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MISC_NOTES.md

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Unsorted Notes

  • set bounding boxes for each line, which will be an equation

  • within the line, bound each character. map it to a ASCII character

  • need to note position and size of each character, especially in relation to other characters

    • think exponents which are raised above the x-height (in an IDEAL world)
    • think subscript which are below the baseline
    • things like fractions have a horizontal line that separates the numerator and denominator
    • square roots are some characters with a character bounding them (radical sign)

  • start with a simple equation, like 2+2=4

characters:

  • numbers (0-9)
  • variables (a-z, A-Z)
  • decimal point (.)
  • sign (+, -)
  • equal sign (=)
  • greek letters/alphabet (α, β, γ, etc.)

operators:

  • addition (+)

  • subtraction (-)

  • multiplication (*, x, •) (two variables next to each other; e.g., AB or 2x is really A times B or 2 times x)

  • division (/, ÷) (two variables separated by a horizontal line; e.g., A/B or 2/x is really A divided by B or 2 divided by x) (fractions)

  • parentheses ((), [], {}) (a variable or expression inside; e.g., (x+2) is really x plus 2)

  • exponents (^) (a variable raised above the x-height; e.g., x^2 is really x squared)

  • square roots (√) (a radical sign with a variable inside; e.g., √x is really the square root of x)

  • trigonometric functions (sin, cos, tan, etc.) (a function with a variable inside; e.g., sin(x) is really the sine of x)

  • logarithms (log) (a function with a variable inside; e.g., log(x) is really the logarithm of x)

  • vector notation (→) (a vector with a variable inside; e.g., →x is really the vector x)

  • matrix notation ([, ]) (a matrix with variables inside; e.g., [x, y] is really the matrix x, y)

-- At this point only characters (numbers, math symbols) are present in the image we are working with -- Segment by line, each object is assigned a line -- Use position and character value to recognize equals, multi-digit numbers (i.e., if 1 and 2 are together with no object in between and their distance is reasonably small they can be assumed to form ‘12’) -- Form math equation using LaTeX -- Generate an output image! (https://github.com/goldsborough/latexpp)

Get contours of each numeric character

of contours is a very rough tell:

1 contour: 1, 2, 3, 5, 7 2 contours: 0, 4, 6, 9 3 contours: 8 Roundness Angle for adjustments

of edges

of corners

other resources