OpenSCAD User Manual/Mathematical Functions

The text in its current form is incomplete.

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

log

Mathematical logarithm. See: Logarithm

lookup

(Inserted by a beginner, may need fixing!)

From a given key-value array, it will interpolate a value for any key using linear interpolation.

Parameters

key 

A lookup key

<key,value array> 

keys and values

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

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.

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

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.

sign

Mathmatical 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);
}