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Lua MathExtra

From FIGHTORDER

Development < Lua Scripting < Lua MathExtra

Additional math functions

New in Engine Version 0.95 and up.

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}clamp ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number min, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number max )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number clamped

Returns x clamped to min and max boundaries.

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}diag ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x1, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x2, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x3, ... )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number diagonal

Returns the length of the diagonal of an n-dimensional box (or the length of an n-component vector). Rather quick method that does not handle intermediate overflows/underflows nor is made for numerical stability.

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}erf ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number erf

Returns erf(x).

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}hypot ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number y )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number sqrt(x*x+y*y)

Returns the length of hypotenuse of right angle triangle with sides x and y, equivalent to sqrt(x*x + y*y), but has better numerical stability and internally handles intermediate overflows/underflows, but is also slower.

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}mix ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number y, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number a )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number (x+(y-x)*a)

Returns linear interpolation between x and y with ratio a (x+(y-x)*a).

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}round ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number decimals )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number rounded

Returns x rounded to n decimals, if n is omitted or <=0, rounds to nearest integer. Note that Spring's Lua interpreter uses 32-bit floats for all numbers so max. precision is ~7 decimal digits.

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}sgn ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number sign

Returns 0 if x ==0, 1 if x > 0, -1 if x < 0 sgn(x).

{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}math.{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}smoothstep ( {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number edge0, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number edge1, {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number x )
return: {{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}{{#css:

 span.value {
   color:#e65c00;
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.type {
   color:#0099cc; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }
 span.prefix {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
 }   
 span.name {
   color:#105289; 
   font-family: ‘Lucida Console’, Monaco, monospace;
   font-weight:bold;
 }
 span.var {
   font-family: ‘Lucida Console’, Monaco, monospace;
 }

}}number smoothstep

Returns smoothstep(edge0, edge1, v).