Description of IFS Builder 3d scripting language

• General structure of an IFS script file
• Example. The Koch Snowflake
• Sets and Maps
• Basic Maps of Sets
• Camera
• Lighting
  • 1. Lighting parameters of the scene
  • 2. Light sources
  • 3. Specular properties of surfaces
• Substitutions
• Arithmetical expressions
• Random-generated fractals
• Control statements
• Angles measurement units
• Animation

	camera <camera attributes>;
	light <light source2 attributes>;
	light <light source2 attributes>;
	...
	background(r,g,b,l); // background color/brightness
	
	<formulas, maps, substitutions>
	set s1 = <structure of the set1>;
	set s2 = <structure of the set2>;
	...
	build <structure of the set3> <material1>;
	build <structure of the set4> <material2>;

	camera  position (0,0,-80) vertical(0,1,0) fov(50);
	light   color (0,1,0)   position (1, 1,-3) shadows(0);
	light   color (1, 1, 0) position (3,-1,-1) shadows(0);
	ambient(1,1,1,.05);
	background(0,1,1,0.5); // set background color

	s = sqrt(3);
	f1 := translate(1/2, 1/2/s,0) * scale(1/s) * rotate(0,0,-1,150);
	f2 := translate(1,0,0) * scale(1/s) * rotate(0,0,-1,-150);
	f3 := translate(-1/2,s/2,0) * scale(s) * rotate(0,0,-1,30);
	f4 := translate(-1/2,-s/2,0) * scale(s) * rotate(0,0,-1,-90);
	f5 := translate(1,0,0) * scale(s) * rotate(0,0,-1,150);

	set KochCurve = (f1 + f2) KochCurve; // define the Koch curve
	set Snowflake = (f3 + f4 + f5) KochCurve;
	build Snowflake;

Note for explanation about difference between the equals '=' sign and ':=' see substitutions section.

Sets and Maps

Sets in the program are specified by equations like: set S = f1(S) + f2(S) + ... + fn(S); Here S means a set in 3-dimensional space, the plus sign '+' denotes union of sets, and f1,...,fn are affine or Mebius maps in 3D space, each of these is defined as composition of basic maps.

Note that mathematicians use ∪ sign to denote a union of sets, so the correct mathematical notation for the equation above is: S = f1(S) ∪ f2(S) ∪ ... ∪ fn(S). The program uses the plus sign, due to keyboard and character table (ASCII) limititations.

Composion of maps is written with the superposition sign '*'. For example translate(tx,ty,tz) * scale(k) * M means contract the set M by factor k and than translate all its points by vector (tx,ty,tz). Sign of maps superposition can be omitted. Moreover, associativity rule of '+' and '*' operations can be applied, e.g.: f1*(f2+f3)=f1*f2+f1*f3.
Associativity also works with sets, e.g. S=(f1+f2)S is the same as S=f1(S)+f2(S) .

Example of a Map:

	f1 := translate(-1,0,0) * scale(1/2);

Example of a set definition:

	Segment = scale(0.5) * (translate(1,0,0) + translate(-1,0,0)) Segment;

The lighting of the scene is calculated by well known ray-tracing algorithm, which requires light sorces and specular properties of surfaces (color, reflectivity, e.t.c.) to be defined.

Note: Color/Brightness in the scripting file can be defined in the form of (r,g,b,lum), where r,g,b is color, and lum is luminescence.
Parameter lum can be omitted, in this case lum=1 will be assumed.

• There are 3 types of light sources supported: "Lamp", "Floodlight", "Sun" (point source, directional source and parallel source).
• Light source can ba added to the scene by specifying light keyword with following attributes.
• Type of light source is automatically determined by specified attributes.
• Number of light sources in the scene cab be arbitrary, and they can be of any different types.

Properties of a surface can be specified just after the build command. Since the build keyword can be specified more then once, it is possible to create objects with different colors and properties of surfaces in one scene.

Property	Note	Description
ambient(r,g,b,lum)	Arguments can be given in the form of (r,g,b) or (lum)	Defines color/brightness of the ambient color component.
diffuse(r,g,b,lum)		Defines color/brightness of the diffuse color component.
specular(r,g,b,lum)		Defines color/brightness of the specular color component.
color(r,g,b)	for convinience	Defines color of the ambient and diffuse components and assigns specular component to (1,1,1).
metall(r,g,b)		Defines metallic surface: sets color of the diffuse and specular component.

	<name> := <value>;

	sum := a + b;
	result = sum * 3;

	 result = a + b * 3;

• Names of variables can consist of characters a-z,A-Z and the underscore character "_"
  
• Supported real-valued functions:
   ln(x), exp(x), sqrt(x), abs(x), sign(x), sin(x), cos(x), atan(x)
   atan2(y,x), arg(x,y) - these two functions returns arctg(y/x)
   rnd(x) - random number in the [0,x] segment
  
• Real, logical and bit operations:
   = += -= *= /= + - * / , () ?: ++ -- == != < <= > >=
  
• Predefined constants: PI and E.
  

• The attractor and each its copy (a set obtained by IFS maps from the attractor and from other copies), has a corresponding pseudo-random number. This number for attractor can be set by calling randState(arg) function before a build operator, where real-valued arg belongs to the [0,1] segment. For example: randState(rnd(1));
• The operator (...)%n (where n is an integer) selects n maps from parenthesis, using pseudo-random number assigned to the current copy of attractor.
• Operator (...)%n allows to assign to each map a weight (a real positive number), by placing it into braces after the map. Weights are used to calculate probabilities for the map selecting operator. For each map its probability is calculated by dividing its weight by the total maps weight in the current (...)%n operator. If a weight was not specified for some map, then it's supposed to be a unity by default. Example: (f1{2}+f2{3})%1
• If a copy of the atractor of IFS consist of some subcopies, then subcopies inherit by default the pseuodo-random number from the copy. But if f|m construction has ben found, then the random number of the subcopy, obtained from current copy by the f map, is changed by m-th way, i.e. it's changed by applying pseudo-random generator which depends on the parameter m. So, if two map have the same parameter m, e.g. in (f1|1+f2|1) construction, then copies obtained by applying f1,f2 maps, will obtain the same pseudo-random number, and so will be divided by (...)%n operator in the same way.

• { operator1; operator2; ... }
  Block statement. It executes the sequence of operators, located in braces.
  
• if(expresion) operator1; [ else оператор2;]
  Conditional statement. Executes operator1 if expresion is not equal to zero, otherwise executes оператор2.
  
• for(initialization; expresion; iteration) operator;
  First executes initialization. Then in a loop calculates the expresion, and while it is not zero executes operator and iteration.
• while(condition) body;
  While condition is not zero executes the body.
• do { body; } while(condition);
  Executes the body, then checks the condition, and while it is not zero repeats executing the body.
• echo <variables and strings>;
  Print to the output log the variables and the text located in double quotes, all arguments should be delimited by comma or spaces.