OpenSCAD User Manual/Mathematical Functions

abs

Mathematical absolute value function. Returns the positive value of a signed decimal number.

Usage examples:

abs(-5.0);
abs(0);
abs(8.0);

Results:

5.0
0.0
8.0

acos

Mathematical arccosine, or inverse cosine, function.

asin

Mathematical arcsine, or inverse sine, function.

atan

Mathematical arctangent, or inverse tangent, function. Returns the principal value of the arc tangent of x, expressed in degrees. See: atan function

atan2

Mathematical two-argument atan function. Returns the principal value of the arc tangent of y/x, expressed in degrees. See: atan2

ceil

Mathematical ceiling function. See: Ceil Function

cos

Mathematical cosine function.

Usage Examples:
for(i=[0:36]) translate([i*10,0,0])cylinder(r=5,h=cos(i*10)*50+60);	OpenSCAD Cos Function‎

exp

Mathematical exp function. Returns the base-e exponential function of x, which is the number e raised to the power x. See: Exponent

floor

Mathematical floor function. See: Floor Function

ln

Mathematical natural logarithm. See: Natural logarithm

len

Mathematical length function. Returns the length of an array, a vector or a string parameter.

Usage examples:

str1="abcdef"; len_str1=len(str1);
echo(str1,len_str1);

a=6; len_a=len(a);
echo(a,len_a);

array1=[1,2,3,4,5,6,7,8]; len_array1=len(array1);
echo(array1,len_array1);

array2=[[0,0],[0,1],[1,0],[1,1]]; len_array2=len(array2);
echo(array2,len_array2);

len_array2_2=len(array2[2]);
echo(array2[2],len_array2_2);

Results:

ECHO: "abcdef", 6
ECHO: 6, undef
ECHO: [1, 2, 3, 4, 5, 6, 7, 8], 8
ECHO: [[0, 0], [0, 1], [1, 0], [1, 1]], 4
ECHO: [1, 0], 2

Note that the len() function is not defined when a simple variable is passed as the parameter.

This function allows (e.g.) the parsing of an array, a vector or a string.

Usage examples:

str2="4711";
for (i=[0:len(str2)-1])
        echo(str("digit ",i+1,"  :  ",str2[i]));

Results:

ECHO: "digit 1  :  4"
ECHO: "digit 2  :  7"
ECHO: "digit 3  :  1"
ECHO: "digit 4  :  1"

log

Mathematical logarithm. See: Logarithm

lookup

Look up value in table, and linearly interpolate if there's no exact match. The first argument is the value to look up. The second is the lookup table -- a vector of key-value pairs.

Parameters

key 

A lookup key

<key,value array> 

keys and values

Notes
There is a bug where out-of-range keys will return the first value in the list. Newer versions of Openscad should use the top or bottom end of the table as appropriate instead.

Usage example: Will create a sort of 3D chart made out of cylinders of different height.
function get_cylinder_h(p) = lookup(p, [ [ -200, 5 ], [ -50, 20 ], [ -20, 18 ], [ +80, 25 ], [ +150, 2 ] ]); for (i = [-100:5:+100]) { // echo(i, get_cylinder_h(i)); translate([ i, 0, -30 ]) cylinder(r1 = 6, r2 = 2, h = get_cylinder_h(i)*3); }	OpenSCAD Lookup Function

max

Returns the maximum of the two parameters.

Parameters

<a> 

Decimal.

<b> 

Decimal.

Usage Example:

max(3.0,5.0);
max(8.0,3.0);

Results:

5.0
8.0

min

Returns the minimum of the two parameters.

Parameters

<a> 

Decimal.

<b> 

Decimal.

Usage Example:

min(3.0,5.0);
min(8.0,3.0);

Results:

3.0
3.0

norm

!!Note this function is not in 2013.01 and is pending pull request https://github.com/openscad/openscad/pull/333.

Returns the euclidean norm of a vector. Note this returns is the actual numeric length while len returns the number of elements in the vector or array.

Usage examples:

a=[1,2,3,4];
b="abcd";
c=[];
d="";
e=[[1,2,3,4],[1,2,3],[1,2],[1]];
echo(norm(a)); //5.47723
echo(norm(b)); //undef
echo(norm(c)); //0
echo(norm(d)); //undef
echo(norm(e[0])); //5.47723
echo(norm(e[1])); //3.74166
echo(norm(e[2])); //2.23607
echo(norm(e[3])); //1

Results:

ECHO: 5.47723
ECHO: undef
ECHO: 0
ECHO: undef
ECHO: 5.47723
ECHO: 3.74166
ECHO: 2.23607
ECHO: 1

pow

Mathematical power function.

Parameters

<base> 

Decimal. Base.

<exponent> 

Decimal. Exponent.

Usage examples:

for (i = [0:5]) {
 translate([i*25,0,0]) {
   cylinder(h = pow(2,i)*5, r=10);
   echo (i, pow(2,i));
 }
}

rands

Random number generator. Generates a constant vector of pseudo random numbers, much like an array. When generating only one number, you still call it with variable[0]

Parameters

min_value 

Minimum value of random number range

max_value 

Maximum value of random number range

value_count 

Number of random numbers to return as a vector

seed_value (optional) 

Seed value for random number generator for repeatable results.

Usage Examples:

seed=42;
random_vect=rands(5,15,4,seed);
echo( "Random Vector: ",random_vect);
sphere(r=5);
for(i=[0:3]) {
 rotate(360*i/4) {
   translate([10+random_vect[i],0,0])
     sphere(r=random_vect[i]/2);
 }
}

round

The "round" operator returns the greatest or least integer part, respectively, if the numeric input is positive or negative.

Some examples:

round(x.5) = x+1.
round(x.49) = x.
round(-(x.5)) = -(x+1).
round(-(x.49)) = -x.

round(5.4); //-> 5
round(5.5); //-> 6
round(5.6); //-> 6

sign

Mathematical signum function. Returns a unit value that extracts the sign of a value see: Signum function

Parameters

<x> 

Decimal. Value to find the sign of.

Usage examples:

sign(-5.0);
sign(0);
sign(8.0);

Results:

-1.0
0.0
1.0

sin

Mathematical sine function.

Parameters

<degrees> 

Decimal. Angle in degrees.

Usage example 1

for (i = [0:5]) {
 echo(360*i/6, sin(360*i/6)*80, cos(360*i/6)*80);
  translate([sin(360*i/6)*80, cos(360*i/6)*80, 0 ])
   cylinder(h = 200, r=10);
}

Usage example 2:
for(i=[0:36]) translate([i*10,0,0])cylinder(r=5,h=sin(i*10)*50+60);	OpenSCAD Sin Function

sqrt

Mathematical square root function.

Usage Examples:

translate([sqrt(100),0,0])sphere(100);

tan

Mathematical tangent function. Parameters

<degrees> 

Decimal. Angle in degrees.

Usage examples:

for (i = [0:5]) {
 echo(360*i/6, tan(360*i/6)*80);
  translate([tan(360*i/6)*80, 0, 0 ])
   cylinder(h = 200, r=10);
}