Plotter-interpreter

Description: The project realizes an interpreter designed for a Function-Drawing-Language.

1. Environment and Requirement

Operating System: Windows10

Tools: Visual Studio Code

Requirement: Python >= 3.8.0, Numpy >= 1.18.5, Matplotlib >= 3.2.1

2. The Architecture

│-- run.py                  (entrance of the program)
│-- test.txt                (test examples)
│-- testparser.py           (test program for parser)
│-- testscanner.py          (test program for scanner)
├─Parser                    (grammer analysis)
│  │-- parserParser.py      (grammer analysis module)
│  │-- parser_exprnode.py   (define the data structure of grammer tree node)
├─scanner                   (scanner analysis)
│  │-- scannerprocessor.py  (scanner analysis module)
│  │-- token.py             (define the data structure of tokens)
└─semantic                  (semantic analysis)
   │-- semantic.py          (semantic analysis module)

3. Scanner

• Class Token

  For each type of token, an abstract data type needs to be defined to storage. I defines its data structure as the class Tokens, which includes 4 members: type, lexeme, value, and funcptr, which are used to represent the type of token, Content, value and function pointer.

• DFA of Scanner

  

• Details

  • In the construction of the token table, this article uses the functions in the package numpy instead of the functions in the package math.
  • A method BackChar is defined to implement the character rollback operation while reading file.

4. Parser

• Class ExprNode

  In order to construct the syntax tree, I designed the abstract data type of the syntax tree node as ExprNode, which supports realizing the definition of functions, operators and operands.

• Function

  It can calculate the line number through $self.scanner.LineNo$, and can report an error when $token.type != ttype$.

• Grammar Tree

  It prints the syntax tree by designing a pre-order traversal algorithm.

5. Semantic

• Class Semantic

  • Class Semantic is an inheritance of the class Parser.
  • According to the parameters extracted by the ROT, SCALE, and Origin methods, they are turned into the member variables of the object, and the drawing is realized through the FOR statement.

• Attention

  The formula for the rotation of $x$ and $y$ coordinates is shown in formula 1. In the implementation process, the intermediate variable $tmp$ must be used to temporarily store $x$.

$$ \begin{eqnarray} \begin{bmatrix} x'\ y'\\end{bmatrix}= \begin{bmatrix} cos\theta & sin\theta \ -sin\theta & cos\theta \ \end{bmatrix} \begin{bmatrix} x\ y\\end{bmatrix}\tag 1 \end{eqnarray} $$

6. Results

• Examples 1:

  rot is 0;
  origin is (0, 0);
  scale is (2,2+2*5+9-1);
  for T from 1 to 3*(1+3**3) step 1 draw (t,-ln(t));
  scale is (20,0.1);
  for T from 0 to 8 step 0.1 draw (t,exp(t));
  scale is (2,1);
  for T from 0 to 300 step 1 draw (t,0);
  for T from 0 to 300 step 1 draw (0,t);
  for T from 0 to 120 step 1 draw (t,t);  --sss
  scale is (2,0.1);
  for T from 0 to 55 step 1 draw (t,-(t*t));   //sss
  scale is (10,5);
  for T from 0 to 60 step 1 draw (t,sqrt(t));

  

• Examples 2:

  rot is 0;
  origin is (0, 0);
  scale is (100,100);
  for t from 0 to pi*20 step Pi/50 draw ((1-1/(10/7))*cos(T)+1/(10/7)*cos(-T*(((10/7)-1))), (1-1/(10/7))*sin(T)+1/(10/7)*sin(-T*((10/7)-1)));
  origin is (500,500);
  scale is (100,100/3);
  rot is pi/2;
  for T from -pi to pi step pi/50 draw (cos(t),sin(t));
  rot is pi/2 + 2*pi/3;
  for T from -pi to pi step pi/50 draw (cos(t),sin(t));
  rot is pi/2 - 2*pi/3;
  for T from -pi to pi step pi/50 draw (cos(t),sin(t));