Float Expressions

6.1.3.4.2 Clock Identifiers

They are:

    clock | clock_delta | clock_on | final_clock | final_frame
    frame_number | initial_clock | initial_frame

These keywords allow to use the values of the clock which have been set in the command line switch options (or INI-file). They represent float or integer values, read from the animation options. You cannot re-declare these identifiers.

clock
The built-in float identifier clock is used to control animations in POV-Ray. Unlike some animation packages, the action in POV-Ray animated scenes does not depend upon the integer frame numbers. Rather you should design your scenes based upon the float identifier clock. For non-animated scenes its default value is 0 but you can set it to any float value using the INI file option Clock=n.n or the command-line switch +Kn.n to pass a single float value your scene file.

Other INI options and switches may be used to animate scenes by automatically looping through the rendering of frames using various values for clock. By default, the clock value is 0 for the initial frame and 1 for the final frame. All other frames are interpolated between these values.
For example if your object is supposed to rotate one full turn over the course of the animation you could specify rotate 360*clock*y. Then as clock runs from 0 to 1, the object rotates about the y-axis from 0 to 360 degrees.

Although the value of clock will change from frame-to-frame, it will never change throughout the parsing of a scene.

clock_delta
The built-in float identifier clock_delta returns the amount of time between clock values in animations in POV-Ray. While most animations only need the clock value itself, some animation calculations are easier if you know how long since the last frame. Caution must be used when designing such scenes. If you render a scene with too few frames, the results may be different than if you render with more frames in a given time period. On non-animated scenes, clock_delta defaults to 1.0. See section "Animation Options" for more details.

clock_on
With this identifier the status of the clock can be checked: 1 is on, 0 is off.

  #if(clock_on=0)
    //stuff for still image
  #else
    //some animation
  #end

frame_number
If you rather want to define the action in POV-Ray animated scenes depending upon the integer frame numbers, this identifier can be used.
It reads the number of the frame currently being rendered.

  #if(frame_number=1)
    //stuff for first image or frame
  #end
  #if(frame_number=2)
    //stuff for second image or frame
  #end
  #if(frame_number=n)
    //stuff for n th image or frame
  #end

initial_clock
This identifier reads the value set through the INI file option Initial_Clock=n.n or the command-line switch +KIn.n.

final_clock
This identifier reads the value set through the INI file option Final_Clock=n.n or the command-line switch +KFn.n.

initial_frame
This identifier reads the value set through the INI file option Initial_Frame=n or the command-line switch +KFIn.

final_frame
This identifier reads the value set through the INI file option Final_Frame=n or the command-line switch +KFFn.

Note: that these values are the ones actually used. When the option 'cyclic animation' is set, they could be different from the ones originally set in the options.

#if (image_width < 300) crand 0.1 #else crand 0.5 #end or: image_map { pattern image_width, image_width { //make pattern resolution gradient x //dependent of render width color_map { [ 0.0 ... ] [ 1.0 ... ] } } }

#local Temp_Vers = version; // Save previous value #version 1.0; // Change to 1.0 mode ... // Version 1.0 stuff goes here... #version Temp_Vers; // Restore previous version

object { MyBlob } // sturm defaults off, but // hierarchy defaults on object { MyBlob sturm } // turn sturm on object { MyBlob sturm on } // turn sturm on object { MyBlob sturm off } // turn sturm off object { MyBlob hierarchy } // does nothing, hierarchy was // already on object { MyBlob hierarchy off } // turn hierarchy off

6.1.3.6 Float Functions

POV-Ray defines a variety of built-in functions for manipulating floats, vectors and strings. Function calls consist of a keyword which specifies the name of the function followed by a parameter list enclosed in parentheses. Parameters are separated by commas. For example:

 keyword(param1,param2)

The following are the functions which return float values. They take one or more float, integer, vector, or string parameters. Assume that A and B are any valid expression that evaluates to a float; I is a float which is truncated to integer internally, S, S1, S2 etc. are strings, and V, V1, V2 etc. are any vector expressions.O is an objectidentifier to a pre-decalred object.

abs(A) Absolute value of A. If A is negative, returns -A otherwise returns A.

acos(A) Arc-cosine of A. Returns the angle, measured in radians, whose cosine is A.

acosh(A) inverse hyperbolic cosine of A.

asc(S) Returns an integer value in the range 0 to 255 that is the ASCII value of the first character of the string S. For example asc("ABC") is 65 because that is the value of the character "A".

asin(A) Arc-sine of A. Returns the angle, measured in radians, whose sine is A.

asinh(A) invers hyperbolic sine of A

atan2(A,B) Arc-tangent of (A/B). Returns the angle, measured in radians, whose tangent is (A/B). Returns appropriate value even if B is zero. Use atan2(A,1) to compute usual atan(A) function.

atanh(A) invers hyperbolic tangent of A

ceil(A) Ceiling of A. Returns the smallest integer greater than A. Rounds up to the next higher integer.

cos(A) Cosine of A. Returns the cosine of the angle A, where A is measured in radians.

cosh(A) The hyperbolic cosine of A.

defined(IDENTIFIER) Returns


  true

if the identifier is currently defined, false otherwise. This is especially useful for detecting end-of-file after a


  #read

directive because the file identifier is automatically undefined when end-of-file is reached. See "The #read Directive" for details.

degrees(A) Convert radians to degrees. Returns the angle measured in degrees whose value in radians is A. Formula is degrees=A/pi*180.0.

dimensions( ARRAY_IDENTIFIER ) Returns the number of dimensions of a previously declared array identifier. For example if you do #declare MyArray=array[6][10] then dimensions(MyArray) returns the value 2.

dimension_size( ARRAY_IDENTIFIER, FLOAT ) Returns the size of a given dimension of a previously declared array identifier. Dimensions are numbered left-to-right starting with 1. For example if you do #declare MyArray=array[6][10] then dimension_size(MyArray,2) returns the value 10.

div(A,B) Integer division. The integer part of (A/B).

exp(A) Exponential of A. Returns the value of e raised to the power A where e is the base of the natural logarithm, i.e. the non-repeating value approximately equal to 2.71828182846.

file_exists(S) Attempts to open the file specified by the string S. The current directory and all library directories specified by the Library_Path or +L options are also searched. See "Library Paths" for details. Returns 1 if successful and 0 if unsuccessful.

floor(A) Floor of A. Returns the largest integer less than A. Rounds down to the next lower integer.

inside(O,V) It returns either 0.0, when the vector V is outside the object, specified by the object-identifier O, or 1.0 if it is inside.

Note: inside does not accept object-identifiers to non-solid objects.

int(A) Integer part of A. Returns the truncated integer part of A. Rounds towards zero.

log(A) Logarithm of A. Returns the logarithm base 10 of the value A.

ln(A) Natural logarithm of A. Returns the natural logarithm base e of the value A.

max(A,B,...) Maximum of two or more float values. Returns A if A larger than B. Otherwise returns B.

min(A,B,...) Minimum of two or more float values. Returns A if A smaller than B. Otherwise returns B.

mod(A,B) Value of A modulo B. Returns the remainder after the integer division of A/B. Formula is mod=((A/B)-int(A/B))*B.

pow(A,B) Exponentiation. Returns the value of A raised to the power B.

Note:For a negative A and a non-integer B the function has no defined return value. The result then may depend on the platform POV-Ray is compiled on.

radians(A) Convert degrees to radians. Returns the angle measured in radians whose value in degrees is A. Formula is radians=A*pi/180.0.

rand(I) Returns the next pseudo-random number from the stream specified by the positive integer I. You must call seed() to initialize a random stream before calling rand(). The numbers are uniformly distributed, and have values between 0.0 and 1.0, inclusively. The numbers generated by separate streams are independent random variables.

seed(I) Initializes a new pseudo-random stream with the initial seed value A. The number corresponding to this random stream is returned. Any number of pseudo-random streams may be used as shown in the example below:

  #declare R1 = seed(0);
  #declare R2 = seed(12345);
  sphere { <rand(R1), rand(R1), rand(R1)>, rand(R2) }

Multiple random generators are very useful in situations where you use rand() to place a group of objects, and then decide to use rand() in another location earlier in the file to set some colors or place another group of objects. Without separate rand() streams, all of your objects would move when you added more calls to rand(). This is very annoying.

select(A, B, C [,D]). It can be used with three or four parameters. Select compares the first argument with zero, depending on the outcome it will return B, C or D. A,B,C,D can be floats or funtions.
When used with three parameters, if A < 0 it will return B, else C (A >= 0).
When used with four parameters, if A < 0 it will return B. If A = 0 it will return C. Else it will return D (A > 0).

Example:
If A has the consecutive values -2, -1, 0, 1, and 2 :

                           //    A =  -2 -1 0 1 2
  select (A, -1, 0, 1)     //returns  -1 -1 0 1 1 
  select (A, -1, 1)        //returns  -1 -1 1 1 1

sin(A) Sine of A. Returns the sine of the angle A, where A is measured in radians.

sinh(A) The hyperbolic sine of A.

strcmp(S1,S2) Compare string S1 to

S2

. Returns a float value zero if the strings are equal, a positive number if S1 comes after S2 in the ASCII collating sequence, else a negative number.

strlen(S) Length of S. Returns an integer value that is the number of characters in the string S.

sqrt(A) Square root of A. Returns the value whose square is A.

tan(A) Tangent of A. Returns the tangent of the angle A, where A is measured in radians.

tanh(A) The hyperbolic tangent of A.

val(S) Convert string S to float. Returns a float value that is represented by the text in string S. For example val("123.45") is 123.45 as a float.

vdot(V1,V2) Dot product of V1 and V2. Returns a float value that is the dot product (sometimes called scalar product) of V1 with V2. It is directly proportional to the length of the two vectors and the cosine of the angle between them. Formula is vdot=V1.x*V2.x + V1.y*V2.y + V1.z*V2.z. See the animated demo scene VECT2.POV for an illustration.

vlength(V) Length of V. Returns a float value that is the length of vector V. Formula is vlength=sqrt(vdot(A,A)). Can be used to compute the distance between two points. Dist=vlength(V2-V1).

See section "Vector Functions" and section "String Functions" for other functions which are somewhat float-related but which return vectors and strings. In addition to the above built-in functions, you may also define your own functions using the #macro directive. See the section "User Defined Macros" for more details.

`( )`	expressions in parentheses first
`+A -A !A`	unary minus, unary plus and logical "not"
`A*B A/B`	multiplication and division
`A+B A-B`	addition and subtraction

`(A < B)`	A is less than B
`(A <= B)`	A is less than or equal to B
`(A = B)`	A is equal to B (actually abs(A-B)<EPSILON)
`(A != B)`	A is not equal to B (actually abs(A-B)>=EPSILON)
`(A >= B)`	A is greater than or equal to B
`(A > B)`	A is greater than B

`(A & B)`	true only if both A and B are true, false otherwise
`(A \| B)`	true if either A or B or both are true

6.1.3 Float Expressions

6.1.3.1 Float Literals

6.1.3.2 Float Identifiers

6.1.3.3 Float Operators

6.1.3.4 Built-in Float Identifiers

6.1.3.4.1 Constant Identifiers

6.1.3.4.2 Clock Identifiers

6.1.3.4.3 Image Size Identifiers

6.1.3.4.4 Version Identifier

6.1.3.5 Boolean Keywords

6.1.3.6 Float Functions