Initial Commit
This commit is contained in:
Kyler
commit
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class Equation:
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def __init__(self, xf, yf, cf=(255,255,255), wf=1):
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self.xf = xf
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self.yf = yf
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self.cf = cf
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self.wf = wf
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def _xf(self, t):
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if callable(self.xf):
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return self.xf(t)
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else:
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return t
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def _yf(self, t):
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if callable(self.yf):
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return self.yf(t)
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else:
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return t
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def _cf(self, t, r):
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if callable(self.cf):
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return self.cf(t, r)
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else:
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return self.cf
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def _wf(self, t, r):
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if callable(self.wf):
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return self.wf(t, r)
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else:
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return self.wf
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def plot(self, r=(0, 12, 0.1), scale=(1,1)):
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t = r[0]
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prev_x = self._xf(t)
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prev_y = self._yf(t)
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while t <= r[1]:
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x = self._xf(t)
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y = self._yf(t)
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c = self._cf(t, r)
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w = self._wf(t, r)
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yield (
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int(prev_x * scale[0]),
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int(prev_y * scale[1]),
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int(x * scale[0]),
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int(y * scale[1]),
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c,
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w,
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)
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prev_x, prev_y = x, y
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t += r[2]
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# Kyler Olsen
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# Apr 2024
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# Hypotrochoid Example
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SCREEN {
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Width Scale: 100,
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Height Scale: 100,
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FPS: 60,
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}
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R = 7;
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r = 4;
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d = 1;
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ANIM offset {R:0 <= x <= 8*pi,S:π/128}
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GRAPH {
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X: (R - r) * cos(t) + d * cos(((R - r) / r) * t),
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Y: (R - r) * sin(t) - d * sin(((R - r) / r) * t),
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T: ANIM {R:0+offset <= x <= 8*pi+offset,S:π/32},
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C_w: ((t - r[0]) / (r[1] - r[0]))
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}
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import pygame
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import sys
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import math
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from equation import Equation
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# Initialize Pygame
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pygame.init()
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# Screen dimensions
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# Screen setup
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# screen = pygame.display.set_mode((800, 600))
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screen = pygame.display.set_mode()
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pygame.display.set_caption("Equation Plotter")
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class Hypotrochoid(Equation):
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def __init__(self, R, r, d, c=(255,255,255)):
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self.R = R
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self.r = r
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self.d = d
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super().__init__(self._h_xf, self._h_yf, self._h_cf, 5)
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def _h_xf(self, t):
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return (self.R - self.r) * math.cos(t) + self.d * math.cos(((self.R - self.r) / self.r) * t)
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def _h_yf(self, t):
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return (self.R - self.r) * math.sin(t) - self.d * math.sin(((self.R - self.r) / self.r) * t)
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def _h_cf(self, t, r):
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c = int(((t - r[0]) / (r[1] - r[0])) * 255)
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return c, c, c
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# def _h_wf(self, t, r):
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# return int(((t - r[0]) / (r[1] - r[0])) * 5)
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def main(equ):
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SCREEN_WIDTH = screen.get_width()
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SCREEN_HEIGHT = screen.get_height()
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HALF_WIDTH = SCREEN_WIDTH // 2
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HALF_HEIGHT = SCREEN_HEIGHT // 2
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# Main loop
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off = 0
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mouse_x_last, mouse_y_last = pygame.mouse.get_pos()
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running = True
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while running:
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for event in pygame.event.get():
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if event.type == pygame.QUIT:
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running = False
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# Clear the screen
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screen.fill((0,0,0))
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for prev_x, prev_y, x, y, c, w in equ.plot((0 + off, (8 * math.pi) + off, math.pi/32), (100, 100)):
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pygame.draw.line(screen, c, (prev_x + HALF_WIDTH, HALF_HEIGHT - prev_y), (x + HALF_WIDTH, HALF_HEIGHT - y), w)
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pygame.display.flip()
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pygame.time.Clock().tick(60)
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off += math.pi/128
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# if direction:
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# equ.R += 0.1
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# equ.r += 0.05
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# if equ.R >= 20:
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# direction = False
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# else:
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# equ.R -= 0.1
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# equ.r -= 0.05
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# if equ.R <= 6:
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# direction = True
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mouse_x, mouse_y = pygame.mouse.get_pos()
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if 5 < math.sqrt(pow(mouse_x_last - mouse_x, 2) + pow(mouse_y_last - mouse_y, 2)):
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running = False
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pygame.quit()
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sys.exit()
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# main(Equation(None, lambda t: math.sin(t)))
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# main(Hypotrochoid(6, 4, 1))
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main(Hypotrochoid(7, 4, 1))
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# main(Hypotrochoid(15, 14, 1))
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# YTD Graphing Language
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## Lexical Definition
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### Comments
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Comments can either be single-line comments or multi-line comments.
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Single-line comments start with `#` and end at the end of a line.
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### Identifiers
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Can be up to 31 characters in length, and are case sensitive.
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They cannot be a keyword.
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```
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Identifier ::= ID_Start*
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ID_Start ::= <Any latin alphabet ligature: "A"-"Z", "a"-"z">
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```
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### Keywords
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Keywords are not case sensitive.
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```
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screen graph anim img
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sum pi alpha beta
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theta inf product integral
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```
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### Literals
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```
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number ::= decinteger | pointfloat | exponentfloat
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decinteger ::= nonzerodigit (["_"] digit)* | "0"+ (["_"] "0")*
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nonzerodigit ::= "1"..."9"
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digit ::= "0"..."9"
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pointfloat ::= ([digitpart] fraction) | (digitpart ".")
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exponentfloat ::= (digitpart | pointfloat) exponent
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digitpart ::= digit (["_"] digit)*
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fraction ::= "." digitpart
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exponent ::= ("e" | "E") ["+" | "-"] digitpart
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```
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### Punctuation
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```
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+ - * / % ^
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= ! < <= > >=
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{ } [ ] ( )
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_ -> , ; : ∑
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∏ ∞ ≠ ≤ ≥ ∫
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α β π → θ
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```
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#### Punctuation Conversions
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| Original | New |
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| -- | -- |
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| <= | ≤ |
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| >= | ≥ |
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| -> | → |
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#### Keyword Conversions
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| Original | New |
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| -- | -- |
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| sum | ∑ |
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| pi | π |
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| alpha | α |
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| beta | β |
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| inf | ∞ |
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| product | ∏ |
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| integral | ∫ |
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| theta | θ |
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## Syntax
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The syntactical structure starts with a `file` at the root.
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### File
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A `file` can contain any number of the following elements:
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- *Screen*
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- *Graph*
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- *Animation*
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<!-- - *Image* -->
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### Screen
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A *screen* begins with the `screen` keyword. It then has a comma (`,`)
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separated list enclosed in curly braces (`{` and `}`) of *screen parameters*.
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At most only one screen block is allowed per `file`.
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#### Screen parameter
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A *screen parameter* begins with its parameter name then a colon (`:`) followed
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by its value.
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Listed bellow are the possible parameters.
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**Top**
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- Role:
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Sets the Y-Coordinate of the top of the screen to the given value.
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- Required:
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False
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- Default:
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`Unset`
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- Possible Values: Integers, `Unset`
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**Bottom**
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- Role:
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Sets the Y-Coordinate of the bottom of the screen to the given value.
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- Required:
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False
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- Default:
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`Unset`
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- Possible Values: Integers, `Unset`
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**Right**
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- Role:
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Sets the X-Coordinate of the right of the screen to the given value.
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- Required:
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False
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- Default:
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`Unset`
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- Possible Values: Integers, `Unset`
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**Left**
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- Role:
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Sets the X-Coordinate of the left of the screen to the given value
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- Required:
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False
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- Default:
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`Unset`
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- Possible Values: Integers, `Unset`
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**Width**
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- Role:
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Sets the X-Coordinate range of the screen to the given value
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- Required:
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False
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- Default:
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`Unset`
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- Possible Values: Natural Numbers, `Unset`
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- Note:
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Centered on zero if `right` and `left` are unset.
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Has no affect if `right` and `left` are set.
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**Height**
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- Role:
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Sets the Y-Coordinate range of the screen to the given value
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- Required:
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False
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- Default:
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`Unset`
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- Possible Values: Natural Numbers, `Unset`
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- Note:
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Centered on zero if `top` and `bottom` are unset.
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Has no affect if `top` and `bottom` are set.
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**Width Scale**
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- Role:
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Sets the X-Coordinate range of the screen to the screen pixel
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width divided by the given value
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- Required:
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False
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- Default:
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`20`
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- Possible Values: Positive Real Numbers
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- Note:
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Centered on zero if `right` and `left` are unset.
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Has no affect if `right` and `left` are set or if `width` are set.
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**Height Scale**
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- Role:
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Sets the Y-Coordinate range of the screen to the screen pixel
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height divided by the given value
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- Required:
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False
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- Default:
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`20`
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- Possible Values: Positive Real Numbers
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- Note:
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Centered on zero if `top` and `bottom` are unset.
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Has no affect if `top` and `bottom` are set or if `height` are set.
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**FPS**
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- Role:
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Sets the refresh rate of the screen
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- Required:
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False
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- Default:
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`30`
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- Possible Values: Natural Numbers
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### Graph
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A *graph* begins with the `graph` keyword. It then has a comma (`,`)
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separated list enclosed in curly braces (`{` and `}`) of *graph parameters*.
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A graph block defines a graph to be drawn.
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#### Graph parameter
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A *graph parameter* begins with its parameter name then a colon (`:`) followed
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by an `expression`.
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Listed bellow are the possible parameters and their possible roles.
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Any ranges can be the `identifier` of an *animation* or an *inline animation*.
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**X**
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- The `x = f(y)` function for `y` independent cartesian equations.
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- The `x = f(t)` function for parametric equations.
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- The `x` range (animation) for `x` independent cartesian equations.
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**Y**
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- The `y = f(x)` function for `x` independent cartesian equations.
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- The `y = f(t)` function for parametric equations.
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- The `y` range (animation) for `y` independent cartesian equations.
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**T**
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- The `t` range (animation) for parametric equations.
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**R**
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- The `r = f(θ)` function for polar equations.
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**θ**
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- The `θ` range (animation) for polar equations.
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*Color functions*
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- The `c = f(x)` function for `x` independent cartesian equations.
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- The `c = f(y)` function for `y` independent cartesian equations.
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- The `c = f(t)` function for parametric equations.
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- The `c = f(θ)` function for polar equations.
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#### Color Functions
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*Color function* parameter names are **C_x** where the *x* is color space part
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subscript.
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Only one color space can be used in each graph.
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If only alpha is set the default color space is **Grey-scale**.
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Listed bellow are the available color spaces and their subscripts.
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Default value in parenthesis for the unused subscripts of the color spaces.
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- **Grey-scale**: `wa` - Grey-scale (1), Alpha (1)
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- **RGB**: `rgba` - Red (0), Green (0), Blue (0), Alpha (1)
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- **HSL**: `hsla` - Hue (0), Saturation (1), Luminosity (0.5), Alpha (1)
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All values can be a real number between 0 and 1 inclusive.
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Values bellow this range will be interpreted as 0.
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Values above this range will be interpreted as 1.
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### Animation
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An *animation* begins with the `anim` keyword. Unless it is an
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*inline animation* block, the keyword is followed by its `identifier`. It then
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has a comma (`,`) separated list enclosed in curly braces (`{` and `}`)
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of *animation parameters*.
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When an animation is used in an expression, the value it is evaluated as is in
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the range defined, changing by the step every frame.
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#### Animation parameter
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An *animation parameter* begins with its parameter name then a colon (`:`)
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followed by an `expression`. If it is the only parameter the parameter name for
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the range is optional.
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Listed bellow are the possible parameters. Only the *range* parameter is
|
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required.
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**R** Range: `R:` *expression* `≤ x ≤` *expression*
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**S** Step: `S:` *expression*
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- Default is `1/10` unless a range expression is multiplied by `π` then it
|
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is `π/32`.
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**D** Direction: `D:` *direction*
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- `increase` (default)
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- `decrease`
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- `bounce`
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||||
### Expressions
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||||
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||||
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||||
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||||
#### Unary Expression
|
||||
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||||
A `unary expression` is made up of one `expression` and one `unary operator`.
|
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The operator may come before or after the expression.
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||||
#### Binary Expression
|
||||
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||||
A `binary expression` is made up of one `expression`, then one
|
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`binary operator`, then another `expression`.
|
||||
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||||
#### Function
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||||
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||||
A `function` starts with an `identifier` followed by a comma (`,`)
|
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separated list enclosed in parentheses (`(` and `)`) of *function arguments*.
|
||||
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||||
##### Function Argument
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||||
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A *function argument* is an `expression`.
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||||
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#### Enclosed Expression
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||||
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An `enclosed expression` is simply an `expression` enclosed in parentheses
|
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(`(` and `)`).
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||||
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||||
#### Operator
|
||||
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||||
Here are all operators and their types and names in order of precedence.
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||||
|
||||
| Operator | Type | Name |
|
||||
| -- | -- | -- |
|
||||
| `-` | Unary (Prefix) | Negate *Operator* |
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||||
| `!` | Unary (Postfix) | Factorial *Operator* |
|
||||
| `^` | Binary | Exponential *Operator* |
|
||||
| `_` | Binary | Subscript *Operator* |
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||||
| `/` | Binary | Division *Operator* |
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||||
| `%` | Binary | Modulus *Operator* |
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||||
| `*` | Binary | Multiplication *Operator* |
|
||||
| `-` | Binary | Subtraction *Operator* |
|
||||
| `+` | Binary | Addition *Operator* |
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||||
| `=` | Binary | Assignment *Operator* |
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||||
|
||||
#### 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 (`;`).
|
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|
||||
## 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
|
||||
Loading…
Reference in New Issue