Homework 4 and 5: Simple Drawing Program Part 3

New Features

Add assignment, grouping, and programmability to your simple drawing program.

Input Language

Commands

A drawing consists of zero or more commands. A command can be an assignment, a drawing parameter setting, a picture, or a control structure. Each command is written with a command name and parameters separated by whitespace and surrounded by parentheses. The parameters of a command can be numerical expressions or other pictures. A picture is either a picture element or a transformation of a picture.

Numerical Expressions

A numerical expression can be a primitive expression or compound expression. Primitive expressions are as follows:

N: where N is a floating-point number, e.g., 0, -1, 3.14
X: where X is a symbol. A symbol is a valid Python identifier. (You may call str.isidentifier() to determine if a string is a valid identifier.) The last assignment to the symbol determines its value. If X does not have a value, then the expression is invalid.

Compound numerical expressions are compositions of other numerical expressions (primitive or compound):

(+ A B): The sum of A and B
(- A B): The difference of A and B
(* A B): The product of A and B
(/ A B): The quotient of A and B
(sin A): The sine of A degrees
(cos A): The cosine of A degrees

Handle all numbers in floating point.

Assignment

(:= X E): Where X is a symbol and E a numerical expression. This command will evaluate the numerical expression E, and then store that value to the symbol X. Any subsequent references to X before the next assignment to X will evaluate to that value. For example, the following code: (:= X 1) (linewidth X) (:= X 2) (line 0 0 X X) should produce
1 setlinewidth 0 0 moveto 2 2 lineto stroke

Picture Elements

Create picture elements using the commands below. Parameters of the picture elements are numerical expressions.

The coordinate (0,0) is the origin and is the lower left corner of the drawing. X-coordinate values increase to the right and y-coordinate values increase to the top.

(line X₀ Y₀ X₁ Y₁): Draw a line with the first endpoint at (X₀, Y₀) and the second endpoint at (X₁, Y₁).
(rect X Y W H): Draw the outline of a rectangle whose lower left corner is at (X,Y), and which has a width of W and height of H. Draw the rectangle counter-clockwise starting from the lower left corner.
(filledrect X Y W H): Same as rect, but fill the rectangle rather than simply drawing its boundary.
(tri X Y R): Draw the outline of an equilateral triangle whose center is at (X, Y) with one of the vertices at (X + R, Y). Draw the triangle counter-clockwise starting from (X + R, Y). This order applies to all the following picture elements.
(filledtri X Y R): Same as tri, but fill the triangle rather than simply drawing its boundary.
(square X Y R): Draw the outline of a square whose center is at (X, Y) with one of the vertices at (X + R, Y).
(filledsquare X Y R): Same as square, but fill the square rather than simply drawing its boundary.
(penta X Y R): Draw the outline of a regular pentagon whose center is at (X, Y) with one of the vertices at (X + R, Y).
(filledpenta X Y R): Same as penta, but fill the pentagon rather than simply drawing its boundary.
(hexa X Y R): Draw the outline of a regular hexagon whose center is at (X, Y) with one of the vertices at (X + R, Y).
(filledhexa X Y R): Same as hexa, but fill the hexagon rather than simply drawing its boundary.
(ngon X Y R N): Draw the outline of a regular N-gon for integer N > 2, whose center is at (X, Y) with one of the vertices at (X + R, Y).
(filledngon X Y R N): Same as ngon, but fill the ngon rather than simply drawing its boundary.
(sector X Y R B E): Draw the outline of a circular sector where (X, Y) is the center, R is the radius, B and E are the beginning and ending angles, respectively, measured in degrees counterclockwise from the positive x-axis. Draw this sector in the following order: (1) the line from the center to the beginning angle on the arc (2) the arc from the beginning angle to the ending angle counterclockwise, and (3) the line from the ending angle on the arc back to the center.
(filledsector X Y R B E): Same as sector, but fill the circular sector rather than simply drawing its boundary.
(group P₁ P₂ ... P_N): Draw pictures P₁ through P_N, in that order. Any transformations applied to this picture element will be applied to all of the members of the group.

Transformations

Create transformations using the commands below. Parameters of transformations are a picture followed by numerical expressions.

(translate P X Y): Translate the picture P by X units along the x-axis and Y units along the y-axis.
(rotate P X): Rotate the picture P by X degrees about the origin.
(scale P S): Scale the picture P by a factor of S, where S > 0. If (X ,Y) was a vertice on the picture, then its new coordinate after scaling is (X * S, Y * S).

Drawing Parameters

Create drawing parameters using the commands below. Parameters of the drawing parameter are numerical expressions.

(color R G B): Set the current color to (R,G,B). The arguments must be numbers between 0 and 1, inclusive. Initially, R = G = B = 0 (i.e. black).
(linewidth W): Set the current line width to W, which must be a non-negative number. This meaning of this width value is as that of PostScript, meaning you can pass this value directly to PostScript commands. The initial value of the line width is 1.

Control Structure

(for I L U E₁ ... E_N): Execute commands E₁ to E_N multiple times, first with the symbol I set to the integer L, then to L+1, ..., up to and including U. Does nothing if U < L or N == 0 (e.g., there are no commands). At the end of the command, the symbol I has the value max(L, U).

Zero or more whitespaces are allowed between a parenthesis and the start or end of a command, and between commands. At least one character of whitespace is required to separate arguments within a command.

For example, the following would draw a thick blue square, rotated 45 degrees.
(linewidth 5) (color 0 0 1) (rotate (rect 100 100 100 100) 45)

We will test your program with only valid drawing input. In other words, your program need not handle input errors.

Encapsulated PostScript

The output of your program will be an Encapsulated PostScript (EPS) document. You can view an EPS file with any PostScript viewer. A popular one is gv available on Linux. An EPS file has the following form:

%!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 0 0 1239 1752
commands

The commands of the PostScript language are in postfix notation. The actual PostScript language is free form, meaning operands and operators can be separated by arbitrary whitespace. Your output, however, must mimic the reference program to make your program easier to debug and grade. Each command will start on a newline with operands separated by a single space.

The origin of a PostScript starts at (0,0) in the lower left corner, with x-coordinates increasing to the right and y-coordinates increasing to the top. To draw something, one builds a path, and then strokes it or fills it. The PostScript interpreter maintains a graphics state, which for our purposes consists of

A current point, (x,y) coordinate, which is initially undefined.
A current path.
A current color, a 3-tuple (r,g,b), where each color intensity r,g,b is between 0 and 1 inclusive. (0,0,0) is black and (1,1,1) is white.
A current line thickness, which indicates the thickness of lines drawn when stroking.

You can use the following subset of the PostScript language to construct your PostScript file. In this subset, all operands are decimal numbers (e.g. 0.1, 2.3, 45).

X Y moveto: Set the current point to (X, Y).
X Y lineto: Add a line segment to the current path starting at the current point and going to (X, Y), which becomes the new current point.
X Y R B E arc: Draw an arc centered at (X, Y) with radius R, beginning at B and ending at E degrees measured counterclockwise from the positive x axis. Both B and E must be in the range of [0, 360). (The last requirement is not imposed by PostScript, but it normalizes your output to be comparable to that of the reference program.)
stroke: Draw lines with the current line width and color over all the segments in the current path. Clear the current path and undefine the current point.
fill: Fill the interior of the current line path with the current color. Clear the current path and set the current point to undefined.
W setlinewidth: Set the current line width to W. The initial value of the line width is 1.
R G B setrgbcolor: Set the current color to (R, G, B).

To tolerate small errors in floating point computation, the gradebot uses cmpfloat.py (SHA-1: 08ed50ecf4b0356527da25e967b06483876f7f75) to compare the output of your program to that of the reference program. When they are equal, cmpfloat.py outputs nothing.

Masterpiece

You have been designing test cases to ensure that your program is correct, but may not have had the chance to enjoy the fruits of the labor that you have put into the drawing program. After studying the input language above, express your artistic creativity. Create a masterpiece.drw input file for the drawing program that produces a marvelous EPS output. You may use the reference program to produce the EPS output before finishing your own program.

We will exhibit your submitted masterpieces after Homework 4 to the entire university community. While this exercise is to help you understand all the commands of the drawing program, you may also take this opportunity to demonstrate your creativity. We will give awards for masterpieces chosen by a panel of celebrity judges. More information is available here.

Here are some examples of masterpieces. Be ambitious. Demonstrate your creativity.

Hints

Process the input through the following stages:

Tokenzier: reads input, and outputs a sequence of tokens, such as (, ), line, translate, color, etc.
Parser: reads tokens from the tokenizer, and outputs a parse tree per command.
Evaluator: evaluates each parse tree recursively.