Binary, Octal, and Hexadecimal Systems

 

Commonly Used Numeral Systems in Computer Science are:

Base	Decimal (base 10)	Binary (base 2)	Hexadecimal (base 16)
Digits (or Symbols) A16 is 10 in decimal B16 is 11 in decimal C16 is 1 in decimal D16 is 13 in decimal E16 is 14 in decimal F16 is 15 in decimal	0, 1, 2, 3,..., 9	0, 1	0, 1, 2 ..., 9, A, B, C, D, E, F
Condensed Notation	499	1 1111 0011	1F3 [Hint: convert groups of 4 bits start at far right into 1 hexadecimal digit]
Expanded Notation	4*102 + 9*101 + 9*100	1*28 + 1*27 + 1*26 + 1*25 + 1*24 + 0*23 + 0*22 + 1*21 + 1*20	1*162 + F*161 + 3*160
Converting to Decimal	400 + 90 + 9	256 + 128 + 64 + 32 + 16 + 0 + 0 + 2 + 1	1*256+15*16 + 3
Solution	499	499	499

Lecture 4 : Arithmetic Operations : Decimal, Binary, and Hexadecimal Systems

 

Operation & Notes	Decimal (base 10)	Binary (base 2)	Hexadecimal (base 16)
Addition (+) Watch "carryover"	132 + 039 = 171	1000 0100 + 0010 0111 = ___________ 1010 1011	8416 + 2716 = AB16
Subtraction (-) Borrowing is a bit tricky. egatives are in Explorations. Subtraction is usually done using "adding by negatives" in binary	132 - 039 = 93	1000 0100 - 0010 0111 = __________ 0101 1101	8416 - 2716 = 5D16
Multiply (*) by the Base Number Multiplying by a base just "left shifts" the digits Multiplying by digits other than the base is more complex and requires memorizing "times tables" for each base	13 * 102 = 13 * 100 = 1300	0000 1101 * 210 = 0000 1101 * 102 = 0001 1010 [hint: shift all bits left by 1 position, called "bit-shift" or << operator]	D * 16310 = D * 100016 = D00016
Divide (/) by the Base Number Dividing by a denominator that is a power of the base system will simply "right shifts" the digits of the numerator Dividing by digits other than powers of the base systemis more complex and requires memorizing "times tables" for each base.	128 / 101 = 128 / 10 = 12.8 = 1*101+ 2*100 + 8*10-1	1000 0000 / 2110 = 1000 0000 / 102 = 0100 0000 [hint: shift all bits right by 1 position, called "bit-shift" or >> operator]	80 / 16110 = 80 / 1016 = 816

 

Scoring Rubric :

Name ________________________________	Points Assigned	Date Assigned: ____________
1. Convert Practice Problems	/ 20
2. Assessment - writing test questions [5 pts per question with answer]	/ 20
3. Exploration I - Topic is _________________________ a) description b) at least 1 example math problem and solution (may be handwritten) c) 3rd person, double spaced, 12-point Times New Roman, 1 page d) fact with an inline citation to a reliable, identifiable source in footnote	/ 20
4. Exploration II - Topic is _________________________ a) description b) at least 1 example math problem and solution (may be handwritten) c) 3rd person, double spaced, 12-point Times New Roman, 1 page d) fact with an inline citation to a reliable, identifiable source in footnote	/ 30
Engineering Notebook - update of ToC, project header, important formulas/code, calculations, collaborators, notes, marking of Essential Knowledge statements, etc. [MAY BE SCORED LATER IN COURSE]	/ 10	- 5 pts if late
TOTAL NOTE: absence of inline citation to a reliable, identifiable source is ground for a ZERO on this section of project. College Board also imposes more strict penalties for plagiarism.	/ 100	Date Due: ________________

P3: Project 3 : Data Representation & Encodings : Numbers, Colors, Characters & IP

 

Summary :

1. Computers store, retrieve and manipulate binary data.

2. Humans use mathematics and other encoding systems (i.e. human-based languages) to represent information.

3. Computer Scientists apply mathematics and other encoding systems (computer languages & protocols) to translate information into binary data to be processed by computers as well as decode the binary data into information that is useful for humans.

Learning Objectives : Students will...

Explore : Topics I : binary encodings of numbers (select up to 2 topics for a maximum of 50 pts)

1. Write a program that illustrates each of the 6 Sources of Errors. [50 points]

2. Write a program that converts floating point numbers (doubles?) to binary and vice-versa. Do NOT use Java's Integer, Float, or Double classes to parse the input due to miscalculations. Do USE arrays or ArrayLists of digits and write your own parse method using Strings. [50 points]

3. Write 5 floating point numbers in decimal and convert to IEEE754 binary representation. [5 points per number conversion, maximum 25 pts]

4. Write 5 IEEE754 floating point numbers in binary and convert to decimal representation (5 points per number conversion, maximum 25 pts]

5. List the IEEE754 floating point representations for the following unusual "numbers": NaN (not a number), 0, positive infinity and negative infinity. [25 points]

6. Write 5 multiple-choice or short answer questions with correct answers for a test. Note which Essential Knowledge (EK's) statement(s) matches each question. [5 points per problem, maximum 25pts]

Explore : Topics II : encodings of colors and text (select up to 2 topics for a maximum of 50 pts)

1. Color Encodings [pick a maximum 1 of the following 5 options]

   1. Convert the following RGBA hexadecimal values: FFFFFFFF, 00000000, C0C0C000, 88000088, 00888888 into decimal and describe, in english, what color each represents. [ 4 pts each for max 25 pts]
   2. List the following colors in RGBA format using hexadecimal, decimal, and percentages: light-yellow, cyan, clear (no color), dark gray, light gray. [ 4 pts each for max 50 pts (Note: 4pts * 4 colors * 3 numbers = 54 pts)]
   3. List 5 examples for each of the 3 other color-encoding format/schema's besides sRGBA (i.e. CMYK, HSL, HSV) that are commonly used [3 pts each example, 5pts for clarity/organization, 50 pts max]
   4. Write a JavaScript or Java program to convert your own name (FirstLast) to a color schema (RGBA integer values) [50 pts].
   5. Write 5 multiple-choice-multiple-select or short answer questions with correct answers for a test. Note which Essential Knowledge (EK's) statement(s) matches each question. (5 points per problem)

2. Character Encodings [pick a maximum of 1 of the following 10 options]

   1. Write your own name (FirstLast) in ASCII decimal and hexadecimal encodings [25 pts]
   2. Write your own name (FirstLast) in Unicode decimal and hexadecimal encodings [25 pts]
   3. List the first 32 values of the ASCII encodings and explain what any one of the devices (listed below) will do with each of those 32 characters. Hint: several will be ignored by the devices [25 pts]:
      1. printer,
      2. TTY device,
      3. braille reader,
      4. Computer (Unix-based OS)
      5. Computer (MS Windows-based OS)
      6. Internet protocol such as email/MIME, FTP, www or SMS
   4. List the 8 escape-codes in US-ASCII, and describe how they are used in a Java [25 pts]
   5. List the default text-based encoding that are used in XHTM, HTML5, MacOS, MS Windows, and Linux. [25 pts]
   6. Write a Java program using the 8 escape-codes [50 pts]
   7. Write a JavaScript program to convert 4-letter names to US-ASCII decimals. [50 pts].
   8. Write a JavaScript program to convert 4-letter names to Unicode binary. [50 pts].
   9. Write 5 multiple-choice-multiple-select or short answer questions with correct answers for a test. Note which Essential Knowledge (EK's) statement(s) matches each question. (5 points per problem)

Explore : Topics III : encodings on the Internet (select 1 topics for a maximum of 50 pts)

1. Addresses : List the IPv4 and IPv6 addresses of 5 common websites including www.ecusd7.org and www.meinzeit.com [25 pts]

2. Convert : encode your own name (FirstLast) to Unicode values then to an IPv4 address. Note that there are multiple ways to accomplish this conversion. [25 pts]

3. Identify : list 25 commonly-used PORT numbers, the services (i.e. programs) assigned to them, and their purpose. [25 pts]

4. Identify : list 10 commonly used (or reserved) IPv4 addresses along with associated port numbers for a private network. For example: 192.168.0.1:53 is often the homeowners private router or host to the internet using port 53 (i.e. domain name service or DNS). [50 pts]

5. Program : write JavaScript program to convert your own name (FirstLast) to Unicode values then to an IPv4. Note that there are multiple ways to accomplish this conversion. [50 pts].

6. Synthesize : Write 5 multiple-choice or single-word questions with correct answers for a test. Note which Essential Knowledge (EK's) statement(s) matches each question.[5 points per problem, maximum 25 pts]

 

Instruction : a series of 3 Lectures will be given :

Scoring Rubric :

Student Name: _____________________________________________
Exploration I (Numeric Encodings - IEEE754) Topic and number _____________________________________________ Topic and number _____________________________________________	max 50
Exploration II (Color or Text Encodings) Topic and number _____________________________________________ Topic and number _____________________________________________	max 50
Exploration III (Internet Addressing & Protocols) Topic and number _____________________________________________	max 50
Engineering Notebook - update of ToC, project header, important formulas/code, calculations, collaborators, notes, marking of Essential Knowledge statements, etc.	max 10
Project Total	max 100

 

P4: Project 4 : Higher-level Protocols on the Internet, Objects, and Languages

HyperText Transfer Protocol (http), HyperText Markup Language (HTML), Document Object Model (DOM), and JavaScript as overseen by Internet Engineering Task Force (IETF)

 

Learning Objectives - students will:

1. Learn the basics of HTML tag structure & Document Object Model (DOM) :

2. Learn the basics of Javascript programming language as used in HTML & programmatically manipulating the DOM :

3. Learn the basics of Swapping, Looping, Conditionals, and Functions in Javascript within HTML :

 

Scoring Rubric :

	Name ______________________________	Student Score	Possible Maximum Score
I.	HTML -- Find Learning Objective (LO) associated with HTML tags -- Create an HTML comment tag identifying and addressing one Essential Knowledge (EK) statement from -- Create a paragraph (i.e. <P> tag) with an id attribute of "idLO631" identifying and addressing a 2nd EK -- CIRCLE in pen the id attribute and and mark with a"I".		20
II.	HTML -- Find Learning Objective (LO) associated with HTML tags -- Create a header tag with a class attribute of "classLO" and innerHTML identifying and addressing on EK -- Create a 2nd header tag with a class attribute of "classLO" and innerHTML identifying and addressing -- CIRCLE in pen the two class attributes and mark with a"II".		10
III.	DOM & JavaScript : ---- Find Learning Objective (LO) associated with HTML tags and write a JavaScript comment identifying and addressing an EK -- Write and call a JavaScript function that manipulates the DOM via id="idLO631" attribute. -- Write and call a JavaScript function that manipulates the DOM by changing the background color of all tags with the class="classLO" attribute. -- CIRCLE in pen the relevant JavaScript and mark with a "III".		20
IV.	Basic Algorithm: Swap. CIRCLE in pen the relevant JavaScript and mark with a "IV".		10
V.	Basic Algorithm: Conditional. CIRCLE in pen the relevant JavaScript and mark with a "V".		20
VI.	Basic Algorithm: Loop [include a comment about any other algorithm that was used within the body of the loop]. CIRCLE in pen the relevant Javascript and mark with a "VI".		20
	Engineering Notebook - update of ToC, project header, important formulas/code, calculations, collaborators, notes, marking of Essential Knowledge statements, etc. -- Use appropriate indenting in your HTML and JavaScript code/printout.		10
	TOTAL		100

 

Instructional Design Technique

1. Demonstration and discussion of each objective via webpage using a browser and text editor (for source code)

• By demonstrating the various features through an actual webpage/website, the students will gain insights into the interacting pieces (HTML, DOM, Javascript, webpage parsing & layout)

• Demo 1 - Basic Javascript in HTML

• Demo 2 - Javascript Functions

• Demo 3 - Advanced Javascript - Analog Clock

2. Demonstration of an advanced JavaScript program (analog clock)

   1. Debugging Hint: learn to use the debugging tool (F12) built into every browser...especially useful in Firefox and Chrome.
   2. Debugging Hint: instead of System.out.println("...") in Java, use console.log("..."); in JavaScript
   3. Debugging Hint: in the browser Debugging Tool (F12), learn to use the Console to identify JavaScript errors, network errors, CSS errors, security issues, and console output (from console.log() method)

3. Online resources & references

   • W3C Tutorial Wiki - official standards-based website

   • W3Schools.com - often-used resource for scripts & examples of HTML, DOM, JavaScript, CSS and other web-related details

   • Wikipedia DOM Entry (browser DOM history & other links)

   • Wikipedia Javascript Entry (JavaScript history & other links)

   • Javascript and the DOM - a Hierachy of Javascript Objects as connected to the DOM

   • Java and JavaScript - Ham & Hamsters (differences between Java and JavaScript languages)

   • JavaScript for New Developers who know at least one other language

Assessement Technique

1. Informal feedback during demonstration & discussion.
   

2. HTML + Javascript webpage assignment. Each student will select a webpage to create (HTML+Javascript) to accomplish goals agreed upon by instructor...tied to identifying and explaining one or more Essential Knowledge statements.

1. Instructor will guide the student assignment to require an artifact (webpage) that demonstrates student learning of each objective in an original way.

2. Instructor will guide the student assignment to avoid excessively difficult artifact that is clearly beyond the student's current ability.

3. Instructor will guide the student assignment to avoid "simplistic" artifact (i.e. mere copying of demonstration) that does not provide any clear evidence of student learning.

4. Student will read Learning Objective 6.3.1 and write HTML and JavaScript comments identifying and addressing two of the Essential Knowledge statements

3. The following must be demonstrated by each student:

1. Creating a basic webpage using HTML including an HTML comment

2. Creating an "id" and "class" attribute within 2 or more HTML tags

3. Manipulating the HTML tags containing one or more "id" and "class" attributes programmatically via Javascript including JavaScript comments.

4. Write the following algorithms (methods/functions) using Javascript to manipulate the DOM

   • swap

   • loop

   • conditional (if...then...)

Specifications

• Turn in the HTML & Javascript source code on disk or printout

• Print out this grading rubric.

• Follow expectations for professional programming (commenting, indentation, etc.).

  • NOTE: JavaScript comments are similar to Java but HTML comments are actually tags (i.e. <!-- ... -->)

P5: Project 5 : Three Dimensional Modeling and Visualization usinga RayTracer (Pov-Ray)

[using a scene description language to create images]

 

Learning Objectives - Students will :

1. become familiar with a scene-description programming language used in a ray-tracer [PovRay.org] to create photo-realistic 3 dimensional images.

2. create a sequence of increasingly complex programs to learn the fundementals of a scene description language

3. write traditional computer language algorithms such as loops, conditionals, variables and abstract constructs (objects)

4. investigate more complex and abstract 3 dimensional mathematical constructs such as animations (time-dependant) or constructive solid geometry

 

Scoring Rubric

Name ________________________________	Approval
Image # 1 - box, sphere, plane, cylinder;	X	30
Image # 2 - description:		30
Image # 3 - description of advanced feature:		30
Engineering Notebook - update of ToC, project header, important formulas/code, calculations, collaborators, notes, marking of Essential Knowledge statements, etc.		10
Project Total	100

 

Instructional Design Technique :

1. Illustration of the Hall-of-Fame winners hosted at http://hof.povray.org/

2. Demonstration of a basic scene description program featuring:

   1. Setup : Camera, Light Source, and a Plane with color and translation

           camera 
           {
               location <-5,3,-20> 
               look_at <0,0,0> 
           }
      
           light_source 
           { 
                 <0,10,-10> 
                 rgb <1,1,1> 
           } 
      
           plane 
           { 
                1*y, -1
                pigment
                {
                    color rgb<0,1,0>
                }
                translate <0,-2,0>
           } 

   2. Declarations and invocation of variable representing objects. Constructive Solid Geometry (CSG)

           #declare myBox = box 
           {    
                 <-1,-1,-1> <1,1,1> 
                 pigment 
                 {  
                     color rgb<1,0,1> 
                 } 
           }
           #declare mySphere = sphere{ <0,0,0>, 1.25 pigment{color rgb<1,0,0> }}
           myBox     // call or draw myBox
           mySphere  // draw mySphere
      
           // Consructive Solid Geometry (CSG)
           #declare cutOut = difference {
                  object {myBox} 
                  object {mySphere} 
           }
           object {cutOut, translate<-5,0,0>} // draw the difference between myBox and mySphere
                              

   3. Use of a loop construct [algorithms]

        #declare ycnt = 0;
        #declare xcnt = -5;  // INITIALIZE the Loop Control Variable (LCV)   
        #while(xcnt < 10)    // TEST the LCV
            object 
            { 
              cutOut  // declared before as a difference of myBox-mySphere
              translate<xcnt,ycnt,0>    
              rotate <0,ycnt*10,0>
            } 
            #declare ycnt = xcnt*xcnt + 1; // calculate the parabola
            #declare xcnt = xcnt + .25;    // UPDATE the LCV
        #end 
                     

   4. Use of macro (i.e. procedure) with parameters, vector/list, and algorithm

      
      camera { location <-7,3,-7 > look_at < 0,0,0> } 
      
      light_source { < 0,10,-10> rgb < 1,1,1> }  
      
      plane { 1*y, -1 pigment { color rgb <0,1,0 >} translate <0,-2,0 >}
      cylinder { <-10,0,0 > <10,0,0 > .1 pigment{ color rgb <1,0,0 >}}
      cylinder { <0,-10,0 > <0,10,0 > .1 pigment{ color rgb <0,1,0 >}} 
      cylinder { <0,0,-10 > <0,0,10 > .1 pigment{ color rgb <0,0,1 >}}    
      
      #declare ball = object {sphere{ <0,0,0 >, 0.05}};
      
      /**
      * Declaring a macro called "sphereVector" is a procedure or method
      * with parameters (i.e. variables)
      * that can be used anywhere in the macro.
      * PARAMETERS:
      * c1 is a color vector in the form <r,g,b>
      * xs is a number that represents the starting x-coordinate of the image
      * ys is a number that represents the starting y-coordinate of the image
      * Zs is a number that represents the starting Z-coordinate of the image
      */
      #macro sphereVector(c1,xs,ys,zs,num)
      
          #local EndXcoord = num+xs; 
          #local EndYcoord = num+ys; 
          #local EndZcoord = num+zs; 
          
          #local Xcoord = xs;    
          #while (Xcoord < EndXcoord) 
             
              #local Ycoord = ys;     
              #while (Ycoord < EndYcoord) 
                 
                 #local Zcoord = zs;     
                 #while (Zcoord < EndZcoord) 
               
                    object {
                          ball 
                          translate <Xcoord*0.5 Ycoord*0.5 Zcoord*0.5>
                          #if ((Ycoord > 5) & (Zcoord >-3))
                              pigment {color rgb c1}
                          #else
                              pigment {color rgb c1+<0,1,0>} // add colors
                          #end
                    } 
          
                    #local Zcoord = Zcoord + 1; 
                 #end 
                 
                 #local Ycoord = Ycoord + 1;  
              #end
              
              #local Xcoord = Xcoord + 1;  
          #end 
      
      #end
      
      // this macro can be called
      sphereVector(<0,0,1>,0,0,0,10)   //blue, starting at <0,0,0> with a "10-ball" cube
      sphereVector(<1,0,0>,-5,-2,-6,3) //red, shifted <-5,-2,-6> with a "3-ball" cube
      sphereVector(<1,0,1>,-5,4,7,4)   //purple, shifted <-5,4,7> with a "4-ball" cube
                      

   5. Use of animation (i.e. clock variable, frames, and ini files)

      • PovRay does NOT do animation directly. Instead, PovRay will automatically generate a sequence of images (i.e. image1.gif, image2.gif, etc.) called frames using a special automatic "clock" variable. In order for PovRay to generate multiple frames, a separate file called an "ini" file specifies the PovRay file to generate as well as specifying the number of frames and the start/stop clock timings.
      • The code below shows the two files (i.e. animationPOV.pov and animationINI.ini). Note that the animationINI.ini file has a different syntax and structure than the animationPOV.pov file. As well, the animationINI.ini file specifies the number of frames and start/stop clock variable as well as "running" the animationPOV.pov file. The animationPOV.pov file uses the "clock" variable to change aspects on a per-frame basis.

      This is the animationINI.ini file : specifies frames, and clock start and stop times as well as input and ouput files.

      ; this is an INI comment (semicolon)
      
      ; this file should be saved as "animationINI.ini" for use in POVRay
      
      Initial_Frame = 0   ; matches clock variable so clock step per frame
      
      Final_Frame   = 10  ; = 1.0/(Final_Frame-Initial_Frame) = 1/10
      
      Initial_Clock = 0.0 ; keep default = 0.0 and have PovRay file use a different startClk
      
      Final_Clock   = 1.0 ; local variables (like endClk) to control actual animation 
      
      Output_File_Name= animation.png ; files named animation0 to animation10
      
      Input_File_Name = animationPOV.pov ; PovRay file to render
                              

      This is the animationPOV.pov file : uses clock variable to control values for translating, rotating, and color over time

         // This is the animationPOV.pov
         camera { location <-7,10,-20 > look_at < 0,0,0> } 
         light_source { < -7,10,-20> rgb 2*< 1,1,1> } 
                                     
         /* The following includes use of the clock variable in a translation up, rotate around y-axis and 
          *  changing colors (light purple to dark purple
          */
          #declare startClk = 1.0; // assume animationINI.ini file specifies clock variable going from 0.0 to 1.0
          #declare endClk   = 10.0; // controls what time will myClock end at
          #declare myClock  = startClk + (endClk-startClk)*clock; // scale the clock variable
                                    
          // now declare our objects and apply myClock to the animation
          #declare ball = object {sphere{ <0,0,0 >, 0.5}};
          object {ball translate<0, 10-myClock, 0> rotate<0,36*myClock,0> pigment{color rgb<2/myClock,0,2/myClock>}}
            
          // show the ground and 3 axes
          plane { 1*y, 0 pigment { color rgb <0,1,0 >} translate <0,-5,0 >}
          cylinder { <-10,0,0 > <10,0,0 > .1 pigment{ color rgb <1,0,0 >}}   // x-axis is red
          cylinder { <0,-10,0 > <0,10,0 > .1 pigment{ color rgb <0,1,0 >}}   // y-axis is green
          cylinder { <0,0,-10 > <0,0,10 > .1 pigment{ color rgb <0,0,1 >}}   // z-axis is blue
      
                                   

3. Illustration of Advanced modeling & visualization techniques [i.e. advanced algorithms] hosted at:

   1. Germany - Tutorials & Examples - Friedrich A. Lohmueller
   2. Japan - Gallery with Examples - Tsutomu Higo

Instructions :

• Using the POV-Ray program and the scene description language, create a series of 3 dimensional graphic images.

1. The first image should be an include: 1) box, 2)plane 3) sphere, and 4) cylinder. You may use Mr. Meinzen's website and POV-Ray tutorial for help or generate your own.

2. The 2nd image requires a more complex design of your choice. Discuss and get prior approval from Mr. Meinzen before starting. The 2nd image will require the use of at least one of each of the following algorithms: loop, conditional (if...then), variable declaration, and declared object. Specify in your code's comments how you used abstraction and algorithms within your 2nd image.

3. The 3rd image(s) may be either an animation or require a complex POV-Ray mathematical feature...see below. Discuss and get prior approval from Mr. Meinzen before starting. Specify in your code's comments how you used abstraction and algorithms within your 3rd image.

Specifications :

• First image due within 3 days of assignment

• 2nd and 3rd images due as discussed and approved by Mr. Meinzen

• Alternative images / graphics and grading may be allowed with discussion and approval by Mr. Meinzen.

• A Hardcopy (i.e. printout) of the above rubric, your source code, and image is to be turned in for Mr. Meinzen to score.

• Commenting, indenting and choice of appropriate variable names will be included in the scoring.

• Any student who loses or does not get pre-approval before an image is due will receive only 50% credit.

Notes

Educational Websites	2nd Image Ideas	3rd Image Ideas
Tutorials & Examples- Friedrich A. Lohmueller (German author)	constructive solid geometry (merge, union, difference, etc.)	animation
Gallery with Examples - Tsutomu Higo (Japanese author)	while loops, conditionals, defined variables, defined objects	mathematical constructions (i.e. parabaloids, surface of revolutions, etc.)
	blob and translucent objects	fractal
	matrix to "shear" shapes	polynomial (coefficient matrix)
		texture maps
Big Projects for 2nd & 3rd images
Color as a Math 3D Vector, ColorCube.com, wikipedia, webpage colorschemes.Mathematical Art (commercial), HyperCubes

 

Other Computational Science Projects

 

Look at each the following decision-making algorithm as applied to life-choices. Investigate one topic and write a single-page paper illustrating how the algorithm is used in your (or your family's) life.

 

Synopsis of Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian and Tom Griffiths.

1. Choosing only the Best: when to stop looking and decide... the "37% Rule"
1. Situation: We have to make a single "best" decision out of several potential choices. Unfortunately, we can only select or reject each choice one at a time before we can consider the next choice.
2. Computer Science Perspective: "Optimal Stopping Algorithm" and "Secretary Problem"
1. Estimate the total number of options (or estimate time spent looking/waiting or estimate the "cost" of looking/waiting).
2. Do not select the first 37% (actually the percentage is exactly 1/e) of the options and, instead, learn from the first 37% of those options (called: .
3. After learning as much as you can from the first 37%, choose the first option that is "better" than any of the first 37% you've already seen.
3. Real-life Example:
1. You want to buy a house in a "hot market" and another person may buy the house later that day. How do you decide to make an offer on the "best" house? If you wait too long, you will lose the house to another buyer.
2. Interviewing candidates one-at-a-time and deciding whether to offer a job to them or to look at the next candidate?
3. You can date as many people as you like but only one at at time. How do you decid which person to marry?
4. You want to sell your house but can only consider one offer at a time. How do you determine to accept a "good" offer or wait for a possible 'better" offer?
5. When you are deciding on a parking space in a crowded lot, do you select the first free spot or keep driving to get a potentially better spot?
2. Choosing Latest versus the Greatest: when to explore new options and when to use the known favorites
1. Situation: We have to decide when new experiences should be chosen over a existing favorites. Should we go to a new restaurant or an old favorite restaurant?
2. Computer Science Perspective: Use the "Win-Stay Lose-Switch Algorithm", "Bandit Problem", and "Prisoner's Dilemma" to minimize regret. Or, for more complicated decisions, use a "Gittins Index" which stands for "git while the gittens good."
3. Real-life Example:
1. For "better-than-random" choices: You are at a casion using a gambling machine (one-armed bandits). You should keep using the same machine until you lose. When you lose the first time, you switch to another machine and keep playing it until you lose. Then switch to a 3rd machine, and so on.
2. When to try a new selection: You have a favorite restaurant but, at the first bad meal, you switch to another new restaurant.
3. When deciding to leave a well-paying job for a risky adventure, consider which option-when you are 80-years-old-would cause you to have the least regret...the minimal regret option becomes your decision
4. In clinical trials, hisorically two groups are created. One is a control group that receives a plecebo (fake pill) will the other group is the expermental group that gets the new medicine. After a set period of time, the results of each group are analyzed to determine the likelihood of the effect of the medicine.
   However, this may be immoral in life-and-death situations such as new treatments to save babies lives. A newer statistical approach is to use "adaptive" trials. See ECMO research and the "Tuskegee Suyphilis Study"
3. Making Order out of Chaos: when to keep things sorted and when not to sort
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
4. Forget about it: when is too much information not worth keeping
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
5. First things First: why we set priorities
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
6. Predicting the Future: using Bayes's Rule
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
7. Overfitting to the Data: when to stop thinking so hard
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
8. Relaxation: when to make things easier by loosening the rules
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
9. Randomness: some things are best left to chance
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
10. Networking: how do we connect
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
11. Game Theory: looking into the minds of others
1. Situation:
2. Computer Science Perspective:
3. Real-life Example:
12. Computational Kindness: going easy on others
1. Situation:
2. Computer Science Perspective:
3. Real-life Example: