Mathematical Functions in VEX

Each formula along with some of the characteristics are listed below.

y = 0;            // Constant (value remains the same at all points in time)
y = x;            // Linear (value changes at a constant rate over time)
y = pow(2,x);     // Exponential, these functions grow very rapidly. y = pow(M_E, x); y = exp(x);
y = pow(x,2);     // Quadratic, same as: y = x*x;
y = pow(x,3);     // Cubic, same as: y = x*x*x;
y = 1.0/x;        // Reciprocal, with x in the denominator this will produce asymptotes at the axis
y = log(x);       // Logarithmic, rate of growth diminishes over time
y = sqrt(x);      // Square Root, same as: y = pow(x,0.5);

Mathematical Constants

The following constants are defined in $HFS/houdini/vex/include/math.h and automatically included in all VEX wrangle snippets.

M_E         2.7182818    // sometimes called the natural number, or Euler's number
LN10        2.3025850    // natural logarithm of 10
LN2         0.6931471    // natural logarithm of 2
LOG10E      0.4342944
LOG2E       1.4426950
PI          3.1415926    // 180° in radians, the ratio of the circumference to diameter of a circle
M_TWO_PI    6.2831852    // 360° in radians, the circumference of a unit circle, 2 * PI
PI_2   	    1.5707963    // 90° in radians, 1/4th of the circumference of a unit circle, PI / 2
PI_4	    0.7853981    // 45° in radians, 1/8th of the circumference of a unit circle, PI / 4
SQRT1_2	    0.7071067
SQRT2	    1.4142135
TOLERANCE   0.0001

some curves produced using standard math/VEX functions.

sin wave square wave triangle wave clamp floor frac abs smoothstep

Strings in VEX

abspath() -- Returns the full path of a file.
chr() -- Converts a Unicode codepoint to a UTF8 string.
concat() -- Concatenates all the specified strings into a single string.
decode() -- Decodes a variable name that was previously encoded.
decodeattrib() -- Decodes a geometry attribute name that was previously encoded.
decodeparm() -- Decodes a node parameter name that was previously encoded.
decodeutf8() -- Decodes a UTF8 string into a series of codepoints.
encode() -- Encodes any string into a valid variable name.
encodeattrib() -- Encodes any string into a valid geometry attribute name.
encodeparm() -- Encodes any string into a valid node parameter name.
encodeutf8() -- Encodes a UTF8 string from a series of codepoints.
endswith() -- Indicates if the string ends with the specified string.
find() -- Finds an item in an array or string.
isalpha() -- Returns 1 if all characters in the string are alphabetic.
isdigit() -- Returns 1 if all characters in the string are numeric.
itoa() -- Converts an integer to a string.
join() -- Concatenates all strings of an array, inserting a common spacer.
lstrip() -- Strips leading whitespace from a string.
makevalidvarname() -- Forces a string to conform to the rules for variable names.
match() -- Returns 1 if the subject matches the pattern specified, or 0 if it doesn’t.
opdigits() -- Returns the integer value of the last sequence of digits of a string.
ord() -- Converts a UTF8 string into a codepoint.
pluralize() -- Converts an English noun to its plural.
re_find() -- Matches a regular expression in a string.
re_findall() -- Finds all instances of the given regular expression in the string.
re_match() -- Returns 1 if the entire input string matches the expression.
re_replace() -- Replaces instances of regex_find with regex_replace.
re_split() -- Splits the given string based on regex match.
relativepath() -- Computes the relative path for two full paths.
relpath() -- Returns the relative path to a file.
replace() -- Replaces occurrences of a substring.
replace_match() -- Replaces the matched string pattern with another pattern.
rstrip() -- Strips trailing whitespace from a string.
split() -- Splits a string into tokens.
splitpath() -- Splits a file path into the directory and name parts.
sprintf() -- Formats a string like printf but returns the result as a string instead of printing it.
startswith() -- Returns 1 if the string starts with the specified string.
strip() -- Strips leading and trailing whitespace from a string.
strlen() -- Returns the length of the string.
titlecase() -- Returns a string that is the titlecase version of the input string.
tolower() -- Converts all characters in a string to lower case.
toupper() -- Converts all characters in a string to upper case.

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