Initial Commit

equation.py

@@ -0,0 +1,53 @@
+
+
+class Equation:
+
+    def __init__(self, xf, yf, cf=(255,255,255), wf=1):
+        self.xf = xf
+        self.yf = yf
+        self.cf = cf
+        self.wf = wf
+
+    def _xf(self, t):
+        if callable(self.xf):
+            return self.xf(t)
+        else:
+            return t
+
+    def _yf(self, t):
+        if callable(self.yf):
+            return self.yf(t)
+        else:
+            return t
+
+    def _cf(self, t, r):
+        if callable(self.cf):
+            return self.cf(t, r)
+        else:
+            return self.cf
+
+    def _wf(self, t, r):
+        if callable(self.wf):
+            return self.wf(t, r)
+        else:
+            return self.wf
+
+    def plot(self, r=(0, 12, 0.1), scale=(1,1)):
+        t = r[0]
+        prev_x = self._xf(t)
+        prev_y = self._yf(t)
+        while t <= r[1]:
+            x = self._xf(t)
+            y = self._yf(t)
+            c = self._cf(t, r)
+            w = self._wf(t, r)
+            yield (
+                int(prev_x * scale[0]),
+                int(prev_y * scale[1]),
+                int(x * scale[0]),
+                int(y * scale[1]),
+                c,
+                w,
+            )
+            prev_x, prev_y = x, y
+            t += r[2]

example.graph

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+# Kyler Olsen
+# Apr 2024
+# Hypotrochoid Example
+
+SCREEN {
+    Width Scale: 100,
+    Height Scale: 100,
+
+    FPS: 60,
+}
+
+R = 7;
+r = 4;
+d = 1;
+
+ANIM offset {R:0 <= x <= 8*pi,S:π/128}
+
+GRAPH {
+    X: (R - r) * cos(t) + d * cos(((R - r) / r) * t),
+    Y: (R - r) * sin(t) - d * sin(((R - r) / r) * t),
+    T: ANIM {R:0+offset <= x <= 8*pi+offset,S:π/32},
+    C_w: ((t - r[0]) / (r[1] - r[0]))
+}

main.py

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+import pygame
+import sys
+import math
+from equation import Equation
+
+# Initialize Pygame
+pygame.init()
+
+# Screen dimensions
+
+# Screen setup
+# screen = pygame.display.set_mode((800, 600))
+screen = pygame.display.set_mode()
+pygame.display.set_caption("Equation Plotter")
+
+class Hypotrochoid(Equation):
+
+    def __init__(self, R, r, d, c=(255,255,255)):
+        self.R = R
+        self.r = r
+        self.d = d
+        super().__init__(self._h_xf, self._h_yf, self._h_cf, 5)
+
+    def _h_xf(self, t):
+        return (self.R - self.r) * math.cos(t) + self.d * math.cos(((self.R - self.r) / self.r) * t)
+
+    def _h_yf(self, t):
+        return (self.R - self.r) * math.sin(t) - self.d * math.sin(((self.R - self.r) / self.r) * t)
+
+    def _h_cf(self, t, r):
+        c = int(((t - r[0]) / (r[1] - r[0])) * 255)
+        return c, c, c
+
+    # def _h_wf(self, t, r):
+    #     return int(((t - r[0]) / (r[1] - r[0])) * 5)
+
+def main(equ):
+    SCREEN_WIDTH = screen.get_width()
+    SCREEN_HEIGHT = screen.get_height()
+    HALF_WIDTH = SCREEN_WIDTH // 2
+    HALF_HEIGHT = SCREEN_HEIGHT // 2
+    # Main loop
+    off = 0
+    mouse_x_last, mouse_y_last = pygame.mouse.get_pos()
+    running = True
+    while running:
+        for event in pygame.event.get():
+            if event.type == pygame.QUIT:
+                running = False
+
+        # Clear the screen
+        screen.fill((0,0,0))
+
+        for prev_x, prev_y, x, y, c, w in equ.plot((0 + off, (8 * math.pi) + off, math.pi/32), (100, 100)):
+            pygame.draw.line(screen, c, (prev_x + HALF_WIDTH, HALF_HEIGHT - prev_y), (x + HALF_WIDTH, HALF_HEIGHT - y), w)
+
+        pygame.display.flip()
+        pygame.time.Clock().tick(60)
+        off += math.pi/128
+
+        # if direction:
+        #     equ.R += 0.1
+        #     equ.r += 0.05
+        #     if equ.R >= 20:
+        #         direction = False
+        # else:
+        #     equ.R -= 0.1
+        #     equ.r -= 0.05
+        #     if equ.R <= 6:
+        #         direction = True
+
+        mouse_x, mouse_y = pygame.mouse.get_pos()
+        if 5 < math.sqrt(pow(mouse_x_last - mouse_x, 2) + pow(mouse_y_last - mouse_y, 2)):
+            running = False
+
+    pygame.quit()
+    sys.exit()
+
+# main(Equation(None, lambda t: math.sin(t)))
+# main(Hypotrochoid(6, 4, 1))
+main(Hypotrochoid(7, 4, 1))
+# main(Hypotrochoid(15, 14, 1))

readme.md

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+# YTD Graphing Language
+
+
+
+## Lexical Definition
+
+### Comments
+
+Comments can either be single-line comments or multi-line comments.
+
+Single-line comments start with `#` and end at the end of a line.
+
+### Identifiers
+
+Can be up to 31 characters in length, and are case sensitive.
+They cannot be a keyword.
+
+```
+Identifier ::= ID_Start*
+ID_Start ::= <Any latin alphabet ligature: "A"-"Z", "a"-"z">
+```
+
+### Keywords
+
+Keywords are not case sensitive.
+
+```
+screen  graph   anim    img
+sum     pi      alpha   beta
+theta   inf     product integral
+```
+
+### Literals
+
+```
+number ::=  decinteger | pointfloat | exponentfloat
+decinteger ::=  nonzerodigit (["_"] digit)* | "0"+ (["_"] "0")*
+nonzerodigit ::=  "1"..."9"
+digit ::=  "0"..."9"
+pointfloat    ::=  ([digitpart] fraction) | (digitpart ".")
+exponentfloat ::=  (digitpart | pointfloat) exponent
+digitpart     ::=  digit (["_"] digit)*
+fraction      ::=  "." digitpart
+exponent      ::=  ("e" | "E") ["+" | "-"] digitpart
+```
+
+### Punctuation
+
+```
++   -   *   /   %   ^
+=   !   <   <=  >   >=
+{   }   [   ]   (   )
+_   ->  ,   ;   :   ∑
+∏   ∞   ≠   ≤   ≥   ∫
+α   β   π   →   θ
+```
+
+#### Punctuation Conversions
+
+| Original | New |
+| -- | -- |
+| <= | ≤ |
+| >= | ≥ |
+| -> | → |
+
+#### Keyword Conversions
+
+| Original | New |
+| -- | -- |
+| sum | ∑ |
+| pi | π |
+| alpha | α |
+| beta | β |
+| inf | ∞ |
+| product | ∏ |
+| integral | ∫ |
+| theta | θ |
+
+## Syntax
+
+The syntactical structure starts with a `file` at the root.
+
+### File
+
+A `file` can contain any number of the following elements:
+- *Screen*
+- *Graph*
+- *Animation*
+<!-- - *Image* -->
+
+### Screen
+
+A *screen* begins with the `screen` keyword. It then has a comma (`,`)
+separated list enclosed in curly braces (`{` and `}`) of *screen parameters*.
+At most only one screen block is allowed per `file`.
+
+#### Screen parameter
+
+A *screen parameter* begins with its parameter name then a colon (`:`) followed
+by its value.
+
+Listed bellow are the possible parameters.
+
+**Top**
+- Role:
+    Sets the Y-Coordinate of the top of the screen to the given value.
+- Required:
+    False
+- Default:
+    `Unset`
+- Possible Values: Integers, `Unset`
+
+**Bottom**
+- Role:
+    Sets the Y-Coordinate of the bottom of the screen to the given value.
+- Required:
+    False
+- Default:
+    `Unset`
+- Possible Values: Integers, `Unset`
+
+**Right**
+- Role:
+    Sets the X-Coordinate of the right of the screen to the given value.
+- Required:
+    False
+- Default:
+    `Unset`
+- Possible Values: Integers, `Unset`
+
+**Left**
+- Role:
+    Sets the X-Coordinate of the left of the screen to the given value
+- Required:
+    False
+- Default:
+    `Unset`
+- Possible Values: Integers, `Unset`
+
+**Width**
+- Role:
+    Sets the X-Coordinate range of the screen to the given value
+- Required:
+    False
+- Default:
+    `Unset`
+- Possible Values: Natural Numbers, `Unset`
+- Note:
+    Centered on zero if `right` and `left` are unset.
+    Has no affect if `right` and `left` are set.
+
+**Height**
+- Role:
+    Sets the Y-Coordinate range of the screen to the given value
+- Required:
+    False
+- Default:
+    `Unset`
+- Possible Values: Natural Numbers, `Unset`
+- Note:
+    Centered on zero if `top` and `bottom` are unset.
+    Has no affect if `top` and `bottom` are set.
+
+**Width Scale**
+- Role:
+    Sets the X-Coordinate range of the screen to the screen pixel
+        width divided by the given value
+- Required:
+    False
+- Default:
+    `20`
+- Possible Values: Positive Real Numbers
+- Note:
+    Centered on zero if `right` and `left` are unset.
+    Has no affect if `right` and `left` are set or if `width` are set.
+
+**Height Scale**
+- Role:
+    Sets the Y-Coordinate range of the screen to the screen pixel
+        height divided by the given value
+- Required:
+    False
+- Default:
+    `20`
+- Possible Values: Positive Real Numbers
+- Note:
+    Centered on zero if `top` and `bottom` are unset.
+    Has no affect if `top` and `bottom` are set or if `height` are set.
+
+**FPS**
+- Role:
+    Sets the refresh rate of the screen
+- Required:
+    False
+- Default:
+    `30`
+- Possible Values: Natural Numbers
+
+### Graph
+
+A *graph* begins with the `graph` keyword. It then has a comma (`,`)
+separated list enclosed in curly braces (`{` and `}`) of *graph parameters*.
+A graph block defines a graph to be drawn.
+
+#### Graph parameter
+
+A *graph parameter* begins with its parameter name then a colon (`:`) followed
+by an `expression`.
+
+Listed bellow are the possible parameters and their possible roles.
+Any ranges can be the `identifier` of an *animation* or an *inline animation*.
+
+**X**
+- The `x = f(y)` function for `y` independent cartesian equations.
+- The `x = f(t)` function for parametric equations.
+- The `x` range (animation) for `x` independent cartesian equations.
+
+**Y**
+- The `y = f(x)` function for `x` independent cartesian equations.
+- The `y = f(t)` function for parametric equations.
+- The `y` range (animation) for `y` independent cartesian equations.
+
+**T**
+- The `t` range (animation) for parametric equations.
+
+**R**
+- The `r = f(θ)` function for polar equations.
+
+**θ**
+- The `θ` range (animation) for polar equations.
+
+*Color functions*
+- The `c = f(x)` function for `x` independent cartesian equations.
+- The `c = f(y)` function for `y` independent cartesian equations.
+- The `c = f(t)` function for parametric equations.
+- The `c = f(θ)` function for polar equations.
+
+#### Color Functions
+
+*Color function* parameter names are **C_x** where the *x* is color space part
+subscript.
+Only one color space can be used in each graph.
+If only alpha is set the default color space is **Grey-scale**.
+
+Listed bellow are the available color spaces and their subscripts.
+Default value in parenthesis for the unused subscripts of the color spaces.
+
+- **Grey-scale**: `wa` - Grey-scale (1), Alpha (1)
+- **RGB**: `rgba` -  Red (0), Green (0), Blue (0), Alpha (1)
+- **HSL**: `hsla` -  Hue (0), Saturation (1), Luminosity (0.5), Alpha (1)
+
+All values can be a real number between 0 and 1 inclusive.
+Values bellow this range will be interpreted as 0.
+Values above this range will be interpreted as 1.
+
+### Animation
+
+An *animation* begins with the `anim` keyword. Unless it is an
+*inline animation* block, the keyword is followed by its `identifier`. It then
+has a comma (`,`) separated list enclosed in curly braces (`{` and `}`)
+of *animation parameters*.
+
+When an animation is used in an expression, the value it is evaluated as is in
+the range defined, changing by the step every frame.
+
+#### Animation parameter
+
+An *animation parameter* begins with its parameter name then a colon (`:`)
+followed by an `expression`. If it is the only parameter the parameter name for
+the range is optional.
+
+Listed bellow are the possible parameters. Only the *range* parameter is
+required.
+
+**R** Range: `R:` *expression* `≤ x ≤` *expression*
+
+**S** Step: `S:` *expression*
+- Default is `1/10` unless a range expression is multiplied by `π` then it
+is `π/32`.
+
+**D** Direction: `D:` *direction*
+- `increase` (default)
+- `decrease`
+- `bounce`
+
+### Expressions
+
+
+
+#### Unary Expression
+
+A `unary expression` is made up of one `expression` and one `unary operator`.
+The operator may come before or after the expression.
+
+#### Binary Expression
+
+A `binary expression` is made up of one `expression`, then one
+`binary operator`, then another `expression`.
+
+#### Function
+
+A `function` starts with an `identifier` followed by a comma (`,`)
+separated list enclosed in parentheses (`(` and `)`) of *function arguments*.
+
+##### Function Argument
+
+A *function argument* is an `expression`.
+
+#### Enclosed Expression
+
+An `enclosed expression` is simply an `expression` enclosed in parentheses
+(`(` and `)`).
+
+#### Operator
+
+Here are all operators and their types and names in order of precedence.
+
+| Operator | Type | Name |
+| -- | -- | -- |
+| `-` | Unary (Prefix) | Negate *Operator* |
+| `!` | Unary (Postfix) | Factorial *Operator* |
+| `^` | Binary | Exponential *Operator* |
+| `_` | Binary | Subscript *Operator* |
+| `/` | Binary | Division *Operator* |
+| `%` | Binary | Modulus *Operator* |
+| `*` | Binary | Multiplication *Operator* |
+| `-` | Binary | Subtraction *Operator* |
+| `+` | Binary | Addition *Operator* |
+| `=` | Binary | Assignment *Operator* |
+
+#### Literal
+
+A `literal` is just simply the content of the literal.
+
+#### Identifier
+
+A `identifier` is just simply the name of the identifier.
+
+#### Statement
+
+A `statement` is made up of an `expression` followed by a semicolon (`;`).
+
+## Semantics
+
+### Screen Block
+
+### Graph Block
+
+<!-- ### Image Block
+
+Defines a background image.
+
+Additional image blocks will stack on top of the previous one in the order they
+are in the file.
+
+- **X**: The `x` range (animation) for the background.
+- **Y**: The `y` range (animation) for the background.
+- **R**: The `r` range (animation) for the background.
+- **A or Theta**: The `theta` range (animation) for the background.
+- **C_x**: The color function of the background. -->
+
+### Animation Block